/*
FormFunction - Evaluates the function and corresponding gradient.
Input Parameters:
tao - the Tao context
X - the input vector
ptr - optional user-defined context, as set by TaoSetObjectiveAndGradientRoutine()
Output Parameters:
f - the newly evaluated function
*/
PetscErrorCode FormFunction(Tao tao,Vec P,PetscReal *f,void *ctx0)
{
TS ts;
SNES snes_alg;
PetscErrorCode ierr;
Userctx *ctx = (Userctx*)ctx0;
Vec X;
Mat J;
/* sensitivity context */
PetscScalar *x_ptr;
PetscViewer Xview,Ybusview;
Vec F_alg;
Vec Xdot;
PetscInt row_loc,col_loc;
PetscScalar val;
ierr = VecGetArray(P,&x_ptr);CHKERRQ(ierr);
PG[0] = x_ptr[0];
PG[1] = x_ptr[1];
PG[2] = x_ptr[2];
ierr = VecRestoreArray(P,&x_ptr);CHKERRQ(ierr);
ctx->stepnum = 0;
ierr = VecZeroEntries(ctx->vec_q);CHKERRQ(ierr);
/* Read initial voltage vector and Ybus */
ierr = PetscViewerBinaryOpen(PETSC_COMM_WORLD,"X.bin",FILE_MODE_READ,&Xview);CHKERRQ(ierr);
ierr = PetscViewerBinaryOpen(PETSC_COMM_WORLD,"Ybus.bin",FILE_MODE_READ,&Ybusview);CHKERRQ(ierr);
ierr = VecCreate(PETSC_COMM_WORLD,&ctx->V0);CHKERRQ(ierr);
ierr = VecSetSizes(ctx->V0,PETSC_DECIDE,ctx->neqs_net);CHKERRQ(ierr);
ierr = VecLoad(ctx->V0,Xview);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&ctx->Ybus);CHKERRQ(ierr);
ierr = MatSetSizes(ctx->Ybus,PETSC_DECIDE,PETSC_DECIDE,ctx->neqs_net,ctx->neqs_net);CHKERRQ(ierr);
ierr = MatSetType(ctx->Ybus,MATBAIJ);CHKERRQ(ierr);
/* ierr = MatSetBlockSize(ctx->Ybus,2);CHKERRQ(ierr); */
ierr = MatLoad(ctx->Ybus,Ybusview);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&Xview);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&Ybusview);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(ctx->dmpgrid,&X);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&J);CHKERRQ(ierr);
ierr = MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,ctx->neqs_pgrid,ctx->neqs_pgrid);CHKERRQ(ierr);
ierr = MatSetFromOptions(J);CHKERRQ(ierr);
ierr = PreallocateJacobian(J,ctx);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create timestepping solver context
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr);
ierr = TSSetType(ts,TSCN);CHKERRQ(ierr);
ierr = TSSetIFunction(ts,NULL,(TSIFunction) IFunction,ctx);CHKERRQ(ierr);
ierr = TSSetIJacobian(ts,J,J,(TSIJacobian)IJacobian,ctx);CHKERRQ(ierr);
ierr = TSSetApplicationContext(ts,ctx);CHKERRQ(ierr);
ierr = TSMonitorSet(ts,MonitorUpdateQ,ctx,NULL);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set initial conditions
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = SetInitialGuess(X,ctx);CHKERRQ(ierr);
ierr = VecDuplicate(X,&F_alg);CHKERRQ(ierr);
ierr = SNESCreate(PETSC_COMM_WORLD,&snes_alg);CHKERRQ(ierr);
ierr = SNESSetFunction(snes_alg,F_alg,AlgFunction,ctx);CHKERRQ(ierr);
ierr = MatZeroEntries(J);CHKERRQ(ierr);
ierr = SNESSetJacobian(snes_alg,J,J,AlgJacobian,ctx);CHKERRQ(ierr);
ierr = SNESSetOptionsPrefix(snes_alg,"alg_");CHKERRQ(ierr);
ierr = SNESSetFromOptions(snes_alg);CHKERRQ(ierr);
ctx->alg_flg = PETSC_TRUE;
/* Solve the algebraic equations */
ierr = SNESSolve(snes_alg,NULL,X);CHKERRQ(ierr);
/* Just to set up the Jacobian structure */
ierr = VecDuplicate(X,&Xdot);CHKERRQ(ierr);
ierr = IJacobian(ts,0.0,X,Xdot,0.0,J,J,ctx);CHKERRQ(ierr);
ierr = VecDestroy(&Xdot);CHKERRQ(ierr);
ctx->stepnum++;
ierr = TSSetDuration(ts,1000,ctx->tfaulton);CHKERRQ(ierr);
ierr = TSSetInitialTimeStep(ts,0.0,0.01);CHKERRQ(ierr);
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
/* ierr = TSSetPostStep(ts,SaveSolution);CHKERRQ(ierr); */
ctx->alg_flg = PETSC_FALSE;
/* Prefault period */
ierr = TSSolve(ts,X);CHKERRQ(ierr);
/* Create the nonlinear solver for solving the algebraic system */
/* Note that although the algebraic system needs to be solved only for
Idq and V, we reuse the entire system including xgen. The xgen
variables are held constant by setting their residuals to 0 and
putting a 1 on the Jacobian diagonal for xgen rows
*/
ierr = MatZeroEntries(J);CHKERRQ(ierr);
/* Apply disturbance - resistive fault at ctx->faultbus */
/* This is done by adding shunt conductance to the diagonal location
in the Ybus matrix */
row_loc = 2*ctx->faultbus; col_loc = 2*ctx->faultbus+1; /* Location for G */
val = 1/ctx->Rfault;
ierr = MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);CHKERRQ(ierr);
row_loc = 2*ctx->faultbus+1; col_loc = 2*ctx->faultbus; /* Location for G */
val = 1/ctx->Rfault;
ierr = MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(ctx->Ybus,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(ctx->Ybus,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ctx->alg_flg = PETSC_TRUE;
/* Solve the algebraic equations */
ierr = SNESSolve(snes_alg,NULL,X);CHKERRQ(ierr);
ctx->stepnum++;
/* Disturbance period */
ierr = TSSetDuration(ts,1000,ctx->tfaultoff);CHKERRQ(ierr);
ierr = TSSetInitialTimeStep(ts,ctx->tfaulton,.01);CHKERRQ(ierr);
ctx->alg_flg = PETSC_FALSE;
ierr = TSSolve(ts,X);CHKERRQ(ierr);
/* Remove the fault */
row_loc = 2*ctx->faultbus; col_loc = 2*ctx->faultbus+1;
val = -1/ctx->Rfault;
ierr = MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);CHKERRQ(ierr);
row_loc = 2*ctx->faultbus+1; col_loc = 2*ctx->faultbus;
val = -1/ctx->Rfault;
ierr = MatSetValues(ctx->Ybus,1,&row_loc,1,&col_loc,&val,ADD_VALUES);CHKERRQ(ierr);
ierr = MatAssemblyBegin(ctx->Ybus,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(ctx->Ybus,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatZeroEntries(J);CHKERRQ(ierr);
ctx->alg_flg = PETSC_TRUE;
/* Solve the algebraic equations */
ierr = SNESSolve(snes_alg,NULL,X);CHKERRQ(ierr);
ctx->stepnum++;
/* Post-disturbance period */
ierr = TSSetDuration(ts,1000,ctx->tmax);CHKERRQ(ierr);
ierr = TSSetInitialTimeStep(ts,ctx->tfaultoff,.01);CHKERRQ(ierr);
ctx->alg_flg = PETSC_TRUE;
ierr = TSSolve(ts,X);CHKERRQ(ierr);
ierr = VecGetArray(ctx->vec_q,&x_ptr);CHKERRQ(ierr);
*f = x_ptr[0];
ierr = VecRestoreArray(ctx->vec_q,&x_ptr);CHKERRQ(ierr);
ierr = MatDestroy(&ctx->Ybus);CHKERRQ(ierr);
ierr = VecDestroy(&ctx->V0);CHKERRQ(ierr);
ierr = SNESDestroy(&snes_alg);CHKERRQ(ierr);
ierr = VecDestroy(&F_alg);CHKERRQ(ierr);
ierr = MatDestroy(&J);CHKERRQ(ierr);
ierr = VecDestroy(&X);CHKERRQ(ierr);
ierr = TSDestroy(&ts);CHKERRQ(ierr);
return 0;
}
int main(int argc,char **argv)
{
TS ts; /* ODE integrator */
Vec Y; /* solution will be stored here */
Mat A; /* Jacobian matrix */
PetscErrorCode ierr;
PetscMPIInt size;
PetscInt n = 6;
PetscScalar *y;
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Initialize program
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PetscInitialize(&argc,&argv,(char*)0,help);CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create necessary matrix and vectors
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSetUp(A);CHKERRQ(ierr);
ierr = MatCreateVecs(A,&Y,PETSC_NULL);CHKERRQ(ierr);
ierr = VecGetArray(Y,&y);CHKERRQ(ierr);
y[0] = 0.0;
y[1] = 3.0;
y[2] = y[1];
y[3] = 6.0;
y[4] = 0.0;
y[5] = 0.0;
ierr = VecRestoreArray(Y,&y);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create timestepping solver context
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr);
ierr = TSSetType(ts,TSARKIMEX);CHKERRQ(ierr);
ierr = TSSetEquationType(ts,TS_EQ_DAE_IMPLICIT_INDEX1);CHKERRQ(ierr);
ierr = TSARKIMEXSetFullyImplicit(ts,PETSC_TRUE);CHKERRQ(ierr);
/*ierr = TSSetType(ts,TSROSW);CHKERRQ(ierr);*/
ierr = TSSetIFunction(ts,PETSC_NULL,IFunctionImplicit,PETSC_NULL);CHKERRQ(ierr);
ierr = TSSetIJacobian(ts,A,A,IJacobianImplicit,PETSC_NULL);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set initial conditions
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetSolution(ts,Y);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set solver options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetDuration(ts,100000,0.15);CHKERRQ(ierr);
ierr = TSSetInitialTimeStep(ts,0.0,.001);CHKERRQ(ierr);
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Do Time stepping
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSolve(ts,Y);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Free work space. All PETSc objects should be destroyed when they are no longer needed.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = VecDestroy(&Y);CHKERRQ(ierr);
ierr = TSDestroy(&ts);CHKERRQ(ierr);
ierr = PetscFinalize();
return(0);
}
int main(int argc,char **argv)
{
TS ts; /* ODE integrator */
Vec U; /* solution will be stored here */
Mat A; /* Jacobian matrix */
PetscErrorCode ierr;
PetscMPIInt size;
PetscInt n = 2;
AppCtx ctx;
PetscScalar *u;
PetscReal du[2] = {0.0,0.0};
PetscBool ensemble = PETSC_FALSE,flg1,flg2;
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Initialize program
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PetscInitialize(&argc,&argv,(char*)0,help);CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create necessary matrix and vectors
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
ierr = MatSetType(A,MATDENSE);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSetUp(A);CHKERRQ(ierr);
ierr = MatCreateVecs(A,&U,NULL);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set runtime options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Swing equation options","");CHKERRQ(ierr);
{
ctx.omega_s = 2.0*PETSC_PI*60.0;
ctx.H = 5.0;
ierr = PetscOptionsScalar("-Inertia","","",ctx.H,&ctx.H,NULL);CHKERRQ(ierr);
ctx.D = 5.0;
ierr = PetscOptionsScalar("-D","","",ctx.D,&ctx.D,NULL);CHKERRQ(ierr);
ctx.E = 1.1378;
ctx.V = 1.0;
ctx.X = 0.545;
ctx.Pmax = ctx.E*ctx.V/ctx.X;;
ierr = PetscOptionsScalar("-Pmax","","",ctx.Pmax,&ctx.Pmax,NULL);CHKERRQ(ierr);
ctx.Pm = 0.9;
ierr = PetscOptionsScalar("-Pm","","",ctx.Pm,&ctx.Pm,NULL);CHKERRQ(ierr);
ctx.tf = 1.0;
ctx.tcl = 1.05;
ierr = PetscOptionsReal("-tf","Time to start fault","",ctx.tf,&ctx.tf,NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-tcl","Time to end fault","",ctx.tcl,&ctx.tcl,NULL);CHKERRQ(ierr);
ierr = PetscOptionsBool("-ensemble","Run ensemble of different initial conditions","",ensemble,&ensemble,NULL);CHKERRQ(ierr);
if (ensemble) {
ctx.tf = -1;
ctx.tcl = -1;
}
ierr = VecGetArray(U,&u);CHKERRQ(ierr);
u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
u[1] = 1.0;
ierr = PetscOptionsRealArray("-u","Initial solution","",u,&n,&flg1);CHKERRQ(ierr);
n = 2;
ierr = PetscOptionsRealArray("-du","Perturbation in initial solution","",du,&n,&flg2);CHKERRQ(ierr);
u[0] += du[0];
u[1] += du[1];
ierr = VecRestoreArray(U,&u);CHKERRQ(ierr);
if (flg1 || flg2) {
ctx.tf = -1;
ctx.tcl = -1;
}
}
ierr = PetscOptionsEnd();CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create timestepping solver context
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr);
ierr = TSSetType(ts,TSROSW);CHKERRQ(ierr);
ierr = TSSetIFunction(ts,NULL,(TSIFunction) IFunction,&ctx);CHKERRQ(ierr);
ierr = TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,&ctx);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set initial conditions
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetSolution(ts,U);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set solver options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetDuration(ts,100000,35.0);CHKERRQ(ierr);
ierr = TSSetInitialTimeStep(ts,0.0,.01);CHKERRQ(ierr);
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
/* ierr = TSSetPostStep(ts,PostStep);CHKERRQ(ierr); */
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve nonlinear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
if (ensemble) {
for (du[1] = -2.5; du[1] <= .01; du[1] += .1) {
ierr = VecGetArray(U,&u);CHKERRQ(ierr);
u[0] = PetscAsinScalar(ctx.Pm/ctx.Pmax);
u[1] = ctx.omega_s;
u[0] += du[0];
u[1] += du[1];
ierr = VecRestoreArray(U,&u);CHKERRQ(ierr);
ierr = TSSetInitialTimeStep(ts,0.0,.01);CHKERRQ(ierr);
ierr = TSSolve(ts,U);CHKERRQ(ierr);
}
} else {
ierr = TSSolve(ts,U);CHKERRQ(ierr);
}
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Free work space. All PETSc objects should be destroyed when they are no longer needed.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = VecDestroy(&U);CHKERRQ(ierr);
ierr = TSDestroy(&ts);CHKERRQ(ierr);
ierr = PetscFinalize();
return(0);
}
int main(int argc,char **argv)
{
TS ts; /* nonlinear solver */
Vec U; /* solution, residual vectors */
Mat J; /* Jacobian matrix */
PetscInt maxsteps = 1000;
PetscErrorCode ierr;
DM da;
AppCtx user;
PetscInt i;
char Name[16];
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Initialize program
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
PetscInitialize(&argc,&argv,(char*)0,help);
user.N = 1;
ierr = PetscOptionsGetInt(NULL,"-N",&user.N,NULL);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create distributed array (DMDA) to manage parallel grid and vectors
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = DMDACreate1d(PETSC_COMM_WORLD, DMDA_BOUNDARY_MIRROR,-8,user.N,1,NULL,&da);CHKERRQ(ierr);
for (i=0; i<user.N; i++) {
ierr = PetscSNPrintf(Name,16,"Void size %d",(int)(i+1));
ierr = DMDASetFieldName(da,i,Name);CHKERRQ(ierr);
}
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Extract global vectors from DMDA; then duplicate for remaining
vectors that are the same types
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = DMCreateGlobalVector(da,&U);CHKERRQ(ierr);
ierr = DMCreateMatrix(da,MATAIJ,&J);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create timestepping solver context
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
ierr = TSSetType(ts,TSARKIMEX);CHKERRQ(ierr);
ierr = TSSetDM(ts,da);CHKERRQ(ierr);
ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr);
ierr = TSSetIFunction(ts,NULL,IFunction,&user);CHKERRQ(ierr);
ierr = TSSetIJacobian(ts,J,J,IJacobian,&user);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set initial conditions
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = InitialConditions(da,U);CHKERRQ(ierr);
ierr = TSSetSolution(ts,U);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set solver options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetInitialTimeStep(ts,0.0,.001);CHKERRQ(ierr);
ierr = TSSetDuration(ts,maxsteps,1.0);CHKERRQ(ierr);
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve nonlinear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSolve(ts,U);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Free work space. All PETSc objects should be destroyed when they
are no longer needed.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = VecDestroy(&U);CHKERRQ(ierr);
ierr = MatDestroy(&J);CHKERRQ(ierr);
ierr = TSDestroy(&ts);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
ierr = PetscFinalize();
PetscFunctionReturn(0);
}
int main(int argc,char **argv)
{
TS ts; /* nonlinear solver */
Vec u,r; /* solution, residual vectors */
Mat J,Jmf = PETSC_NULL; /* Jacobian matrices */
PetscInt maxsteps = 1000; /* iterations for convergence */
PetscErrorCode ierr;
DM da;
PetscReal dt;
AppCtx user; /* user-defined work context */
SNES snes;
PetscInt Jtype; /* Jacobian type
0: user provide Jacobian;
1: slow finite difference;
2: fd with coloring; */
PetscInitialize(&argc,&argv,(char *)0,help);
/* Initialize user application context */
user.da = PETSC_NULL;
user.nstencilpts = 5;
user.c = -30.0;
user.boundary = 0; /* 0: Drichlet BC; 1: Neumann BC */
user.viewJacobian = PETSC_FALSE;
ierr = PetscOptionsGetInt(PETSC_NULL,"-nstencilpts",&user.nstencilpts,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(PETSC_NULL,"-boundary",&user.boundary,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsHasName(PETSC_NULL,"-viewJacobian",&user.viewJacobian);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create distributed array (DMDA) to manage parallel grid and vectors
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
if (user.nstencilpts == 5){
ierr = DMDACreate2d(PETSC_COMM_WORLD, DMDA_BOUNDARY_NONE, DMDA_BOUNDARY_NONE,DMDA_STENCIL_STAR,-11,-11,PETSC_DECIDE,PETSC_DECIDE,1,1,PETSC_NULL,PETSC_NULL,&da);CHKERRQ(ierr);
} else if (user.nstencilpts == 9){
ierr = DMDACreate2d(PETSC_COMM_WORLD, DMDA_BOUNDARY_NONE, DMDA_BOUNDARY_NONE,DMDA_STENCIL_BOX,-11,-11,PETSC_DECIDE,PETSC_DECIDE,1,1,PETSC_NULL,PETSC_NULL,&da);CHKERRQ(ierr);
} else {
SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"nstencilpts %d is not supported",user.nstencilpts);
}
user.da = da;
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Extract global vectors from DMDA;
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = DMCreateGlobalVector(da,&u);CHKERRQ(ierr);
ierr = VecDuplicate(u,&r);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create timestepping solver context
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr);
ierr = TSSetType(ts,TSBEULER);CHKERRQ(ierr);
ierr = TSSetDM(ts,da);CHKERRQ(ierr);
ierr = TSSetIFunction(ts,r,FormIFunction,&user);CHKERRQ(ierr);
ierr = TSSetDuration(ts,maxsteps,1.0);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set initial conditions
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = FormInitialSolution(u,&user);CHKERRQ(ierr);
ierr = TSSetSolution(ts,u);CHKERRQ(ierr);
dt = .01;
ierr = TSSetInitialTimeStep(ts,0.0,dt);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set Jacobian evaluation routine
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = DMCreateMatrix(da,MATAIJ,&J);CHKERRQ(ierr);
Jtype = 0;
ierr = PetscOptionsGetInt(PETSC_NULL, "-Jtype",&Jtype,PETSC_NULL);CHKERRQ(ierr);
if (Jtype == 0){ /* use user provided Jacobian evaluation routine */
if (user.nstencilpts != 5) SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"user Jacobian routine FormIJacobian() does not support nstencilpts=%D",user.nstencilpts);
ierr = TSSetIJacobian(ts,J,J,FormIJacobian,&user);CHKERRQ(ierr);
} else { /* use finite difference Jacobian J as preconditioner and '-snes_mf_operator' for Mat*vec */
ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
ierr = MatCreateSNESMF(snes,&Jmf);CHKERRQ(ierr);
if (Jtype == 1){ /* slow finite difference J; */
ierr = SNESSetJacobian(snes,Jmf,J,SNESDefaultComputeJacobian,PETSC_NULL);CHKERRQ(ierr);
} else if (Jtype == 2){ /* Use coloring to compute finite difference J efficiently */
ierr = SNESSetJacobian(snes,Jmf,J,SNESDefaultComputeJacobianColor,0);CHKERRQ(ierr);
} else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Jtype is not supported");
}
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Sets various TS parameters from user options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve nonlinear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSolve(ts,u);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Free work space.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatDestroy(&J);CHKERRQ(ierr);
ierr = MatDestroy(&Jmf);CHKERRQ(ierr);
ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = VecDestroy(&r);CHKERRQ(ierr);
ierr = TSDestroy(&ts);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
ierr = PetscFinalize();
PetscFunctionReturn(0);
}
int main(int argc,char **argv)
{
PetscErrorCode ierr;
PatternCtx user;
TS ts;
Vec x;
DMDALocalInfo info;
double noiselevel = -1.0; // negative value means no initial noise
PetscInitialize(&argc,&argv,(char*)0,help);
// parameter values from pages 21-22 in Hundsdorfer & Verwer (2003)
user.L = 2.5;
user.Du = 8.0e-5;
user.Dv = 4.0e-5;
user.phi = 0.024;
user.kappa = 0.06;
ierr = PetscOptionsBegin(PETSC_COMM_WORLD, "ptn_", "options for patterns", ""); CHKERRQ(ierr);
ierr = PetscOptionsReal("-noisy_init",
"initialize u,v with this much random noise (e.g. 0.2) on top of usual initial values",
"pattern.c",noiselevel,&noiselevel,NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-L","square domain side length; recommend L >= 0.5",
"pattern.c",user.L,&user.L,NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-Du","diffusion coefficient of first equation",
"pattern.c",user.Du,&user.Du,NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-Dv","diffusion coefficient of second equation",
"pattern.c",user.Dv,&user.Dv,NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-phi","dimensionless feed rate (=F in (Pearson, 1993))",
"pattern.c",user.phi,&user.phi,NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-kappa","dimensionless rate constant (=k in (Pearson, 1993))",
"pattern.c",user.kappa,&user.kappa,NULL);CHKERRQ(ierr);
ierr = PetscOptionsEnd(); CHKERRQ(ierr);
//DMDACREATE
ierr = DMDACreate2d(PETSC_COMM_WORLD,
DM_BOUNDARY_PERIODIC, DM_BOUNDARY_PERIODIC,
DMDA_STENCIL_BOX, // for 9-point stencil
4,4,PETSC_DECIDE,PETSC_DECIDE,
2, 1, // degrees of freedom, stencil width
NULL,NULL,&user.da); CHKERRQ(ierr);
//ENDDMDACREATE
ierr = DMSetFromOptions(user.da); CHKERRQ(ierr);
ierr = DMSetUp(user.da); CHKERRQ(ierr);
ierr = DMDASetFieldName(user.da,0,"u"); CHKERRQ(ierr);
ierr = DMDASetFieldName(user.da,1,"v"); CHKERRQ(ierr);
ierr = DMDAGetLocalInfo(user.da,&info); CHKERRQ(ierr);
if (info.mx != info.my) {
SETERRQ(PETSC_COMM_WORLD,1,"pattern.c requires mx == my");
}
ierr = DMDASetUniformCoordinates(user.da, 0.0, user.L, 0.0, user.L, -1.0, -1.0); CHKERRQ(ierr);
ierr = DMSetApplicationContext(user.da,&user); CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,
"running on %d x %d grid with square cells of side h = %.6f ...\n",
info.mx,info.my,user.L/(double)(info.mx)); CHKERRQ(ierr);
//TSSETUP
ierr = TSCreate(PETSC_COMM_WORLD,&ts); CHKERRQ(ierr);
ierr = TSSetProblemType(ts,TS_NONLINEAR); CHKERRQ(ierr);
ierr = TSSetDM(ts,user.da); CHKERRQ(ierr);
ierr = DMDATSSetRHSFunctionLocal(user.da,INSERT_VALUES,
(DMDATSRHSFunctionLocal)FormRHSFunctionLocal,&user); CHKERRQ(ierr);
ierr = DMDATSSetIFunctionLocal(user.da,INSERT_VALUES,
(DMDATSIFunctionLocal)FormIFunctionLocal,&user); CHKERRQ(ierr);
ierr = DMDATSSetIJacobianLocal(user.da,
(DMDATSIJacobianLocal)FormIJacobianLocal,&user); CHKERRQ(ierr);
ierr = TSSetType(ts,TSARKIMEX); CHKERRQ(ierr);
ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP); CHKERRQ(ierr);
ierr = TSSetInitialTimeStep(ts,0.0,5.0); CHKERRQ(ierr); // t_0 = 0.0, dt = 5.0
ierr = TSSetDuration(ts,1000000,200.0); CHKERRQ(ierr); // t_f = 200
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
//ENDTSSETUP
ierr = DMCreateGlobalVector(user.da,&x); CHKERRQ(ierr);
ierr = InitialState(x,noiselevel,&user); CHKERRQ(ierr);
ierr = TSSolve(ts,x); CHKERRQ(ierr);
VecDestroy(&x); TSDestroy(&ts); DMDestroy(&user.da);
PetscFinalize();
return 0;
}
/*
FormFunction - Evaluates the function and corresponding gradient.
Input Parameters:
tao - the Tao context
X - the input vector
ptr - optional user-defined context, as set by TaoSetObjectiveAndGradientRoutine()
Output Parameters:
f - the newly evaluated function
*/
PetscErrorCode FormFunction(Tao tao,Vec P,PetscReal *f,void *ctx0)
{
AppCtx *ctx = (AppCtx*)ctx0;
TS ts;
Vec U; /* solution will be stored here */
Mat A; /* Jacobian matrix */
Mat Jacp; /* Jacobian matrix */
PetscErrorCode ierr;
PetscInt n = 2;
PetscReal ftime;
PetscInt steps;
PetscScalar *u;
PetscScalar *x_ptr,*y_ptr;
Vec lambda[1],q,mu[1];
ierr = VecGetArray(P,&x_ptr);CHKERRQ(ierr);
ctx->Pm = x_ptr[0];
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create necessary matrix and vectors
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
ierr = MatSetType(A,MATDENSE);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSetUp(A);CHKERRQ(ierr);
ierr = MatCreateVecs(A,&U,NULL);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&Jacp);CHKERRQ(ierr);
ierr = MatSetSizes(Jacp,PETSC_DECIDE,PETSC_DECIDE,2,1);CHKERRQ(ierr);
ierr = MatSetFromOptions(Jacp);CHKERRQ(ierr);
ierr = MatSetUp(Jacp);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create timestepping solver context
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr);
ierr = TSSetType(ts,TSBEULER);CHKERRQ(ierr);
ierr = TSSetIFunction(ts,NULL,(TSIFunction) IFunction,ctx);CHKERRQ(ierr);
ierr = TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,ctx);CHKERRQ(ierr);
ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set initial conditions
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = VecGetArray(U,&u);CHKERRQ(ierr);
u[0] = PetscAsinScalar(ctx->Pm/ctx->Pmax);
u[1] = 1.0;
ierr = VecRestoreArray(U,&u);CHKERRQ(ierr);
ierr = TSSetSolution(ts,U);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Save trajectory of solution so that TSAdjointSolve() may be used
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetSaveTrajectory(ts);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set solver options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetDuration(ts,PETSC_DEFAULT,10.0);CHKERRQ(ierr);
ierr = TSSetInitialTimeStep(ts,0.0,.01);CHKERRQ(ierr);
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve nonlinear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSolve(ts,U);CHKERRQ(ierr);
ierr = TSGetSolveTime(ts,&ftime);CHKERRQ(ierr);
ierr = TSGetTimeStepNumber(ts,&steps);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Adjoint model starts here
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatCreateVecs(A,&lambda[0],NULL);CHKERRQ(ierr);
/* Set initial conditions for the adjoint integration */
ierr = VecGetArray(lambda[0],&y_ptr);CHKERRQ(ierr);
y_ptr[0] = 0.0; y_ptr[1] = 0.0;
ierr = VecRestoreArray(lambda[0],&y_ptr);CHKERRQ(ierr);
ierr = MatCreateVecs(Jacp,&mu[0],NULL);CHKERRQ(ierr);
ierr = VecGetArray(mu[0],&x_ptr);CHKERRQ(ierr);
x_ptr[0] = -1.0;
ierr = VecRestoreArray(mu[0],&x_ptr);CHKERRQ(ierr);
ierr = TSAdjointSetCostGradients(ts,1,lambda,mu);CHKERRQ(ierr);
ierr = TSAdjointSetRHSJacobian(ts,Jacp,RHSJacobianP,ctx);CHKERRQ(ierr);
ierr = TSAdjointSetCostIntegrand(ts,1,(PetscErrorCode (*)(TS,PetscReal,Vec,Vec,void*))CostIntegrand,
(PetscErrorCode (*)(TS,PetscReal,Vec,Vec*,void*))DRDYFunction,
(PetscErrorCode (*)(TS,PetscReal,Vec,Vec*,void*))DRDPFunction,ctx);CHKERRQ(ierr);
ierr = TSAdjointSolve(ts);CHKERRQ(ierr);
ierr = TSAdjointGetCostIntegral(ts,&q);CHKERRQ(ierr);
ierr = ComputeSensiP(lambda[0],mu[0],ctx);CHKERRQ(ierr);
ierr = VecGetArray(q,&x_ptr);CHKERRQ(ierr);
*f = -ctx->Pm + x_ptr[0];
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Free work space. All PETSc objects should be destroyed when they are no longer needed.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&Jacp);CHKERRQ(ierr);
ierr = VecDestroy(&U);CHKERRQ(ierr);
ierr = VecDestroy(&lambda[0]);CHKERRQ(ierr);
ierr = VecDestroy(&mu[0]);CHKERRQ(ierr);
ierr = TSDestroy(&ts);CHKERRQ(ierr);
return 0;
}
int main(int argc, char **argv)
{
MPI_Comm comm;
PetscMPIInt rank;
PetscErrorCode ierr;
User user;
PetscLogDouble v1, v2;
PetscInt nplot = 0;
char fileName[2048];
ierr = PetscInitialize(&argc, &argv, (char*) 0, help);CHKERRQ(ierr);
comm = PETSC_COMM_WORLD;
ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
ierr = PetscNew(&user);CHKERRQ(ierr);
ierr = PetscNew(&user->algebra);CHKERRQ(ierr);
ierr = PetscNew(&user->model);CHKERRQ(ierr);
ierr = PetscNew(&user->model->physics);CHKERRQ(ierr);
Algebra algebra = user->algebra;
ierr = LoadOptions(comm, user);CHKERRQ(ierr);
ierr = PetscTime(&v1);CHKERRQ(ierr);
ierr = CreateMesh(comm, user);CHKERRQ(ierr);
ierr = PetscTime(&v2);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,
"Read and Distribute mesh takes %f sec \n", v2 - v1);CHKERRQ(ierr);
ierr = SetUpLocalSpace(user);CHKERRQ(ierr); //Set up the dofs of each element
ierr = ConstructGeometryFVM(&user->facegeom, &user->cellgeom, user);CHKERRQ(ierr);
ierr = LimiterSetup(user);CHKERRQ(ierr);
if (user->TimeIntegralMethod == EXPLICITMETHOD) { // explicit method
if(user->myownexplicitmethod){// Using the fully explicit method based on my own routing
ierr = PetscPrintf(PETSC_COMM_WORLD,"Using the fully explicit method based on my own routing\n");CHKERRQ(ierr);
user->current_time = user->initial_time;
user->current_step = 1;
ierr = DMCreateGlobalVector(user->dm, &algebra->solution);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) algebra->solution, "solution");CHKERRQ(ierr);
ierr = VecSet(algebra->solution, 0);CHKERRQ(ierr);
ierr = SetInitialCondition(user->dm, algebra->solution, user);CHKERRQ(ierr);
if(1){
PetscViewer viewer;
ierr = OutputVTK(user->dm, "intialcondition.vtk", &viewer);CHKERRQ(ierr);
ierr = VecView(algebra->solution, viewer);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Outputing the initial condition intialcondition.vtk!!! \n");CHKERRQ(ierr);
}
ierr = VecDuplicate(algebra->solution, &algebra->fn);CHKERRQ(ierr);
ierr = VecDuplicate(algebra->solution, &algebra->oldsolution);CHKERRQ(ierr);
if(user->Explicit_RK2||user->Explicit_RK4){
ierr = PetscPrintf(PETSC_COMM_WORLD,"Use the second order Runge Kutta method \n");CHKERRQ(ierr);
}else{
ierr = PetscPrintf(PETSC_COMM_WORLD,"Use the first order forward Euler method \n");CHKERRQ(ierr);
}
nplot = 0; //the plot step
while(user->current_time < (user->final_time - 0.05 * user->dt)){
user->current_time = user->current_time + user->dt;
ierr = FormTimeStepFunction(user, algebra, algebra->solution, algebra->fn);CHKERRQ(ierr);
if(0){
PetscViewer viewer;
ierr = OutputVTK(user->dm, "function.vtk", &viewer);CHKERRQ(ierr);
ierr = VecView(algebra->fn, viewer);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
}
if(user->Explicit_RK2){
/*
U^n_1 = U^n + 0.5*dt*f(U^n)
U^{n+1} = U^n + dt*f(U^n_1)
*/
ierr = VecCopy(algebra->solution, algebra->oldsolution);CHKERRQ(ierr);
//note that algebra->oldsolution and algebra->solution are both U^n
ierr = VecAXPY(algebra->solution, 0.5*user->dt, algebra->fn);CHKERRQ(ierr);
//U^n_1 = U^n + 0.5*dt*f(U^n), now algebra->solution is U^n_1, and algebra->fn is f(U^n)
ierr = FormTimeStepFunction(user, algebra, algebra->solution, algebra->fn);CHKERRQ(ierr);
//algebra->fn is f(U^n_1)
// reset the algebra->solution to U^n
ierr = VecCopy(algebra->oldsolution, algebra->solution);CHKERRQ(ierr);
ierr = VecAXPY(algebra->solution, user->dt, algebra->fn);CHKERRQ(ierr);
// now algebra->solution is U^{n+1} = U^n + dt*f(U^n_1)
}else if(user->Explicit_RK4){
/* refer to https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods
k_1 = f(U^n)
U^n_1 = U^n + 0.5*dt*k_1
k_2 = f(U^n_1)
U^n_2 = U^n + 0.5*dt*k_2
k_3 = f(U^n_2)
U^n_3 = U^n + 0.5*dt*k_3
k_4 = f(U^n_3)
U^{n+1} = U^n + dt/6*(k_1 + 2*k_2 + 2*k_3 + k_4)
*/
Vec VecTemp; // store the U^n_1
Vec k1, k2, k3, k4;
ierr = VecDuplicate(algebra->solution, &k1);CHKERRQ(ierr);
ierr = VecDuplicate(algebra->solution, &k2);CHKERRQ(ierr);
ierr = VecDuplicate(algebra->solution, &k3);CHKERRQ(ierr);
ierr = VecDuplicate(algebra->solution, &k4);CHKERRQ(ierr);
ierr = VecCopy(algebra->solution, algebra->oldsolution);CHKERRQ(ierr);
ierr = VecCopy(algebra->fn, k1);CHKERRQ(ierr);
//note that algebra->oldsolution and algebra->solution are both U^n
ierr = VecAXPY(algebra->solution, 0.5*user->dt, k1);CHKERRQ(ierr);
//U^n_1 = U^n + 0.5*dt*k1, now algebra->solution is U^n_1, and algebra->fn is f(U^n)
ierr = FormTimeStepFunction(user, algebra, algebra->solution, algebra->fn);CHKERRQ(ierr);
//algebra->fn is f(U^n_1)
ierr = VecCopy(algebra->fn, k2);CHKERRQ(ierr);
// reset the algebra->solution to U^n
ierr = VecCopy(algebra->oldsolution, algebra->solution);CHKERRQ(ierr);
ierr = VecAXPY(algebra->solution, 0.5*user->dt, k2);CHKERRQ(ierr);
//U^n_2 = U^n + 0.5*dt*k2, now algebra->solution is U^n_2, and algebra->fn is f(U^n_1)
ierr = FormTimeStepFunction(user, algebra, algebra->solution, algebra->fn);CHKERRQ(ierr);
//algebra->fn is f(U^n_2)
ierr = VecCopy(algebra->fn, k3);CHKERRQ(ierr);
// reset the algebra->solution to U^n
ierr = VecCopy(algebra->oldsolution, algebra->solution);CHKERRQ(ierr);
ierr = VecAXPY(algebra->solution, 0.5*user->dt, k3);CHKERRQ(ierr);
//U^n_3 = U^n + 0.5*dt*k3, now algebra->solution is U^n_3, and algebra->fn is f(U^n_2)
ierr = FormTimeStepFunction(user, algebra, algebra->solution, algebra->fn);CHKERRQ(ierr);
//algebra->fn is f(U^n_3)
ierr = VecCopy(algebra->fn, k4);CHKERRQ(ierr);
//U^{n+1} = U^n + dt/6*(k_1 + 2*k_2 + 2*k_3 + k_4)
PetscReal temp;
temp = user->dt/6;
// reset the algebra->solution to U^n
ierr = VecCopy(algebra->oldsolution, algebra->solution);CHKERRQ(ierr);
ierr = VecAXPY(algebra->solution, temp, k1);CHKERRQ(ierr);
// now algebra->solution is U^n + dt/6*k_1
ierr = VecAXPY(algebra->solution, 2*temp, k2);CHKERRQ(ierr);
// now algebra->solution is U^n + dt/6*k_1 + 2*dt/6*k_2
ierr = VecAXPY(algebra->solution, 2*temp, k3);CHKERRQ(ierr);
// now algebra->solution is U^n + dt/6*k_1 + 2*dt/6*k_2 + 2*dt/6*k_3
ierr = VecAXPY(algebra->solution, temp, k4);CHKERRQ(ierr);
// now algebra->solution is U^n + dt/6*k_1 + 2*dt/6*k_2 + 2*dt/6*k_3 + dt/6*k_4
ierr = VecDestroy(&k1);CHKERRQ(ierr);
ierr = VecDestroy(&k2);CHKERRQ(ierr);
ierr = VecDestroy(&k3);CHKERRQ(ierr);
ierr = VecDestroy(&k4);CHKERRQ(ierr);
}else{
ierr = VecCopy(algebra->solution, algebra->oldsolution);CHKERRQ(ierr);
ierr = VecAXPY(algebra->solution, user->dt, algebra->fn);CHKERRQ(ierr);
}
{// Monitor the solution and function norms
PetscReal norm;
PetscLogDouble space =0;
PetscInt size;
PetscReal fnnorm;
ierr = VecNorm(algebra->fn,NORM_2,&fnnorm);CHKERRQ(ierr);
//ierr = VecView(algebra->fn, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = VecNorm(algebra->solution,NORM_2,&norm);CHKERRQ(ierr);
ierr = VecGetSize(algebra->solution, &size);CHKERRQ(ierr);
norm = norm/size;
fnnorm = fnnorm/size;
if (norm>1.e5) {
SETERRQ2(PETSC_COMM_WORLD, PETSC_ERR_LIB,
"The norm of the solution is: %f (current time: %f). The explicit method is going to DIVERGE!!!", norm, user->current_time);
}
if (user->current_step%10==0) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"Step %D at time %g with solution norm = %g and founction norm = %g \n",
user->current_step, user->current_time, norm, fnnorm);CHKERRQ(ierr);
}
// ierr = PetscMallocGetCurrentUsage(&space);CHKERRQ(ierr);
// if (user->current_step%10==0) {
// ierr = PetscPrintf(PETSC_COMM_WORLD,"Current space PetscMalloc()ed %g M\n",
// space/(1024*1024));CHKERRQ(ierr);
// }
}
{ // Monitor the difference of two steps' solution
PetscReal norm;
ierr = VecAXPY(algebra->oldsolution, -1, algebra->solution);CHKERRQ(ierr);
ierr = VecNorm(algebra->oldsolution,NORM_2,&norm);CHKERRQ(ierr);
if (user->current_step%10==0) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"Step %D at time %g with ||u_k-u_{k-1}|| = %g \n",
user->current_step, user->current_time, norm);CHKERRQ(ierr);
}
if((norm<1.e-6)||(user->current_step > user->max_time_its)){
if(norm<1.e-6) ierr = PetscPrintf(PETSC_COMM_WORLD,"\n Convergence with ||u_k-u_{k-1}|| = %g < 1.e-6\n\n", norm);CHKERRQ(ierr);
if(user->current_step > user->max_time_its) ierr = PetscPrintf(PETSC_COMM_WORLD,"\n Convergence with reaching the max time its\n\n");CHKERRQ(ierr);
break;
}
}
// output the solution
if (user->output_solution && (user->current_step%user->steps_output==0)){
PetscViewer viewer;
Vec solution_unscaled; // Note the the algebra->solution is scaled by the density, so this is for the unscaled solution
nplot = user->current_step/user->steps_output;
// update file name for the current time step
ierr = VecDuplicate(algebra->solution, &solution_unscaled);CHKERRQ(ierr);
ierr = ReformatSolution(algebra->solution, solution_unscaled, user);CHKERRQ(ierr);
ierr = PetscSNPrintf(fileName, sizeof(fileName),"%s_%d.vtk",user->solutionfile, nplot);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Outputing solution %s (current time %f)\n", fileName, user->current_time);CHKERRQ(ierr);
ierr = OutputVTK(user->dm, fileName, &viewer);CHKERRQ(ierr);
ierr = VecView(solution_unscaled, viewer);CHKERRQ(ierr);
ierr = VecDestroy(&solution_unscaled);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
}
user->current_step++;
}
ierr = VecDestroy(&algebra->fn);CHKERRQ(ierr);
}else{ // Using the fully explicit method based on the PETSC TS routing
PetscReal ftime;
TS ts;
TSConvergedReason reason;
PetscInt nsteps;
//PetscReal minRadius;
//ierr = DMPlexTSGetGeometry(user->dm, NULL, NULL, &minRadius);CHKERRQ(ierr);
//user->dt = 0.9*4 * minRadius / 1.0;
ierr = PetscPrintf(PETSC_COMM_WORLD,"Using the fully explicit method based on the PETSC TS routing\n");CHKERRQ(ierr);
ierr = DMCreateGlobalVector(user->dm, &algebra->solution);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) algebra->solution, "solution");CHKERRQ(ierr);
ierr = VecSet(algebra->solution, 0.0);CHKERRQ(ierr);
ierr = SetInitialCondition(user->dm, algebra->solution, user);CHKERRQ(ierr);
ierr = TSCreate(comm, &ts);CHKERRQ(ierr);
ierr = TSSetType(ts, TSEULER);CHKERRQ(ierr);
ierr = TSSetDM(ts, user->dm);CHKERRQ(ierr);
ierr = TSMonitorSet(ts,TSMonitorFunctionError,(void*)user,NULL);CHKERRQ(ierr);
ierr = TSSetRHSFunction(ts, NULL, MyRHSFunction, user);CHKERRQ(ierr);
ierr = TSSetDuration(ts, 1000, user->final_time);CHKERRQ(ierr);
ierr = TSSetInitialTimeStep(ts, user->initial_time, user->dt);CHKERRQ(ierr);
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
ierr = TSSolve(ts, algebra->solution);CHKERRQ(ierr);
ierr = TSGetSolveTime(ts, &ftime);CHKERRQ(ierr);
ierr = TSGetTimeStepNumber(ts, &nsteps);CHKERRQ(ierr);
ierr = TSGetConvergedReason(ts, &reason);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"%s at time %g after %D steps\n",TSConvergedReasons[reason],ftime,nsteps);CHKERRQ(ierr);
ierr = TSDestroy(&ts);CHKERRQ(ierr);
}
if(user->benchmark_couette) {
ierr = DMCreateGlobalVector(user->dm, &algebra->exactsolution);CHKERRQ(ierr);
ierr = ComputeExactSolution(user->dm, user->current_time, algebra->exactsolution, user);CHKERRQ(ierr);
}
if(user->benchmark_couette) {
PetscViewer viewer;
PetscReal norm;
ierr = OutputVTK(user->dm, "exact_solution.vtk", &viewer);CHKERRQ(ierr);
ierr = VecView(algebra->exactsolution, viewer);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
ierr = VecAXPY(algebra->exactsolution, -1, algebra->solution);CHKERRQ(ierr);
ierr = VecNorm(algebra->exactsolution,NORM_INFINITY,&norm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Final time at %f, Error: ||u_k-u|| = %g \n", user->current_time, norm);CHKERRQ(ierr);
ierr = OutputVTK(user->dm, "Error.vtk", &viewer);CHKERRQ(ierr);
ierr = VecView(algebra->exactsolution, viewer);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
}
ierr = VecDestroy(&algebra->solution);CHKERRQ(ierr);
if(user->myownexplicitmethod){ierr = VecDestroy(&algebra->oldsolution);CHKERRQ(ierr);}
ierr = VecDestroy(&algebra->exactsolution);CHKERRQ(ierr);
ierr = DMDestroy(&user->dm);CHKERRQ(ierr);
} else if (user->TimeIntegralMethod == IMPLICITMETHOD) { // Using the fully implicit method
ierr = PetscPrintf(PETSC_COMM_WORLD,"Using the fully implicit method\n");CHKERRQ(ierr);
ierr = SNESCreate(comm,&user->snes);CHKERRQ(ierr);
ierr = SNESSetDM(user->snes,user->dm);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(user->dm, &algebra->solution);CHKERRQ(ierr);
ierr = VecDuplicate(algebra->solution, &algebra->oldsolution);CHKERRQ(ierr);
ierr = VecDuplicate(algebra->solution, &algebra->f);CHKERRQ(ierr);
ierr = VecDuplicate(algebra->solution, &algebra->fn);CHKERRQ(ierr);
ierr = VecDuplicate(algebra->solution, &algebra->oldfn);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) algebra->solution, "solution");CHKERRQ(ierr);
ierr = SetInitialCondition(user->dm, algebra->solution, user);CHKERRQ(ierr);
ierr = DMSetMatType(user->dm, MATAIJ);CHKERRQ(ierr);
// ierr = DMCreateMatrix(user->dm, &algebra->A);CHKERRQ(ierr);
ierr = DMCreateMatrix(user->dm, &algebra->J);CHKERRQ(ierr);
if (user->JdiffP) {
/*Set up the preconditioner matrix*/
ierr = DMCreateMatrix(user->dm, &algebra->P);CHKERRQ(ierr);
}else{
algebra->P = algebra->J;
}
ierr = MatSetOption(algebra->J, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_FALSE);CHKERRQ(ierr);
/*set nonlinear function */
ierr = SNESSetFunction(user->snes, algebra->f, FormFunction, (void*)user);CHKERRQ(ierr);
/* compute Jacobian */
ierr = SNESSetJacobian(user->snes, algebra->J, algebra->P, FormJacobian, (void*)user);CHKERRQ(ierr);
ierr = SNESSetFromOptions(user->snes);CHKERRQ(ierr);
/* do the solve */
if (user->timestep == TIMESTEP_STEADY_STATE) {
ierr = SolveSteadyState(user);CHKERRQ(ierr);
} else {
ierr = SolveTimeDependent(user);CHKERRQ(ierr);
}
if (user->output_solution){
PetscViewer viewer;
Vec solution_unscaled; // Note the the algebra->solution is scaled by the density, so this is for the unscaled solution
ierr = VecDuplicate(algebra->solution, &solution_unscaled);CHKERRQ(ierr);
ierr = ReformatSolution(algebra->solution, solution_unscaled, user);CHKERRQ(ierr);
ierr = OutputVTK(user->dm, "solution.vtk", &viewer);CHKERRQ(ierr);
ierr = VecView(solution_unscaled, viewer);CHKERRQ(ierr);
ierr = VecDestroy(&solution_unscaled);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
}
if(user->benchmark_couette) {
PetscViewer viewer;
PetscReal norm;
ierr = OutputVTK(user->dm, "exact_solution.vtk", &viewer);CHKERRQ(ierr);
ierr = VecView(algebra->exactsolution, viewer);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
ierr = VecAXPY(algebra->exactsolution, -1, algebra->solution);CHKERRQ(ierr);
ierr = VecNorm(algebra->exactsolution,NORM_INFINITY,&norm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Error: ||u_k-u|| = %g \n", norm);CHKERRQ(ierr);
ierr = OutputVTK(user->dm, "Error.vtk", &viewer);CHKERRQ(ierr);
ierr = VecView(algebra->exactsolution, viewer);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
}
ierr = VecDestroy(&algebra->solution);CHKERRQ(ierr);
ierr = VecDestroy(&algebra->f);CHKERRQ(ierr);
ierr = VecDestroy(&algebra->oldsolution);CHKERRQ(ierr);
ierr = VecDestroy(&algebra->fn);CHKERRQ(ierr);
ierr = VecDestroy(&algebra->oldfn);CHKERRQ(ierr);
ierr = SNESDestroy(&user->snes);CHKERRQ(ierr);
ierr = DMDestroy(&user->dm);CHKERRQ(ierr);
} else {
SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"WRONG option for the time integral method. Using the option '-time_integral_method 0 or 1'");
}
ierr = VecDestroy(&user->cellgeom);CHKERRQ(ierr);
ierr = VecDestroy(&user->facegeom);CHKERRQ(ierr);
ierr = DMDestroy(&user->dmGrad);CHKERRQ(ierr);
ierr = PetscFunctionListDestroy(&LimitList);CHKERRQ(ierr);
ierr = PetscFree(user->model->physics);CHKERRQ(ierr);
ierr = PetscFree(user->algebra);CHKERRQ(ierr);
ierr = PetscFree(user->model);CHKERRQ(ierr);
ierr = PetscFree(user);CHKERRQ(ierr);
{
PetscLogDouble space =0;
ierr = PetscMallocGetCurrentUsage(&space);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Unfreed space at the End %g M\n", space/(1024*1024));CHKERRQ(ierr);
}
ierr = PetscFinalize();
return(0);
}
int main(int argc,char **argv)
{
TS ts; /* nonlinear solver */
Vec x; /* solution, residual vectors */
Mat A; /* Jacobian matrix */
Mat Jacp; /* JacobianP matrix */
PetscInt steps;
PetscReal ftime =0.5;
PetscBool monitor = PETSC_FALSE;
PetscScalar *x_ptr;
PetscMPIInt size;
struct _n_User user;
PetscErrorCode ierr;
Vec lambda[2],mu[2];
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Initialize program
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
PetscInitialize(&argc,&argv,NULL,help);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
if (size != 1) SETERRQ(PETSC_COMM_SELF,1,"This is a uniprocessor example only!");
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set runtime options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
user.mu = 1;
user.next_output = 0.0;
ierr = PetscOptionsGetReal(NULL,NULL,"-mu",&user.mu,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,NULL,"-monitor",&monitor,NULL);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create necessary matrix and vectors, solve same ODE on every process
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,2,2);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSetUp(A);CHKERRQ(ierr);
ierr = MatCreateVecs(A,&x,NULL);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&Jacp);CHKERRQ(ierr);
ierr = MatSetSizes(Jacp,PETSC_DECIDE,PETSC_DECIDE,2,1);CHKERRQ(ierr);
ierr = MatSetFromOptions(Jacp);CHKERRQ(ierr);
ierr = MatSetUp(Jacp);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create timestepping solver context
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
ierr = TSSetType(ts,TSRK);CHKERRQ(ierr);
ierr = TSSetRHSFunction(ts,NULL,RHSFunction,&user);CHKERRQ(ierr);
ierr = TSSetDuration(ts,PETSC_DEFAULT,ftime);CHKERRQ(ierr);
ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);CHKERRQ(ierr);
if (monitor) {
ierr = TSMonitorSet(ts,Monitor,&user,NULL);CHKERRQ(ierr);
}
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set initial conditions
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = VecGetArray(x,&x_ptr);CHKERRQ(ierr);
x_ptr[0] = 2; x_ptr[1] = 0.66666654321;
ierr = VecRestoreArray(x,&x_ptr);CHKERRQ(ierr);
ierr = TSSetInitialTimeStep(ts,0.0,.001);CHKERRQ(ierr);
/*
Have the TS save its trajectory so that TSAdjointSolve() may be used
*/
ierr = TSSetSaveTrajectory(ts);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set runtime options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve nonlinear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSolve(ts,x);CHKERRQ(ierr);
ierr = TSGetSolveTime(ts,&ftime);CHKERRQ(ierr);
ierr = TSGetTimeStepNumber(ts,&steps);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"mu %g, steps %D, ftime %g\n",(double)user.mu,steps,(double)ftime);CHKERRQ(ierr);
ierr = VecView(x,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Start the Adjoint model
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatCreateVecs(A,&lambda[0],NULL);CHKERRQ(ierr);
ierr = MatCreateVecs(A,&lambda[1],NULL);CHKERRQ(ierr);
/* Reset initial conditions for the adjoint integration */
ierr = VecGetArray(lambda[0],&x_ptr);CHKERRQ(ierr);
x_ptr[0] = 1.0; x_ptr[1] = 0.0;
ierr = VecRestoreArray(lambda[0],&x_ptr);CHKERRQ(ierr);
ierr = VecGetArray(lambda[1],&x_ptr);CHKERRQ(ierr);
x_ptr[0] = 0.0; x_ptr[1] = 1.0;
ierr = VecRestoreArray(lambda[1],&x_ptr);CHKERRQ(ierr);
ierr = MatCreateVecs(Jacp,&mu[0],NULL);CHKERRQ(ierr);
ierr = MatCreateVecs(Jacp,&mu[1],NULL);CHKERRQ(ierr);
ierr = VecGetArray(mu[0],&x_ptr);CHKERRQ(ierr);
x_ptr[0] = 0.0;
ierr = VecRestoreArray(mu[0],&x_ptr);CHKERRQ(ierr);
ierr = VecGetArray(mu[1],&x_ptr);CHKERRQ(ierr);
x_ptr[0] = 0.0;
ierr = VecRestoreArray(mu[1],&x_ptr);CHKERRQ(ierr);
ierr = TSSetCostGradients(ts,2,lambda,mu);CHKERRQ(ierr);
/* Set RHS Jacobian for the adjoint integration */
ierr = TSSetRHSJacobian(ts,A,A,RHSJacobian,&user);CHKERRQ(ierr);
/* Set RHS JacobianP */
ierr = TSAdjointSetRHSJacobian(ts,Jacp,RHSJacobianP,&user);CHKERRQ(ierr);
ierr = TSAdjointSolve(ts);CHKERRQ(ierr);
ierr = VecView(lambda[0],PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = VecView(lambda[1],PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = VecView(mu[0],PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = VecView(mu[1],PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Free work space. All PETSc objects should be destroyed when they
are no longer needed.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = MatDestroy(&Jacp);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&lambda[0]);CHKERRQ(ierr);
ierr = VecDestroy(&lambda[1]);CHKERRQ(ierr);
ierr = VecDestroy(&mu[0]);CHKERRQ(ierr);
ierr = VecDestroy(&mu[1]);CHKERRQ(ierr);
ierr = TSDestroy(&ts);CHKERRQ(ierr);
PetscFinalize();
PetscFunctionReturn(0);
}
int main(int argc,char **argv)
{
TS ts; /* nonlinear solver */
Vec X; /* solution, residual vectors */
Mat J; /* Jacobian matrix */
PetscInt steps,maxsteps,mx;
PetscErrorCode ierr;
DM da;
PetscReal ftime,hx,dt;
struct _User user; /* user-defined work context */
TSConvergedReason reason;
PetscInitialize(&argc,&argv,(char*)0,help);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create distributed array (DMDA) to manage parallel grid and vectors
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = DMDACreate1d(PETSC_COMM_WORLD,DMDA_BOUNDARY_NONE,-11,2,2,NULL,&da);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Extract global vectors from DMDA;
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = DMCreateGlobalVector(da,&X);CHKERRQ(ierr);
/* Initialize user application context */
ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Advection-reaction options","");
{
user.A = 1;
user.B = 3;
user.alpha = 0.02;
user.uleft = 1;
user.uright = 1;
user.vleft = 3;
user.vright = 3;
ierr = PetscOptionsReal("-A","Reaction rate","",user.A,&user.A,NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-B","Reaction rate","",user.B,&user.B,NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-alpha","Diffusion coefficient","",user.alpha,&user.alpha,NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-uleft","Dirichlet boundary condition","",user.uleft,&user.uleft,NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-uright","Dirichlet boundary condition","",user.uright,&user.uright,NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-vleft","Dirichlet boundary condition","",user.vleft,&user.vleft,NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-vright","Dirichlet boundary condition","",user.vright,&user.vright,NULL);CHKERRQ(ierr);
}
ierr = PetscOptionsEnd();CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create timestepping solver context
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
ierr = TSSetDM(ts,da);CHKERRQ(ierr);
ierr = TSSetType(ts,TSARKIMEX);CHKERRQ(ierr);
ierr = TSSetRHSFunction(ts,NULL,FormRHSFunction,&user);CHKERRQ(ierr);
ierr = TSSetIFunction(ts,NULL,FormIFunction,&user);CHKERRQ(ierr);
ierr = DMCreateMatrix(da,MATAIJ,&J);CHKERRQ(ierr);
ierr = TSSetIJacobian(ts,J,J,FormIJacobian,&user);CHKERRQ(ierr);
ftime = 10.0;
maxsteps = 10000;
ierr = TSSetDuration(ts,maxsteps,ftime);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set initial conditions
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = FormInitialSolution(ts,X,&user);CHKERRQ(ierr);
ierr = TSSetSolution(ts,X);CHKERRQ(ierr);
ierr = VecGetSize(X,&mx);CHKERRQ(ierr);
hx = 1.0/(PetscReal)(mx/2-1);
dt = 0.4 * PetscSqr(hx) / user.alpha; /* Diffusive stability limit */
ierr = TSSetInitialTimeStep(ts,0.0,dt);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set runtime options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve nonlinear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSolve(ts,X);CHKERRQ(ierr);
ierr = TSGetSolveTime(ts,&ftime);CHKERRQ(ierr);
ierr = TSGetTimeStepNumber(ts,&steps);CHKERRQ(ierr);
ierr = TSGetConvergedReason(ts,&reason);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"%s at time %G after %D steps\n",TSConvergedReasons[reason],ftime,steps);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Free work space.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatDestroy(&J);CHKERRQ(ierr);
ierr = VecDestroy(&X);CHKERRQ(ierr);
ierr = TSDestroy(&ts);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **argv)
{
TS ts; /* ODE integrator */
Vec U; /* solution */
Mat A; /* Jacobian matrix */
PetscErrorCode ierr;
PetscMPIInt size;
PetscInt n = 4;
AppCtx ctx;
PetscScalar *u;
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Initialize program
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
PetscInitialize(&argc,&argv,(char*)0,help);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create necessary matrix and vectors
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSetUp(A);CHKERRQ(ierr);
ierr = MatCreateVecs(A,&U,NULL);CHKERRQ(ierr);
ctx.k1 = 1.0e-5;
ctx.k2 = 1.0e5;
ctx.k3 = 1.0e-16;
ctx.sigma2 = 1.0e6;
ierr = VecDuplicate(U,&ctx.initialsolution);CHKERRQ(ierr);
ierr = VecGetArray(ctx.initialsolution,&u);CHKERRQ(ierr);
u[0] = 0.0;
u[1] = 1.3e8;
u[2] = 5.0e11;
u[3] = 8.0e11;
ierr = VecRestoreArray(ctx.initialsolution,&u);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create timestepping solver context
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr);
ierr = TSSetType(ts,TSROSW);CHKERRQ(ierr);
ierr = TSSetIFunction(ts,NULL,(TSIFunction) IFunction,&ctx);CHKERRQ(ierr);
ierr = TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,&ctx);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set initial conditions
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = Solution(ts,0,U,&ctx);CHKERRQ(ierr);
ierr = TSSetInitialTimeStep(ts,4.0*3600,1.0);CHKERRQ(ierr);
ierr = TSSetSolution(ts,U);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set solver options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetDuration(ts,1000000,518400.0);CHKERRQ(ierr);
ierr = TSSetMaxStepRejections(ts,100);CHKERRQ(ierr);
ierr = TSSetMaxSNESFailures(ts,-1);CHKERRQ(ierr); /* unlimited */
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve nonlinear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSolve(ts,U);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Free work space. All PETSc objects should be destroyed when they
are no longer needed.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = VecDestroy(&ctx.initialsolution);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = VecDestroy(&U);CHKERRQ(ierr);
ierr = TSDestroy(&ts);CHKERRQ(ierr);
ierr = PetscFinalize();
PetscFunctionReturn(0);
}
/* Solves the specified ODE and computes the error if exact solution is available */
PetscErrorCode SolveODE(char* ptype, PetscReal dt, PetscReal tfinal, PetscInt maxiter, PetscReal *error, PetscBool *exact_flag)
{
PetscErrorCode ierr; /* Error code */
TS ts; /* time-integrator */
Vec Y; /* Solution vector */
Vec Yex; /* Exact solution */
PetscInt N; /* Size of the system of equations */
TSType time_scheme; /* Type of time-integration scheme */
Mat Jac = NULL; /* Jacobian matrix */
PetscFunctionBegin;
N = GetSize((const char *)&ptype[0]);
if (N < 0) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_ARG_SIZ,"Illegal problem specification.\n");
ierr = VecCreate(PETSC_COMM_WORLD,&Y);CHKERRQ(ierr);
ierr = VecSetSizes(Y,N,PETSC_DECIDE);CHKERRQ(ierr);
ierr = VecSetUp(Y);CHKERRQ(ierr);
ierr = VecSet(Y,0);CHKERRQ(ierr);
/* Initialize the problem */
ierr = Initialize(Y,&ptype[0]);
/* Create and initialize the time-integrator */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
/* Default time integration options */
ierr = TSSetType(ts,TSEULER);CHKERRQ(ierr);
ierr = TSSetDuration(ts,maxiter,tfinal);CHKERRQ(ierr);
ierr = TSSetInitialTimeStep(ts,0.0,dt);CHKERRQ(ierr);
ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);CHKERRQ(ierr);
/* Read command line options for time integration */
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
/* Set solution vector */
ierr = TSSetSolution(ts,Y);CHKERRQ(ierr);
/* Specify left/right-hand side functions */
ierr = TSGetType(ts,&time_scheme);CHKERRQ(ierr);
if ((!strcmp(time_scheme,TSEULER)) || (!strcmp(time_scheme,TSRK)) || (!strcmp(time_scheme,TSSSP))) {
/* Explicit time-integration -> specify right-hand side function ydot = f(y) */
ierr = TSSetRHSFunction(ts,NULL,RHSFunction,&ptype[0]);CHKERRQ(ierr);
} else if ((!strcmp(time_scheme,TSBEULER)) || (!strcmp(time_scheme,TSARKIMEX))) {
/* Implicit time-integration -> specify left-hand side function ydot-f(y) = 0 */
/* and its Jacobian function */
ierr = TSSetIFunction(ts,NULL,IFunction,&ptype[0]);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&Jac);CHKERRQ(ierr);
ierr = MatSetSizes(Jac,PETSC_DECIDE,PETSC_DECIDE,N,N);CHKERRQ(ierr);
ierr = MatSetFromOptions(Jac);CHKERRQ(ierr);
ierr = MatSetUp(Jac);CHKERRQ(ierr);
ierr = TSSetIJacobian(ts,Jac,Jac,IJacobian,&ptype[0]);CHKERRQ(ierr);
}
/* Solve */
ierr = TSSolve(ts,Y);CHKERRQ(ierr);
/* Exact solution */
ierr = VecDuplicate(Y,&Yex);CHKERRQ(ierr);
ierr = ExactSolution(Yex,&ptype[0],tfinal,exact_flag);
/* Calculate Error */
ierr = VecAYPX(Yex,-1.0,Y);CHKERRQ(ierr);
ierr = VecNorm(Yex,NORM_2,error);CHKERRQ(ierr);
*error = PetscSqrtReal(((*error)*(*error))/N);
/* Clean up and finalize */
ierr = MatDestroy(&Jac);CHKERRQ(ierr);
ierr = TSDestroy(&ts);CHKERRQ(ierr);
ierr = VecDestroy(&Yex);CHKERRQ(ierr);
ierr = VecDestroy(&Y);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
int main(int argc,char **argv)
{
TS ts; /* nonlinear solver */
Vec x,r; /* solution, residual vectors */
PetscInt steps,maxsteps = 100; /* iterations for convergence */
PetscErrorCode ierr;
DM da;
PetscReal ftime;
SNES ts_snes;
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Initialize program
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
PetscInitialize(&argc,&argv,(char*)0,help);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create distributed array (DMDA) to manage parallel grid and vectors
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,-8,-8,PETSC_DECIDE,PETSC_DECIDE,
2,1,NULL,NULL,&da);CHKERRQ(ierr);
ierr = DMDASetFieldName(da,0,"u");CHKERRQ(ierr);
ierr = DMDASetFieldName(da,1,"v");CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Extract global vectors from DMDA; then duplicate for remaining
vectors that are the same types
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = DMCreateGlobalVector(da,&x);CHKERRQ(ierr);
ierr = VecDuplicate(x,&r);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create timestepping solver context
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
ierr = TSSetDM(ts,da);CHKERRQ(ierr);
ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr);
ierr = TSSetRHSFunction(ts,NULL,FormFunction,da);CHKERRQ(ierr);
ierr = TSSetDuration(ts,maxsteps,1.0);CHKERRQ(ierr);
ierr = TSMonitorSet(ts,MyTSMonitor,0,0);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Customize nonlinear solver
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetType(ts,TSBEULER);CHKERRQ(ierr);
ierr = TSGetSNES(ts,&ts_snes);
ierr = SNESMonitorSet(ts_snes,MySNESMonitor,NULL,NULL);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set initial conditions
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = FormInitialSolution(da,x);CHKERRQ(ierr);
ierr = TSSetInitialTimeStep(ts,0.0,.0001);CHKERRQ(ierr);
ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);CHKERRQ(ierr);
ierr = TSSetSolution(ts,x);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set runtime options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve nonlinear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSolve(ts,x);CHKERRQ(ierr);
ierr = TSGetSolveTime(ts,&ftime);CHKERRQ(ierr);
ierr = TSGetTimeStepNumber(ts,&steps);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Free work space. All PETSc objects should be destroyed when they
are no longer needed.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&r);CHKERRQ(ierr);
ierr = TSDestroy(&ts);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
ierr = PetscFinalize();
PetscFunctionReturn(0);
}
int main(int argc,char **argv)
{
TS ts; /* time integrator */
Vec x,r; /* solution, residual vectors */
PetscInt steps,Mx;
PetscErrorCode ierr;
DM da;
PetscReal dt;
UserCtx ctx;
PetscBool mymonitor;
PetscViewer viewer;
PetscBool flg;
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Initialize program
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
ctx.kappa = 1.0;
ierr = PetscOptionsGetReal(NULL,NULL,"-kappa",&ctx.kappa,NULL);CHKERRQ(ierr);
ctx.allencahn = PETSC_FALSE;
ierr = PetscOptionsHasName(NULL,NULL,"-allen-cahn",&ctx.allencahn);CHKERRQ(ierr);
ierr = PetscOptionsHasName(NULL,NULL,"-mymonitor",&mymonitor);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create distributed array (DMDA) to manage parallel grid and vectors
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_PERIODIC, 10,1,2,NULL,&da);CHKERRQ(ierr);
ierr = DMSetFromOptions(da);CHKERRQ(ierr);
ierr = DMSetUp(da);CHKERRQ(ierr);
ierr = DMDASetFieldName(da,0,"Heat equation: u");CHKERRQ(ierr);
ierr = DMDAGetInfo(da,0,&Mx,0,0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
dt = 1.0/(ctx.kappa*Mx*Mx);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Extract global vectors from DMDA; then duplicate for remaining
vectors that are the same types
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = DMCreateGlobalVector(da,&x);CHKERRQ(ierr);
ierr = VecDuplicate(x,&r);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create timestepping solver context
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
ierr = TSSetDM(ts,da);CHKERRQ(ierr);
ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr);
ierr = TSSetRHSFunction(ts,NULL,FormFunction,&ctx);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Customize nonlinear solver
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetType(ts,TSCN);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set initial conditions
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = FormInitialSolution(da,x);CHKERRQ(ierr);
ierr = TSSetTimeStep(ts,dt);CHKERRQ(ierr);
ierr = TSSetMaxTime(ts,.02);CHKERRQ(ierr);
ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_INTERPOLATE);CHKERRQ(ierr);
ierr = TSSetSolution(ts,x);CHKERRQ(ierr);
if (mymonitor) {
ctx.ports = NULL;
ierr = TSMonitorSet(ts,MyMonitor,&ctx,MyDestroy);CHKERRQ(ierr);
}
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set runtime options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve nonlinear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSolve(ts,x);CHKERRQ(ierr);
ierr = TSGetStepNumber(ts,&steps);CHKERRQ(ierr);
ierr = PetscOptionsHasName(NULL,NULL,"-square_initial",&flg);CHKERRQ(ierr);
if (flg) {
ierr = PetscViewerBinaryOpen(PETSC_COMM_WORLD,"InitialSolution.heat",FILE_MODE_WRITE,&viewer);CHKERRQ(ierr);
ierr = VecView(x,viewer);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
}
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Free work space. All PETSc objects should be destroyed when they
are no longer needed.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&r);CHKERRQ(ierr);
ierr = TSDestroy(&ts);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
int main(int argc,char **argv)
{
PetscFunctionList plist = NULL;
char pname[256];
TS ts; /* nonlinear solver */
Vec x,r; /* solution, residual vectors */
Mat A; /* Jacobian matrix */
Problem problem;
PetscBool use_monitor;
PetscInt steps,maxsteps = 1000,nonlinits,linits,snesfails,rejects;
PetscReal ftime;
MonitorCtx mon;
PetscErrorCode ierr;
PetscMPIInt size;
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Initialize program
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
PetscInitialize(&argc,&argv,(char*)0,help);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");
/* Register the available problems */
ierr = PetscFunctionListAdd(&plist,"rober",&RoberCreate);CHKERRQ(ierr);
ierr = PetscFunctionListAdd(&plist,"ce",&CECreate);CHKERRQ(ierr);
ierr = PetscFunctionListAdd(&plist,"orego",&OregoCreate);CHKERRQ(ierr);
ierr = PetscStrcpy(pname,"ce");CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set runtime options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Timestepping benchmark options","");CHKERRQ(ierr);
{
ierr = PetscOptionsFList("-problem_type","Name of problem to run","",plist,pname,pname,sizeof(pname),NULL);CHKERRQ(ierr);
use_monitor = PETSC_FALSE;
ierr = PetscOptionsBool("-monitor_error","Display errors relative to exact solutions","",use_monitor,&use_monitor,NULL);CHKERRQ(ierr);
}
ierr = PetscOptionsEnd();CHKERRQ(ierr);
/* Create the new problem */
ierr = PetscNew(&problem);CHKERRQ(ierr);
problem->comm = MPI_COMM_WORLD;
{
PetscErrorCode (*pcreate)(Problem);
ierr = PetscFunctionListFind(plist,pname,&pcreate);CHKERRQ(ierr);
if (!pcreate) SETERRQ1(PETSC_COMM_SELF,1,"No problem '%s'",pname);
ierr = (*pcreate)(problem);CHKERRQ(ierr);
}
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create necessary matrix and vectors
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,problem->n,problem->n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSetUp(A);CHKERRQ(ierr);
ierr = MatGetVecs(A,&x,NULL);CHKERRQ(ierr);
ierr = VecDuplicate(x,&r);CHKERRQ(ierr);
mon.comm = PETSC_COMM_WORLD;
mon.problem = problem;
ierr = VecDuplicate(x,&mon.x);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create timestepping solver context
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr);
ierr = TSSetType(ts,TSROSW);CHKERRQ(ierr); /* Rosenbrock-W */
ierr = TSSetIFunction(ts,NULL,problem->function,problem->data);CHKERRQ(ierr);
ierr = TSSetIJacobian(ts,A,A,problem->jacobian,problem->data);CHKERRQ(ierr);
ierr = TSSetDuration(ts,maxsteps,problem->final_time);CHKERRQ(ierr);
ierr = TSSetMaxStepRejections(ts,10);CHKERRQ(ierr);
ierr = TSSetMaxSNESFailures(ts,-1);CHKERRQ(ierr); /* unlimited */
if (use_monitor) {
ierr = TSMonitorSet(ts,&MonitorError,&mon,NULL);CHKERRQ(ierr);
}
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set initial conditions
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = (*problem->solution)(0,x,problem->data);CHKERRQ(ierr);
ierr = TSSetInitialTimeStep(ts,0.0,.001);CHKERRQ(ierr);
ierr = TSSetSolution(ts,x);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set runtime options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve nonlinear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSolve(ts,x);CHKERRQ(ierr);
ierr = TSGetSolveTime(ts,&ftime);CHKERRQ(ierr);
ierr = TSGetTimeStepNumber(ts,&steps);CHKERRQ(ierr);
ierr = TSGetSNESFailures(ts,&snesfails);CHKERRQ(ierr);
ierr = TSGetStepRejections(ts,&rejects);CHKERRQ(ierr);
ierr = TSGetSNESIterations(ts,&nonlinits);CHKERRQ(ierr);
ierr = TSGetKSPIterations(ts,&linits);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"steps %D (%D rejected, %D SNES fails), ftime %G, nonlinits %D, linits %D\n",steps,rejects,snesfails,ftime,nonlinits,linits);CHKERRQ(ierr);
if (problem->hasexact) {
ierr = MonitorError(ts,steps,ftime,x,&mon);CHKERRQ(ierr);
}
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Free work space. All PETSc objects should be destroyed when they
are no longer needed.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&r);CHKERRQ(ierr);
ierr = VecDestroy(&mon.x);CHKERRQ(ierr);
ierr = TSDestroy(&ts);CHKERRQ(ierr);
if (problem->destroy) {
ierr = (*problem->destroy)(problem);CHKERRQ(ierr);
}
ierr = PetscFree(problem);CHKERRQ(ierr);
ierr = PetscFunctionListDestroy(&plist);CHKERRQ(ierr);
ierr = PetscFinalize();
PetscFunctionReturn(0);
}
int main(int argc,char **argv)
{
TS ts; /* ODE integrator */
Vec U,V; /* solution will be stored here */
Vec F; /* residual vector */
Mat J; /* Jacobian matrix */
PetscMPIInt rank;
PetscScalar *u,*v;
AppCtx app;
PetscInt direction[2];
PetscBool terminate[2];
TSAdapt adapt;
PetscErrorCode ierr;
ierr = PetscInitialize(&argc,&argv,NULL,help);CHKERRQ(ierr);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
app.Cd = 0.0;
app.Cr = 0.9;
app.bounces = 0;
app.maxbounces = 10;
ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"ex44 options","");CHKERRQ(ierr);
ierr = PetscOptionsReal("-Cd","Drag coefficient","",app.Cd,&app.Cd,NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-Cr","Restitution coefficient","",app.Cr,&app.Cr,NULL);CHKERRQ(ierr);
ierr = PetscOptionsInt("-maxbounces","Maximum number of bounces","",app.maxbounces,&app.maxbounces,NULL);CHKERRQ(ierr);
ierr = PetscOptionsEnd();CHKERRQ(ierr);
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
/*ierr = TSSetSaveTrajectory(ts);CHKERRQ(ierr);*/
ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr);
ierr = TSSetType(ts,TSALPHA2);CHKERRQ(ierr);
ierr = TSSetDuration(ts,PETSC_MAX_INT,PETSC_MAX_REAL);CHKERRQ(ierr);
ierr = TSSetTimeStep(ts,0.1);CHKERRQ(ierr);
ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);CHKERRQ(ierr);
ierr = TSGetAdapt(ts,&adapt);CHKERRQ(ierr);
ierr = TSAdaptSetStepLimits(adapt,0.0,0.5);CHKERRQ(ierr);
direction[0] = -1; terminate[0] = PETSC_FALSE;
direction[1] = -1; terminate[1] = PETSC_TRUE;
ierr = TSSetEventHandler(ts,2,direction,terminate,Event,PostEvent,&app);CHKERRQ(ierr);
ierr = MatCreateAIJ(PETSC_COMM_WORLD,1,1,PETSC_DECIDE,PETSC_DECIDE,1,NULL,0,NULL,&J);CHKERRQ(ierr);
ierr = MatSetFromOptions(J);CHKERRQ(ierr);
ierr = MatSetUp(J);CHKERRQ(ierr);
ierr = MatCreateVecs(J,NULL,&F);CHKERRQ(ierr);
ierr = TSSetI2Function(ts,F,I2Function,&app);CHKERRQ(ierr);
ierr = TSSetI2Jacobian(ts,J,J,I2Jacobian,&app);CHKERRQ(ierr);
ierr = VecDestroy(&F);CHKERRQ(ierr);
ierr = MatDestroy(&J);CHKERRQ(ierr);
ierr = TSGetI2Jacobian(ts,&J,NULL,NULL,NULL);CHKERRQ(ierr);
ierr = MatCreateVecs(J,&U,NULL);CHKERRQ(ierr);
ierr = MatCreateVecs(J,&V,NULL);CHKERRQ(ierr);
ierr = VecGetArray(U,&u);CHKERRQ(ierr);
ierr = VecGetArray(V,&v);CHKERRQ(ierr);
u[0] = 5.0*rank; v[0] = 20.0;
ierr = VecRestoreArray(U,&u);CHKERRQ(ierr);
ierr = VecRestoreArray(V,&v);CHKERRQ(ierr);
ierr = TS2SetSolution(ts,U,V);CHKERRQ(ierr);
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
ierr = TSSolve(ts,NULL);CHKERRQ(ierr);
ierr = VecDestroy(&U);CHKERRQ(ierr);
ierr = VecDestroy(&V);CHKERRQ(ierr);
ierr = TSDestroy(&ts);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
int main(int argc,char **argv)
{
TS ts; /* ODE integrator */
Vec U; /* solution will be stored here */
Mat A; /* Jacobian matrix */
PetscErrorCode ierr;
PetscMPIInt size;
PetscInt n = 2;
AppCtx ctx;
PetscScalar *u;
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Initialize program
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create necessary matrix and vectors
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSetUp(A);CHKERRQ(ierr);
ierr = MatCreateVecs(A,&U,NULL);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set runtime options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Reaction options","");CHKERRQ(ierr);
{
ctx.omega_s = 1.0;
ierr = PetscOptionsScalar("-omega_s","","",ctx.omega_s,&ctx.omega_s,NULL);CHKERRQ(ierr);
ctx.H = 1.0;
ierr = PetscOptionsScalar("-H","","",ctx.H,&ctx.H,NULL);CHKERRQ(ierr);
ctx.E = 1.0;
ierr = PetscOptionsScalar("-E","","",ctx.E,&ctx.E,NULL);CHKERRQ(ierr);
ctx.V = 1.0;
ierr = PetscOptionsScalar("-V","","",ctx.V,&ctx.V,NULL);CHKERRQ(ierr);
ctx.X = 1.0;
ierr = PetscOptionsScalar("-X","","",ctx.X,&ctx.X,NULL);CHKERRQ(ierr);
ierr = VecGetArray(U,&u);CHKERRQ(ierr);
u[0] = 1;
u[1] = .7;
ierr = VecRestoreArray(U,&u);CHKERRQ(ierr);
ierr = PetscOptionsGetVec(NULL,NULL,"-initial",U,NULL);CHKERRQ(ierr);
}
ierr = PetscOptionsEnd();CHKERRQ(ierr);
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&ctx.rand);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(ctx.rand);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create timestepping solver context
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr);
ierr = TSSetType(ts,TSROSW);CHKERRQ(ierr);
ierr = TSSetIFunction(ts,NULL,(TSIFunction) IFunction,&ctx);CHKERRQ(ierr);
ierr = TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,&ctx);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set initial conditions
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetSolution(ts,U);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set solver options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetDuration(ts,100000,2000.0);CHKERRQ(ierr);
ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);CHKERRQ(ierr);
ierr = TSSetInitialTimeStep(ts,0.0,.001);CHKERRQ(ierr);
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve nonlinear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSolve(ts,U);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Free work space. All PETSc objects should be destroyed when they are no longer needed.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = VecDestroy(&U);CHKERRQ(ierr);
ierr = TSDestroy(&ts);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&ctx.rand);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
int main(int argc,char **argv)
{
PetscErrorCode ierr;
int time; /* amount of loops */
struct in put;
PetscScalar rh; /* relative humidity */
PetscScalar x; /* memory varialbe for relative humidity calculation */
PetscScalar deep_grnd_temp; /* temperature of ground under top soil surface layer */
PetscScalar emma; /* absorption-emission constant for air */
PetscScalar pressure1 = 101300; /* surface pressure */
PetscScalar mixratio; /* mixing ratio */
PetscScalar airtemp; /* temperature of air near boundary layer inversion */
PetscScalar dewtemp; /* dew point temperature */
PetscScalar sfctemp; /* temperature at surface */
PetscScalar pwat; /* total column precipitable water */
PetscScalar cloudTemp; /* temperature at base of cloud */
AppCtx user; /* user-defined work context */
MonitorCtx usermonitor; /* user-defined monitor context */
PetscMPIInt rank,size;
TS ts;
SNES snes;
DM da;
Vec T,rhs; /* solution vector */
Mat J; /* Jacobian matrix */
PetscReal ftime,dt;
PetscInt steps,dof = 5;
PetscBool use_coloring = PETSC_TRUE;
MatFDColoring matfdcoloring = 0;
PetscBool monitor_off = PETSC_FALSE;
PetscInitialize(&argc,&argv,(char*)0,help);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
/* Inputs */
readinput(&put);
sfctemp = put.Ts;
dewtemp = put.Td;
cloudTemp = put.Tc;
airtemp = put.Ta;
pwat = put.pwt;
if (!rank) PetscPrintf(PETSC_COMM_SELF,"Initial Temperature = %g\n",sfctemp); /* input surface temperature */
deep_grnd_temp = sfctemp - 10; /* set underlying ground layer temperature */
emma = emission(pwat); /* accounts for radiative effects of water vapor */
/* Converts from Fahrenheit to Celsuis */
sfctemp = fahr_to_cel(sfctemp);
airtemp = fahr_to_cel(airtemp);
dewtemp = fahr_to_cel(dewtemp);
cloudTemp = fahr_to_cel(cloudTemp);
deep_grnd_temp = fahr_to_cel(deep_grnd_temp);
/* Converts from Celsius to Kelvin */
sfctemp += 273;
airtemp += 273;
dewtemp += 273;
cloudTemp += 273;
deep_grnd_temp += 273;
/* Calculates initial relative humidity */
x = calcmixingr(dewtemp,pressure1);
mixratio = calcmixingr(sfctemp,pressure1);
rh = (x/mixratio)*100;
if (!rank) printf("Initial RH = %.1f percent\n\n",rh); /* prints initial relative humidity */
time = 3600*put.time; /* sets amount of timesteps to run model */
/* Configure PETSc TS solver */
/*------------------------------------------*/
/* Create grid */
ierr = DMDACreate2d(PETSC_COMM_WORLD,DMDA_BOUNDARY_PERIODIC,DMDA_BOUNDARY_PERIODIC,DMDA_STENCIL_STAR,-20,-20,
PETSC_DECIDE,PETSC_DECIDE,dof,1,NULL,NULL,&da);CHKERRQ(ierr);
ierr = DMDASetUniformCoordinates(da, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0);CHKERRQ(ierr);
/* Define output window for each variable of interest */
ierr = DMDASetFieldName(da,0,"Ts");CHKERRQ(ierr);
ierr = DMDASetFieldName(da,1,"Ta");CHKERRQ(ierr);
ierr = DMDASetFieldName(da,2,"u");CHKERRQ(ierr);
ierr = DMDASetFieldName(da,3,"v");CHKERRQ(ierr);
ierr = DMDASetFieldName(da,4,"p");CHKERRQ(ierr);
/* set values for appctx */
user.da = da;
user.Ts = sfctemp;
user.fract = put.fr; /* fraction of sky covered by clouds */
user.dewtemp = dewtemp; /* dew point temperature (mositure in air) */
user.csoil = 2000000; /* heat constant for layer */
user.dzlay = 0.08; /* thickness of top soil layer */
user.emma = emma; /* emission parameter */
user.wind = put.wnd; /* wind spped */
user.pressure1 = pressure1; /* sea level pressure */
user.airtemp = airtemp; /* temperature of air near boundar layer inversion */
user.Tc = cloudTemp; /* temperature at base of lowest cloud layer */
user.init = put.init; /* user chosen initiation scenario */
user.lat = 70*0.0174532; /* converts latitude degrees to latitude in radians */
user.deep_grnd_temp = deep_grnd_temp; /* temp in lowest ground layer */
/* set values for MonitorCtx */
usermonitor.drawcontours = PETSC_FALSE;
ierr = PetscOptionsHasName(NULL,"-drawcontours",&usermonitor.drawcontours);CHKERRQ(ierr);
if (usermonitor.drawcontours) {
PetscReal bounds[] = {1000.0,-1000., -1000.,-1000., 1000.,-1000., 1000.,-1000., 1000,-1000, 100700,100800};
ierr = PetscViewerDrawOpen(PETSC_COMM_WORLD,0,0,0,0,300,300,&usermonitor.drawviewer);CHKERRQ(ierr);
ierr = PetscViewerDrawSetBounds(usermonitor.drawviewer,dof,bounds);CHKERRQ(ierr);
}
usermonitor.interval = 1;
ierr = PetscOptionsGetInt(NULL,"-monitor_interval",&usermonitor.interval,NULL);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Extract global vectors from DA;
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = DMCreateGlobalVector(da,&T);CHKERRQ(ierr);
ierr = VecDuplicate(T,&rhs);CHKERRQ(ierr); /* r: vector to put the computed right hand side */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr);
ierr = TSSetType(ts,TSBEULER);CHKERRQ(ierr);
ierr = TSSetRHSFunction(ts,rhs,RhsFunc,&user);CHKERRQ(ierr);
/* Set Jacobian evaluation routine - use coloring to compute finite difference Jacobian efficiently */
ierr = DMSetMatType(da,MATAIJ);CHKERRQ(ierr);
ierr = DMCreateMatrix(da,&J);CHKERRQ(ierr);
ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
if (use_coloring) {
ISColoring iscoloring;
ierr = DMCreateColoring(da,IS_COLORING_GLOBAL,&iscoloring);CHKERRQ(ierr);
ierr = MatFDColoringCreate(J,iscoloring,&matfdcoloring);CHKERRQ(ierr);
ierr = MatFDColoringSetFromOptions(matfdcoloring);CHKERRQ(ierr);
ierr = MatFDColoringSetUp(J,iscoloring,matfdcoloring);CHKERRQ(ierr);
ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
ierr = MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode (*)(void))SNESTSFormFunction,ts);CHKERRQ(ierr);
ierr = SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor,matfdcoloring);CHKERRQ(ierr);
} else {
ierr = SNESSetJacobian(snes,J,J,SNESComputeJacobianDefault,NULL);CHKERRQ(ierr);
}
/* Define what to print for ts_monitor option */
ierr = PetscOptionsHasName(NULL,"-monitor_off",&monitor_off);CHKERRQ(ierr);
if (!monitor_off) {
ierr = TSMonitorSet(ts,Monitor,&usermonitor,NULL);CHKERRQ(ierr);
}
ierr = FormInitialSolution(da,T,&user);CHKERRQ(ierr);
dt = TIMESTEP; /* initial time step */
ftime = TIMESTEP*time;
if (!rank) printf("time %d, ftime %g hour, TIMESTEP %g\n",time,ftime/3600,dt);
ierr = TSSetInitialTimeStep(ts,0.0,dt);CHKERRQ(ierr);
ierr = TSSetDuration(ts,time,ftime);CHKERRQ(ierr);
ierr = TSSetSolution(ts,T);CHKERRQ(ierr);
ierr = TSSetDM(ts,da);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set runtime options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve nonlinear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSolve(ts,T);CHKERRQ(ierr);
ierr = TSGetSolveTime(ts,&ftime);CHKERRQ(ierr);
ierr = TSGetTimeStepNumber(ts,&steps);CHKERRQ(ierr);
if (!rank) PetscPrintf(PETSC_COMM_WORLD,"Solution T after %g hours %d steps\n",ftime/3600,steps);
if (matfdcoloring) {ierr = MatFDColoringDestroy(&matfdcoloring);CHKERRQ(ierr);}
if (usermonitor.drawcontours) {
ierr = PetscViewerDestroy(&usermonitor.drawviewer);CHKERRQ(ierr);
}
ierr = MatDestroy(&J);CHKERRQ(ierr);
ierr = VecDestroy(&T);CHKERRQ(ierr);
ierr = VecDestroy(&rhs);CHKERRQ(ierr);
ierr = TSDestroy(&ts);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
PetscFinalize();
return 0;
}
int main(int argc,char **argv)
{
TS ts; /* ODE integrator */
Vec x; /* solution */
PetscErrorCode ierr;
DM da;
AppCtx appctx;
Vec lambda[1];
PetscScalar *x_ptr;
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Initialize program
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
PetscFunctionBeginUser;
appctx.D1 = 8.0e-5;
appctx.D2 = 4.0e-5;
appctx.gamma = .024;
appctx.kappa = .06;
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create distributed array (DMDA) to manage parallel grid and vectors
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = DMDACreate2d(PETSC_COMM_WORLD,DM_BOUNDARY_PERIODIC,DM_BOUNDARY_PERIODIC,DMDA_STENCIL_STAR,65,65,PETSC_DECIDE,PETSC_DECIDE,2,1,NULL,NULL,&da);CHKERRQ(ierr);
ierr = DMSetFromOptions(da);CHKERRQ(ierr);
ierr = DMSetUp(da);CHKERRQ(ierr);
ierr = DMDASetFieldName(da,0,"u");CHKERRQ(ierr);
ierr = DMDASetFieldName(da,1,"v");CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Extract global vectors from DMDA; then duplicate for remaining
vectors that are the same types
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = DMCreateGlobalVector(da,&x);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create timestepping solver context
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
ierr = TSSetType(ts,TSCN);CHKERRQ(ierr);
ierr = TSSetDM(ts,da);CHKERRQ(ierr);
ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr);
ierr = TSSetRHSFunction(ts,NULL,RHSFunction,&appctx);CHKERRQ(ierr);
ierr = TSSetRHSJacobian(ts,NULL,NULL,RHSJacobian,&appctx);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set initial conditions
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = InitialConditions(da,x);CHKERRQ(ierr);
ierr = TSSetSolution(ts,x);CHKERRQ(ierr);
/*
Have the TS save its trajectory so that TSAdjointSolve() may be used
*/
ierr = TSSetSaveTrajectory(ts);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set solver options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetDuration(ts,PETSC_DEFAULT,2000.0);CHKERRQ(ierr);
ierr = TSSetInitialTimeStep(ts,0.0,.0001);CHKERRQ(ierr);
ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);CHKERRQ(ierr);
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve ODE system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSolve(ts,x);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Start the Adjoint model
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = VecDuplicate(x,&lambda[0]);CHKERRQ(ierr);
/* Reset initial conditions for the adjoint integration */
ierr = VecGetArray(lambda[0],&x_ptr);CHKERRQ(ierr);
ierr = InitializeLambda(da,lambda[0],0.5,0.5);CHKERRQ(ierr);
ierr = TSSetCostGradients(ts,1,lambda,NULL);CHKERRQ(ierr);
ierr = TSAdjointSolve(ts);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Free work space. All PETSc objects should be destroyed when they
are no longer needed.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = VecDestroy(&lambda[0]);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = TSDestroy(&ts);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
int main(int argc,char **argv)
{
TS ts; /* nonlinear solver */
Vec x; /* solution, residual vectors */
Mat A; /* Jacobian matrix */
PetscInt steps;
PetscReal ftime = 0.5;
PetscBool monitor = PETSC_FALSE;
PetscScalar *x_ptr;
PetscMPIInt size;
struct _n_User user;
PetscErrorCode ierr;
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Initialize program
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PetscInitialize(&argc,&argv,NULL,help);CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
if (size != 1) SETERRQ(PETSC_COMM_SELF,1,"This is a uniprocessor example only!");
/* Register user-specified ARKIMEX method */
ierr = RegisterMyARK2();CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set runtime options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
user.imex = PETSC_TRUE;
user.next_output = 0.0;
user.mu = 1.0e6;
ierr = PetscOptionsGetBool(NULL,NULL,"-imex",&user.imex,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,NULL,"-monitor",&monitor,NULL);CHKERRQ(ierr);
ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Physical parameters",NULL);
ierr = PetscOptionsReal("-mu","Stiffness parameter","<1.0e6>",user.mu,&user.mu,NULL);CHKERRQ(ierr);
ierr = PetscOptionsEnd();
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create necessary matrix and vectors, solve same ODE on every process
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,2,2);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSetUp(A);CHKERRQ(ierr);
ierr = MatCreateVecs(A,&x,NULL);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create timestepping solver context
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
ierr = TSSetType(ts,TSBEULER);CHKERRQ(ierr);
ierr = TSSetRHSFunction(ts,NULL,RHSFunction,&user);CHKERRQ(ierr);
ierr = TSSetIFunction(ts,NULL,IFunction,&user);CHKERRQ(ierr);
ierr = TSSetIJacobian(ts,A,A,IJacobian,&user);CHKERRQ(ierr);
ierr = TSSetDuration(ts,PETSC_DEFAULT,ftime);CHKERRQ(ierr);
ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);CHKERRQ(ierr);
if (monitor) {
ierr = TSMonitorSet(ts,Monitor,&user,NULL);CHKERRQ(ierr);
}
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set initial conditions
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = VecGetArray(x,&x_ptr);CHKERRQ(ierr);
x_ptr[0] = 2.0; x_ptr[1] = -6.666665432100101e-01;
ierr = VecRestoreArray(x,&x_ptr);CHKERRQ(ierr);
ierr = TSSetInitialTimeStep(ts,0.0,.001);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set runtime options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve nonlinear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSolve(ts,x);CHKERRQ(ierr);
ierr = TSGetSolveTime(ts,&ftime);CHKERRQ(ierr);
ierr = TSGetTimeStepNumber(ts,&steps);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"steps %D, ftime %g\n",steps,(double)ftime);CHKERRQ(ierr);
ierr = VecView(x,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Free work space. All PETSc objects should be destroyed when they
are no longer needed.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = TSDestroy(&ts);CHKERRQ(ierr);
ierr = PetscFinalize();
PetscFunctionReturn(0);
}
int main(int argc,char **argv)
{
TS ts; /* ODE integrator */
Vec U; /* solution will be stored here */
Mat A; /* Jacobian matrix */
PetscErrorCode ierr;
PetscMPIInt size;
PetscInt n = 2;
PetscScalar *u;
AppCtx app;
PetscInt direction[2];
PetscBool terminate[2];
TSAdapt adapt;
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Initialize program
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");
app.nbounces = 0;
app.maxbounces = 10;
ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"ex21 options","");CHKERRQ(ierr);
ierr = PetscOptionsInt("-maxbounces","","",app.maxbounces,&app.maxbounces,NULL);CHKERRQ(ierr);
ierr = PetscOptionsEnd();CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create necessary matrix and vectors
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
ierr = MatSetType(A,MATDENSE);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSetUp(A);CHKERRQ(ierr);
ierr = MatCreateVecs(A,&U,NULL);CHKERRQ(ierr);
ierr = VecGetArray(U,&u);CHKERRQ(ierr);
u[0] = 0.0;
u[1] = 20.0;
ierr = VecRestoreArray(U,&u);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create timestepping solver context
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
ierr = TSSetSaveTrajectory(ts);CHKERRQ(ierr);
ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr);
ierr = TSSetType(ts,TSROSW);CHKERRQ(ierr);
ierr = TSSetIFunction(ts,NULL,(TSIFunction) IFunction,NULL);CHKERRQ(ierr);
ierr = TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,NULL);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set initial conditions
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetSolution(ts,U);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set solver options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetDuration(ts,1000,30.0);CHKERRQ(ierr);
ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);CHKERRQ(ierr);
ierr = TSSetInitialTimeStep(ts,0.0,0.1);CHKERRQ(ierr);
/* Set directions and terminate flags for the two events */
direction[0] = -1; direction[1] = -1;
terminate[0] = PETSC_FALSE; terminate[1] = PETSC_TRUE;
ierr = TSSetEventHandler(ts,2,direction,terminate,EventFunction,PostEventFunction,(void*)&app);CHKERRQ(ierr);
/* The adapative time step controller could take very large timesteps resulting in
the same event occuring multiple times in the same interval. A maximum step size
limit is enforced here to avoid this issue.
*/
ierr = TSGetAdapt(ts,&adapt);CHKERRQ(ierr);
ierr = TSAdaptSetStepLimits(adapt,0.0,0.5);CHKERRQ(ierr);
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Run timestepping solver
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSolve(ts,U);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Free work space. All PETSc objects should be destroyed when they are no longer needed.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = VecDestroy(&U);CHKERRQ(ierr);
ierr = TSDestroy(&ts);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
int main(int argc,char **argv)
{
TS ts; /* ODE integrator */
Vec U; /* solution will be stored here */
Vec Utrue;
PetscErrorCode ierr;
PetscMPIInt size;
AppCtx ctx;
PetscScalar *u;
IS iss;
IS isf;
PetscInt *indicess;
PetscInt *indicesf;
PetscInt n=2;
PetscReal error,tt;
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Initialize program
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs");
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create index for slow part and fast part
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PetscMalloc1(1,&indicess);CHKERRQ(ierr);
indicess[0]=0;
ierr = PetscMalloc1(1,&indicesf);CHKERRQ(ierr);
indicesf[0]=1;
ierr = ISCreateGeneral(PETSC_COMM_SELF,1,indicess,PETSC_COPY_VALUES,&iss);CHKERRQ(ierr);
ierr = ISCreateGeneral(PETSC_COMM_SELF,1,indicesf,PETSC_COPY_VALUES,&isf);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create necesary vector
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = VecCreate(PETSC_COMM_WORLD,&U);CHKERRQ(ierr);
ierr = VecSetSizes(U,n,PETSC_DETERMINE);CHKERRQ(ierr);
ierr = VecSetFromOptions(U);CHKERRQ(ierr);
ierr = VecDuplicate(U,&Utrue);
ierr = VecCopy(U,Utrue);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set initial condition
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = VecGetArray(U,&u);CHKERRQ(ierr);
u[0] = PetscSqrtScalar(2.0);
u[1] = PetscSqrtScalar(3.0);
ierr = VecRestoreArray(U,&u);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create timestepping solver context
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
ierr = TSSetType(ts,TSMPRK);CHKERRQ(ierr);
ierr = TSSetRHSFunction(ts,NULL,(TSRHSFunction)RHSFunction,&ctx);CHKERRQ(ierr);
ierr = TSRHSSplitSetIS(ts,"slow",iss);CHKERRQ(ierr);
ierr = TSRHSSplitSetIS(ts,"fast",isf);CHKERRQ(ierr);
ierr = TSRHSSplitSetRHSFunction(ts,"slow",NULL,(TSRHSFunctionslow)RHSFunctionslow,&ctx);CHKERRQ(ierr);
ierr = TSRHSSplitSetRHSFunction(ts,"fast",NULL,(TSRHSFunctionfast)RHSFunctionfast,&ctx);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set initial conditions
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetSolution(ts,U);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set solver options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"ODE options","");CHKERRQ(ierr);
{
ctx.Tf = 0.3;
ctx.dt = 0.01;
ierr = PetscOptionsScalar("-Tf","","",ctx.Tf,&ctx.Tf,NULL);CHKERRQ(ierr);
ierr = PetscOptionsScalar("-dt","","",ctx.dt,&ctx.dt,NULL);CHKERRQ(ierr);
}
ierr = PetscOptionsEnd();CHKERRQ(ierr);
ierr = TSSetMaxTime(ts,ctx.Tf);CHKERRQ(ierr);
ierr = TSSetTimeStep(ts,ctx.dt);CHKERRQ(ierr);
ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);CHKERRQ(ierr);
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve linear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSolve(ts,U);CHKERRQ(ierr);
ierr = VecView(U,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Check the error of the Petsc solution
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSGetTime(ts,&tt);CHKERRQ(ierr);
ierr = sol_true(tt,Utrue);CHKERRQ(ierr);
ierr = VecAXPY(Utrue,-1.0,U);CHKERRQ(ierr);
ierr = VecNorm(Utrue,NORM_2,&error);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Print norm2 error
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PetscPrintf(PETSC_COMM_WORLD,"l2 error norm: %g\n", error);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Free work space. All PETSc objects should be destroyed when they are no longer needed.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = VecDestroy(&U);CHKERRQ(ierr);
ierr = TSDestroy(&ts);CHKERRQ(ierr);
ierr = VecDestroy(&Utrue);CHKERRQ(ierr);
ierr = ISDestroy(&iss);CHKERRQ(ierr);
ierr = ISDestroy(&isf);CHKERRQ(ierr);
ierr = PetscFree(indicess);CHKERRQ(ierr);
ierr = PetscFree(indicesf);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
int main(int argc,char **argv)
{
TS ts; /* nonlinear solver */
Vec x; /* solution, residual vectors */
Mat A; /* Jacobian matrix */
PetscInt steps;
PetscReal ftime = 0.5;
PetscBool monitor = PETSC_FALSE;
PetscScalar *x_ptr;
PetscMPIInt size;
struct _n_User user;
PetscErrorCode ierr;
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Initialize program
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
PetscInitialize(&argc,&argv,NULL,help);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
if (size != 1) SETERRQ(PETSC_COMM_SELF,1,"This is a uniprocessor example only!");
ierr = RegisterMyARK2();CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set runtime options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
user.next_output = 0.0;
ierr = PetscOptionsGetBool(NULL,"-monitor",&monitor,NULL);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create necessary matrix and vectors, solve same ODE on every process
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,2,2);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSetUp(A);CHKERRQ(ierr);
ierr = MatCreateVecs(A,&x,NULL);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create timestepping solver context
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
ierr = TSSetType(ts,TSBEULER);CHKERRQ(ierr);
ierr = TSSetIFunction(ts,NULL,IFunction,&user);CHKERRQ(ierr);
ierr = TSSetIJacobian(ts,A,A,IJacobian,&user);CHKERRQ(ierr);
ierr = TSSetDuration(ts,PETSC_DEFAULT,ftime);CHKERRQ(ierr);
if (monitor) {
ierr = TSMonitorSet(ts,Monitor,&user,NULL);CHKERRQ(ierr);
}
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set initial conditions
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = VecGetArray(x,&x_ptr);CHKERRQ(ierr);
x_ptr[0] = -2; x_ptr[1] = -2.355301397608119909925287735864250951918;
ierr = VecRestoreArray(x,&x_ptr);CHKERRQ(ierr);
ierr = TSSetInitialTimeStep(ts,0.0,.001);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set runtime options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve nonlinear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSolve(ts,x);CHKERRQ(ierr);
ierr = TSGetSolveTime(ts,&ftime);CHKERRQ(ierr);
ierr = TSGetTimeStepNumber(ts,&steps);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"steps %D, ftime %g\n",steps,(double)ftime);CHKERRQ(ierr);
ierr = VecView(x,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Free work space. All PETSc objects should be destroyed when they
are no longer needed.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = TSDestroy(&ts);CHKERRQ(ierr);
ierr = PetscFinalize();
PetscFunctionReturn(0);
}
int main(int argc,char **argv)
{
TS ts; /* nonlinear solver */
Vec ic;
PetscBool monitor = PETSC_FALSE;
PetscScalar *x_ptr;
PetscMPIInt size;
struct _n_User user;
PetscErrorCode ierr;
Tao tao;
TaoConvergedReason reason;
KSP ksp;
PC pc;
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Initialize program
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
PetscInitialize(&argc,&argv,NULL,help);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
if (size != 1) SETERRQ(PETSC_COMM_SELF,1,"This is a uniprocessor example only!");
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set runtime options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
user.mu = 1.0;
user.next_output = 0.0;
user.steps = 0;
user.ftime = 0.5;
ierr = PetscOptionsGetReal(NULL,"-mu",&user.mu,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,"-monitor",&monitor,NULL);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create necessary matrix and vectors, solve same ODE on every process
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatCreate(PETSC_COMM_WORLD,&user.A);CHKERRQ(ierr);
ierr = MatSetSizes(user.A,PETSC_DECIDE,PETSC_DECIDE,2,2);CHKERRQ(ierr);
ierr = MatSetFromOptions(user.A);CHKERRQ(ierr);
ierr = MatSetUp(user.A);CHKERRQ(ierr);
ierr = MatCreateVecs(user.A,&user.x,NULL);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create timestepping solver context
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
ierr = TSSetType(ts,TSRK);CHKERRQ(ierr);
ierr = TSSetRHSFunction(ts,NULL,RHSFunction,&user);CHKERRQ(ierr);
ierr = TSSetDuration(ts,PETSC_DEFAULT,user.ftime);CHKERRQ(ierr);
ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);CHKERRQ(ierr);
if (monitor) {
ierr = TSMonitorSet(ts,Monitor,&user,NULL);CHKERRQ(ierr);
}
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set initial conditions
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = VecGetArray(user.x,&x_ptr);CHKERRQ(ierr);
x_ptr[0] = 2.0; x_ptr[1] = 0.66666654321;
ierr = VecRestoreArray(user.x,&x_ptr);CHKERRQ(ierr);
ierr = TSSetTime(ts,0.0);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"mu %g, steps %D, ftime %g\n",(double)user.mu,user.steps,(double)(user.ftime));CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Save trajectory of solution so that TSAdjointSolve() may be used
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetSaveTrajectory(ts);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set runtime options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve nonlinear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSolve(ts,user.x);CHKERRQ(ierr);
ierr = TSGetSolveTime(ts,&(user.ftime));CHKERRQ(ierr);
ierr = TSGetTimeStepNumber(ts,&user.steps);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"mu %g, steps %D, ftime %g\n",(double)user.mu,user.steps,(double)user.ftime);CHKERRQ(ierr);
ierr = VecGetArray(user.x,&x_ptr);CHKERRQ(ierr);
user.x_ob[0] = x_ptr[0];
user.x_ob[1] = x_ptr[1];
ierr = MatCreateVecs(user.A,&user.lambda[0],NULL);CHKERRQ(ierr);
/* Create TAO solver and set desired solution method */
ierr = TaoCreate(PETSC_COMM_WORLD,&tao);CHKERRQ(ierr);
ierr = TaoSetType(tao,TAOCG);CHKERRQ(ierr);
/* Set initial solution guess */
ierr = MatCreateVecs(user.A,&ic,NULL);CHKERRQ(ierr);
ierr = VecGetArray(ic,&x_ptr);CHKERRQ(ierr);
x_ptr[0] = 2.1;
x_ptr[1] = 0.7;
ierr = VecRestoreArray(ic,&x_ptr);CHKERRQ(ierr);
ierr = TaoSetInitialVector(tao,ic);CHKERRQ(ierr);
/* Set routine for function and gradient evaluation */
ierr = TaoSetObjectiveAndGradientRoutine(tao,FormFunctionGradient,(void *)&user);CHKERRQ(ierr);
/* Check for any TAO command line options */
ierr = TaoSetFromOptions(tao);CHKERRQ(ierr);
ierr = TaoGetKSP(tao,&ksp);CHKERRQ(ierr);
if (ksp) {
ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
ierr = PCSetType(pc,PCNONE);CHKERRQ(ierr);
}
ierr = TaoSetTolerances(tao,1e-10,1e-10,1e-10,PETSC_DEFAULT,PETSC_DEFAULT);
/* SOLVE THE APPLICATION */
ierr = TaoSolve(tao); CHKERRQ(ierr);
/* Get information on termination */
ierr = TaoGetConvergedReason(tao,&reason);CHKERRQ(ierr);
if (reason <= 0){
ierr=PetscPrintf(MPI_COMM_WORLD, "Try another method! \n");CHKERRQ(ierr);
}
/* Free TAO data structures */
ierr = TaoDestroy(&tao);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Free work space. All PETSc objects should be destroyed when they
are no longer needed.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatDestroy(&user.A);CHKERRQ(ierr);
ierr = VecDestroy(&user.x);CHKERRQ(ierr);
ierr = VecDestroy(&user.lambda[0]);CHKERRQ(ierr);
ierr = TSDestroy(&ts);CHKERRQ(ierr);
ierr = VecDestroy(&ic);CHKERRQ(ierr);
ierr = PetscFinalize();
PetscFunctionReturn(0);
}
int main(int argc,char **argv)
{
TS ts; /* nonlinear solver */
Vec U; /* solution, residual vectors */
PetscErrorCode ierr;
DM da;
AppCtx appctx;
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Initialize program
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
PetscInitialize(&argc,&argv,(char*)0,help);
appctx.epsilon = 1.0e-3;
appctx.delta = 1.0;
appctx.alpha = 10.0;
appctx.beta = 4.0;
appctx.gamma = 1.0;
appctx.kappa = .75;
appctx.lambda = 1.0;
appctx.mu = 100.;
appctx.cstar = .2;
appctx.upwind = PETSC_TRUE;
ierr = PetscOptionsGetScalar(NULL,"-delta",&appctx.delta,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,"-upwind",&appctx.upwind,NULL);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create distributed array (DMDA) to manage parallel grid and vectors
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE,-8,2,1,NULL,&da);CHKERRQ(ierr);
ierr = DMDASetFieldName(da,0,"rho");CHKERRQ(ierr);
ierr = DMDASetFieldName(da,1,"c");CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Extract global vectors from DMDA; then duplicate for remaining
vectors that are the same types
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = DMCreateGlobalVector(da,&U);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create timestepping solver context
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
ierr = TSSetType(ts,TSROSW);CHKERRQ(ierr);
ierr = TSSetDM(ts,da);CHKERRQ(ierr);
ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr);
ierr = TSSetIFunction(ts,NULL,IFunction,&appctx);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set initial conditions
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = InitialConditions(da,U);CHKERRQ(ierr);
ierr = TSSetSolution(ts,U);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set solver options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetInitialTimeStep(ts,0.0,.0001);CHKERRQ(ierr);
ierr = TSSetDuration(ts,PETSC_DEFAULT,1.0);CHKERRQ(ierr);
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve nonlinear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSolve(ts,U);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Free work space. All PETSc objects should be destroyed when they
are no longer needed.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = VecDestroy(&U);CHKERRQ(ierr);
ierr = TSDestroy(&ts);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
ierr = PetscFinalize();
PetscFunctionReturn(0);
}
/*
FormFunctionGradient - Evaluates the function and corresponding gradient.
Input Parameters:
tao - the Tao context
X - the input vector
ptr - optional user-defined context, as set by TaoSetObjectiveAndGradientRoutine()
Output Parameters:
f - the newly evaluated function
G - the newly evaluated gradient
*/
PetscErrorCode FormFunctionGradient(Tao tao,Vec IC,PetscReal *f,Vec G,void *ctx)
{
User user = (User)ctx;
TS ts;
PetscScalar *x_ptr,*y_ptr;
PetscErrorCode ierr;
PetscScalar *ic_ptr;
ierr = VecCopy(IC,user->x);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create timestepping solver context
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
ierr = TSSetType(ts,TSRK);CHKERRQ(ierr);
ierr = TSSetRHSFunction(ts,NULL,RHSFunction,user);CHKERRQ(ierr);
ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set time
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetTime(ts,0.0);CHKERRQ(ierr);
ierr = TSSetInitialTimeStep(ts,0.0,.001);CHKERRQ(ierr);
ierr = TSSetDuration(ts,2000,0.5);CHKERRQ(ierr);
ierr = TSSetTolerances(ts,1e-7,NULL,1e-7,NULL);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Save trajectory of solution so that TSAdjointSolve() may be used
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetSaveTrajectory(ts);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set runtime options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
ierr = TSSolve(ts,user->x);CHKERRQ(ierr);
ierr = TSGetSolveTime(ts,&user->ftime);CHKERRQ(ierr);
ierr = TSGetTimeStepNumber(ts,&user->steps);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"mu %.6f, steps %D, ftime %g\n",(double)user->mu,user->steps,(double)user->ftime);CHKERRQ(ierr);
ierr = VecGetArray(IC,&ic_ptr);CHKERRQ(ierr);
ierr = VecGetArray(user->x,&x_ptr);CHKERRQ(ierr);
*f = (x_ptr[0]-user->x_ob[0])*(x_ptr[0]-user->x_ob[0])+(x_ptr[1]-user->x_ob[1])*(x_ptr[1]-user->x_ob[1]);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Observed value y_ob=[%f; %f], ODE solution y=[%f;%f], Cost function f=%f\n",(double)user->x_ob[0],(double)user->x_ob[1],(double)x_ptr[0],(double)x_ptr[1],(double)(*f));CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Adjoint model starts here
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/* Redet initial conditions for the adjoint integration */
ierr = VecGetArray(user->lambda[0],&y_ptr);CHKERRQ(ierr);
y_ptr[0] = 2.*(x_ptr[0]-user->x_ob[0]);
y_ptr[1] = 2.*(x_ptr[1]-user->x_ob[1]);
ierr = VecRestoreArray(user->lambda[0],&y_ptr);CHKERRQ(ierr);
ierr = TSSetCostGradients(ts,1,user->lambda,NULL);CHKERRQ(ierr);
/* Set RHS Jacobian for the adjoint integration */
ierr = TSSetRHSJacobian(ts,user->A,user->A,RHSJacobian,user);CHKERRQ(ierr);
ierr = TSAdjointSolve(ts);CHKERRQ(ierr);
ierr = VecCopy(user->lambda[0],G);
ierr = TSDestroy(&ts);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
int main(int argc,char **argv)
{
TS ts; /* time integrator */
TSAdapt adapt;
Vec X; /* solution vector */
Mat J; /* Jacobian matrix */
PetscInt steps,maxsteps,ncells,xs,xm,i;
PetscErrorCode ierr;
PetscReal ftime,dt;
char chemfile[PETSC_MAX_PATH_LEN] = "chem.inp",thermofile[PETSC_MAX_PATH_LEN] = "therm.dat";
struct _User user;
TSConvergedReason reason;
PetscBool showsolutions = PETSC_FALSE;
char **snames,*names;
Vec lambda; /* used with TSAdjoint for sensitivities */
ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Chemistry solver options","");CHKERRQ(ierr);
ierr = PetscOptionsString("-chem","CHEMKIN input file","",chemfile,chemfile,sizeof(chemfile),NULL);CHKERRQ(ierr);
ierr = PetscOptionsString("-thermo","NASA thermo input file","",thermofile,thermofile,sizeof(thermofile),NULL);CHKERRQ(ierr);
user.pressure = 1.01325e5; /* Pascal */
ierr = PetscOptionsReal("-pressure","Pressure of reaction [Pa]","",user.pressure,&user.pressure,NULL);CHKERRQ(ierr);
user.Tini = 1550;
ierr = PetscOptionsReal("-Tini","Initial temperature [K]","",user.Tini,&user.Tini,NULL);CHKERRQ(ierr);
user.diffus = 100;
ierr = PetscOptionsReal("-diffus","Diffusion constant","",user.diffus,&user.diffus,NULL);CHKERRQ(ierr);
ierr = PetscOptionsBool("-draw_solution","Plot the solution for each cell","",showsolutions,&showsolutions,NULL);CHKERRQ(ierr);
user.diffusion = PETSC_TRUE;
ierr = PetscOptionsBool("-diffusion","Have diffusion","",user.diffusion,&user.diffusion,NULL);CHKERRQ(ierr);
user.reactions = PETSC_TRUE;
ierr = PetscOptionsBool("-reactions","Have reactions","",user.reactions,&user.reactions,NULL);CHKERRQ(ierr);
ierr = PetscOptionsEnd();CHKERRQ(ierr);
ierr = TC_initChem(chemfile, thermofile, 0, 1.0);TCCHKERRQ(ierr);
user.Nspec = TC_getNspec();
user.Nreac = TC_getNreac();
ierr = DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_PERIODIC,-1,user.Nspec+1,1,NULL,&user.dm);CHKERRQ(ierr);
ierr = DMDAGetInfo(user.dm,NULL,&ncells,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);CHKERRQ(ierr);
user.dx = 1.0/ncells; /* Set the coordinates of the cell centers; note final ghost cell is at x coordinate 1.0 */
ierr = DMDASetUniformCoordinates(user.dm,0.0,1.0,0.0,1.0,0.0,1.0);CHKERRQ(ierr);
/* set the names of each field in the DMDA based on the species name */
ierr = PetscMalloc1((user.Nspec+1)*LENGTHOFSPECNAME,&names);CHKERRQ(ierr);
ierr = PetscStrcpy(names,"Temp");CHKERRQ(ierr);
TC_getSnames(user.Nspec,names+LENGTHOFSPECNAME);CHKERRQ(ierr);
ierr = PetscMalloc1((user.Nspec+2),&snames);CHKERRQ(ierr);
for (i=0; i<user.Nspec+1; i++) snames[i] = names+i*LENGTHOFSPECNAME;
snames[user.Nspec+1] = NULL;
ierr = DMDASetFieldNames(user.dm,(const char * const *)snames);CHKERRQ(ierr);
ierr = PetscFree(snames);CHKERRQ(ierr);
ierr = PetscFree(names);CHKERRQ(ierr);
ierr = DMCreateMatrix(user.dm,&J);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(user.dm,&X);CHKERRQ(ierr);
ierr = PetscMalloc3(user.Nspec+1,&user.tchemwork,PetscSqr(user.Nspec+1),&user.Jdense,user.Nspec+1,&user.rows);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create timestepping solver context
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
ierr = TSSetDM(ts,user.dm);CHKERRQ(ierr);
ierr = TSSetType(ts,TSARKIMEX);CHKERRQ(ierr);
ierr = TSARKIMEXSetFullyImplicit(ts,PETSC_TRUE);CHKERRQ(ierr);
ierr = TSARKIMEXSetType(ts,TSARKIMEX4);CHKERRQ(ierr);
ierr = TSSetRHSFunction(ts,NULL,FormRHSFunction,&user);CHKERRQ(ierr);
ierr = TSSetRHSJacobian(ts,J,J,FormRHSJacobian,&user);CHKERRQ(ierr);
ftime = 1.0;
maxsteps = 10000;
ierr = TSSetDuration(ts,maxsteps,ftime);CHKERRQ(ierr);
ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set initial conditions
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = FormInitialSolution(ts,X,&user);CHKERRQ(ierr);
ierr = TSSetSolution(ts,X);CHKERRQ(ierr);
dt = 1e-10; /* Initial time step */
ierr = TSSetInitialTimeStep(ts,0.0,dt);CHKERRQ(ierr);
ierr = TSGetAdapt(ts,&adapt);CHKERRQ(ierr);
ierr = TSAdaptSetStepLimits(adapt,1e-12,1e-4);CHKERRQ(ierr); /* Also available with -ts_adapt_dt_min/-ts_adapt_dt_max */
ierr = TSSetMaxSNESFailures(ts,-1);CHKERRQ(ierr); /* Retry step an unlimited number of times */
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Pass information to graphical monitoring routine
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
if (showsolutions) {
ierr = DMDAGetCorners(user.dm,&xs,NULL,NULL,&xm,NULL,NULL);CHKERRQ(ierr);
for (i=xs;i<xs+xm;i++) {
ierr = MonitorCell(ts,&user,i);CHKERRQ(ierr);
}
}
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set runtime options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set final conditions for sensitivities
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = DMCreateGlobalVector(user.dm,&lambda);CHKERRQ(ierr);
ierr = TSSetCostGradients(ts,1,&lambda,NULL);CHKERRQ(ierr);
ierr = VecSetValue(lambda,0,1.0,INSERT_VALUES);CHKERRQ(ierr);
ierr = VecAssemblyBegin(lambda);CHKERRQ(ierr);
ierr = VecAssemblyEnd(lambda);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve ODE
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSolve(ts,X);CHKERRQ(ierr);
ierr = TSGetSolveTime(ts,&ftime);CHKERRQ(ierr);
ierr = TSGetTimeStepNumber(ts,&steps);CHKERRQ(ierr);
ierr = TSGetConvergedReason(ts,&reason);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"%s at time %g after %D steps\n",TSConvergedReasons[reason],(double)ftime,steps);CHKERRQ(ierr);
{
Vec max;
const char * const *names;
PetscInt i;
const PetscReal *bmax;
ierr = TSMonitorEnvelopeGetBounds(ts,&max,NULL);CHKERRQ(ierr);
if (max) {
ierr = TSMonitorLGGetVariableNames(ts,&names);CHKERRQ(ierr);
if (names) {
ierr = VecGetArrayRead(max,&bmax);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF,"Species - maximum mass fraction\n");CHKERRQ(ierr);
for (i=1; i<user.Nspec; i++) {
if (bmax[i] > .01) {ierr = PetscPrintf(PETSC_COMM_SELF,"%s %g\n",names[i],bmax[i]);CHKERRQ(ierr);}
}
ierr = VecRestoreArrayRead(max,&bmax);CHKERRQ(ierr);
}
}
}
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Free work space.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
TC_reset();
ierr = DMDestroy(&user.dm);CHKERRQ(ierr);
ierr = MatDestroy(&J);CHKERRQ(ierr);
ierr = VecDestroy(&X);CHKERRQ(ierr);
ierr = VecDestroy(&lambda);CHKERRQ(ierr);
ierr = TSDestroy(&ts);CHKERRQ(ierr);
ierr = PetscFree3(user.tchemwork,user.Jdense,user.rows);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
int main(int argc,char **argv)
{
AppCtx appctx; /* user-defined application context */
TS ts; /* timestepping context */
Vec U; /* approximate solution vector */
PetscErrorCode ierr;
PetscReal dt;
DM da;
PetscInt M;
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Initialize program and set problem parameters
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PetscInitialize(&argc,&argv,(char*)0,help);CHKERRQ(ierr);
appctx.a = 1.0;
appctx.d = 0.0;
ierr = PetscOptionsGetScalar(NULL,"-a",&appctx.a,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetScalar(NULL,"-d",&appctx.d,NULL);CHKERRQ(ierr);
appctx.upwind = PETSC_TRUE;
ierr = PetscOptionsGetBool(NULL,"-upwind",&appctx.upwind,NULL);CHKERRQ(ierr);
ierr = DMDACreate1d(PETSC_COMM_WORLD,DMDA_BOUNDARY_PERIODIC, -60, 1, 1,NULL,&da);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create vector data structures
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Create vector data structures for approximate and exact solutions
*/
ierr = DMCreateGlobalVector(da,&U);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create timestepping solver context
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
ierr = TSSetDM(ts,da);CHKERRQ(ierr);
/*
For linear problems with a time-dependent f(U,t) in the equation
u_t = f(u,t), the user provides the discretized right-hand-side
as a time-dependent matrix.
*/
ierr = TSSetRHSFunction(ts,NULL,TSComputeRHSFunctionLinear,&appctx);CHKERRQ(ierr);
ierr = TSSetRHSJacobian(ts,NULL,NULL,RHSMatrixHeat,&appctx);CHKERRQ(ierr);
ierr = TSSetSolutionFunction(ts,(PetscErrorCode (*)(TS,PetscReal,Vec,void*))Solution,&appctx);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Customize timestepping solver:
- Set timestepping duration info
Then set runtime options, which can override these defaults.
For example,
-ts_max_steps <maxsteps> -ts_final_time <maxtime>
to override the defaults set by TSSetDuration().
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = DMDAGetInfo(da,PETSC_IGNORE,&M,0,0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
dt = .48/(M*M);
ierr = TSSetInitialTimeStep(ts,0.0,dt);CHKERRQ(ierr);
ierr = TSSetDuration(ts,1000,100.0);CHKERRQ(ierr);
ierr = TSSetType(ts,TSARKIMEX);CHKERRQ(ierr);
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
/*
Evaluate initial conditions
*/
ierr = InitialConditions(ts,U,&appctx);CHKERRQ(ierr);
/*
Run the timestepping solver
*/
ierr = TSSolve(ts,U);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Free work space. All PETSc objects should be destroyed when they
are no longer needed.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSDestroy(&ts);CHKERRQ(ierr);
ierr = VecDestroy(&U);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
/*
Always call PetscFinalize() before exiting a program. This routine
- finalizes the PETSc libraries as well as MPI
- provides summary and diagnostic information if certain runtime
options are chosen (e.g., -log_summary).
*/
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **argv)
{
PetscErrorCode ierr;
DM da; /* structured grid topology object */
TS ts; /* time-stepping object (contains snes) */
SNES snes; /* Newton solver object */
Vec X,residual; /* solution, residual */
Mat J; /* Jacobian matrix */
PetscInt Mx,My,fsteps,steps;
ISColoring iscoloring;
PetscReal tstart,tend,ftime,secperday=3600.0*24.0,Y0;
PetscBool fdflg = PETSC_FALSE, mfileflg = PETSC_FALSE, optflg = PETSC_FALSE;
char mfile[PETSC_MAX_PATH_LEN] = "out.m";
MatFDColoring matfdcoloring;
PorousCtx user; /* user-defined work context */
PetscInitialize(&argc,&argv,(char *)0,help);
ierr = DMDACreate2d(PETSC_COMM_WORLD,
DMDA_BOUNDARY_NONE, DMDA_BOUNDARY_NONE, // correct for zero Dirichlet
DMDA_STENCIL_STAR, // nonlinear diffusion but diffusivity
// depends on soln W not grad W
-21,-21, // default to 20x20 grid but override with
// -da_grid_x, -da_grid_y (or -da_refine)
PETSC_DECIDE,PETSC_DECIDE, // num of procs in each dim
2, // dof = 2: node = (W,Y)
// or node = (P,dPsqr)
// or node = (ddxE,ddyN)
1, // s = 1 (stencil extends out one cell)
PETSC_NULL,PETSC_NULL, // no specify proc decomposition
&da);CHKERRQ(ierr);
ierr = DMSetApplicationContext(da,&user);CHKERRQ(ierr);
/* get Vecs and Mats for this grid */
ierr = DMCreateGlobalVector(da,&X);CHKERRQ(ierr);
ierr = VecDuplicate(X,&residual);CHKERRQ(ierr);
ierr = VecDuplicate(X,&user.geom);CHKERRQ(ierr);
ierr = DMGetMatrix(da,MATAIJ,&J);CHKERRQ(ierr);
/* set up contexts */
tstart = 10.0 * secperday; /* 10 days in seconds */
tend = 30.0 * secperday;
steps = 20;
Y0 = 1.0; /* initial value of Y, for computing initial
value of P; note Ymin = 0.1 is different */
user.da = da;
ierr = DefaultContext(&user);CHKERRQ(ierr);
ierr = PetscOptionsBegin(PETSC_COMM_WORLD,
"","options to (W,P)-space better hydrology model alt","");CHKERRQ(ierr);
{
ierr = PetscOptionsReal("-alt_sigma","nonlinear power","",
user.sigma,&user.sigma,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-alt_Ymin",
"min capacity thickness (esp. in pressure computation)","",
user.Ymin,&user.Ymin,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-alt_Wmin",
"min water amount (esp. in pressure computation)","",
user.Wmin,&user.Wmin,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-alt_Y0",
"constant initial capacity thickness","",
Y0,&Y0,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-alt_Cmelt",
"additional coefficient for amount of melt","",
user.Cmelt,&user.Cmelt,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-alt_Creep",
"creep closure coefficient","",
user.Creep,&user.Creep,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-alt_L","half-width of square region in meters","",
user.L,&user.L,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-alt_tstart_days","start time in days","",
tstart/secperday,&tstart,&optflg);CHKERRQ(ierr);
if (optflg) { tstart *= secperday; }
ierr = PetscOptionsReal("-alt_tend_days","end time in days","",
tend/secperday,&tend,&optflg);CHKERRQ(ierr);
if (optflg) { tend *= secperday; }
ierr = PetscOptionsInt("-alt_steps","number of timesteps to take","",
steps,&steps,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsBool("-alt_converge_check",
"run silent and check for convergence",
"",user.run_silent,&user.run_silent,PETSC_NULL);
CHKERRQ(ierr);
ierr = PetscOptionsString("-mfile",
"name of Matlab file to write results","",
mfile,mfile,PETSC_MAX_PATH_LEN,&mfileflg);
CHKERRQ(ierr);
}
ierr = PetscOptionsEnd();CHKERRQ(ierr);
/* fix remaining parameters */
ierr = DerivedConstants(&user);CHKERRQ(ierr);
ierr = VecStrideSet(user.geom,0,user.H0);CHKERRQ(ierr); /* H(x,y) = H0 */
ierr = VecStrideSet(user.geom,1,0.0);CHKERRQ(ierr); /* b(x,y) = 0 */
ierr = DMDASetUniformCoordinates(da, // square domain
-user.L, user.L, -user.L, user.L, 0.0, 1.0);CHKERRQ(ierr);
ierr = DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,
PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);CHKERRQ(ierr);
user.dx = 2.0 * user.L / (Mx-1);
user.dy = 2.0 * user.L / (My-1);
/* setup TS = timestepping object */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
ierr = TSSetType(ts,TSCN);CHKERRQ(ierr);
ierr = TSSetRHSFunction(ts,residual,RHSFunction,&user);CHKERRQ(ierr);
/* use coloring to compute rhs Jacobian efficiently */
ierr = PetscOptionsGetBool(PETSC_NULL,"-fd",&fdflg,PETSC_NULL);CHKERRQ(ierr);
if (fdflg){
ierr = DMGetColoring(da,IS_COLORING_GLOBAL,MATAIJ,&iscoloring);CHKERRQ(ierr);
ierr = MatFDColoringCreate(J,iscoloring,&matfdcoloring);CHKERRQ(ierr);
ierr = MatFDColoringSetFromOptions(matfdcoloring);CHKERRQ(ierr);
ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
ierr = MatFDColoringSetFunction(matfdcoloring,
(PetscErrorCode (*)(void))RHSFunction,&user);CHKERRQ(ierr);
ierr = TSSetRHSJacobian(ts,J,J,TSDefaultComputeJacobianColor,
matfdcoloring);CHKERRQ(ierr);
} else { /* default case */
ierr = TSSetRHSJacobian(ts,J,J,RHSJacobian,&user);CHKERRQ(ierr);
}
/* set initial state: W = barenblatt, P = pi (W/Y0)^sigma */
ierr = InitialState(da,&user,tstart,Y0,X);CHKERRQ(ierr);
/* set up times for time-stepping */
ierr = TSSetInitialTimeStep(ts,tstart,
(tend - tstart) / (PetscReal)steps);CHKERRQ(ierr);
ierr = TSSetDuration(ts,steps,tend);CHKERRQ(ierr);
ierr = TSSetExactFinalTime(ts,PETSC_TRUE);CHKERRQ(ierr);
ierr = TSMonitorSet(ts,MyTSMonitor,&user,PETSC_NULL);CHKERRQ(ierr);
/* Set SNESVI type and supply upper and lower bounds. */
ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
ierr = SNESVISetComputeVariableBounds(snes,FormPositivityBounds);
CHKERRQ(ierr);
/* ask user to finalize settings */
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
/* report on setup */
if (!user.run_silent) {
ierr = PetscPrintf(PETSC_COMM_WORLD,
"setup done: square side length = %.3f km\n"
" grid Mx,My = %d,%d\n"
" spacing dx,dy = %.3f,%.3f m\n"
" times tstart:dt:tend = %.3f:%.3f:%.3f days\n",
2.0 * user.L / 1000.0, Mx, My, user.dx, user.dy,
tstart / secperday, (tend-tstart)/(steps*secperday), tend / secperday);
CHKERRQ(ierr);
}
if (mfileflg) {
if (!user.run_silent) {
ierr = PetscPrintf(PETSC_COMM_WORLD,
"writing initial W,P and geometry H,b to Matlab file %s ...\n",
mfile);CHKERRQ(ierr);
}
ierr = print2vecmatlab(da,X,"W_init","P_init",mfile,PETSC_FALSE);CHKERRQ(ierr);
ierr = print2vecmatlab(da,user.geom,"H","b",mfile,PETSC_TRUE);CHKERRQ(ierr);
}
/* run time-stepping with implicit steps */
ierr = TSSolve(ts,X,&ftime);CHKERRQ(ierr);
/* make a report on run and final state */
ierr = TSGetTimeStepNumber(ts,&fsteps);CHKERRQ(ierr);
if ((!user.run_silent) && (ftime != tend)) {
ierr = PetscPrintf(PETSC_COMM_WORLD,
"***WARNING3***: reported final time wrong: ftime(=%.12e) != tend(=%.12e) (days)\n",
ftime / secperday, tend / secperday);CHKERRQ(ierr); }
if ((!user.run_silent) && (fsteps != steps)) {
ierr = PetscPrintf(PETSC_COMM_WORLD,
"***WARNING4***: reported number of steps wrong: fsteps(=%D) != steps(=%D)\n",
fsteps, steps);CHKERRQ(ierr); }
if (mfileflg) {
if (!user.run_silent) {
ierr = PetscPrintf(PETSC_COMM_WORLD,
"writing final fields to %s ...\n",mfile);CHKERRQ(ierr);
}
ierr = print2vecmatlab(da,X,"W_final","P_final",mfile,PETSC_TRUE);CHKERRQ(ierr);
ierr = printfigurematlab(da,2,"W_init","W_final",mfile,PETSC_TRUE);CHKERRQ(ierr);
ierr = printfigurematlab(da,3,"P_init","P_final",mfile,PETSC_TRUE);CHKERRQ(ierr);
}
if (user.run_silent) {
ierr = PetscPrintf(PETSC_COMM_WORLD, "%6d %6d %9.3f %.12e\n",
Mx, My, (tend-tstart)/secperday, user.maxrnorm);CHKERRQ(ierr);
}
/* Free work space. */
ierr = MatDestroy(&J);CHKERRQ(ierr);
if (fdflg) { ierr = MatFDColoringDestroy(&matfdcoloring);CHKERRQ(ierr); }
ierr = VecDestroy(&X);CHKERRQ(ierr);
ierr = VecDestroy(&user.geom);CHKERRQ(ierr);
ierr = VecDestroy(&residual);CHKERRQ(ierr);
ierr = TSDestroy(&ts);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
ierr = PetscFinalize();CHKERRQ(ierr);
PetscFunctionReturn((PetscInt)(user.not_converged_warning));
}
int main(int argc,char **argv)
{
PetscErrorCode ierr;
PetscInt time_steps=100,iout,NOUT=1;
PetscMPIInt size;
Vec global;
PetscReal dt,ftime,ftime_original;
TS ts;
PetscViewer viewfile;
Mat J = 0;
Vec x;
Data data;
PetscInt mn;
PetscBool flg;
MatColoring mc;
ISColoring iscoloring;
MatFDColoring matfdcoloring = 0;
PetscBool fd_jacobian_coloring = PETSC_FALSE;
SNES snes;
KSP ksp;
PC pc;
PetscViewer viewer;
char pcinfo[120],tsinfo[120];
TSType tstype;
PetscBool sundials;
ierr = PetscInitialize(&argc,&argv,(char*)0,help);CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
/* set data */
data.m = 9;
data.n = 9;
data.a = 1.0;
data.epsilon = 0.1;
data.dx = 1.0/(data.m+1.0);
data.dy = 1.0/(data.n+1.0);
mn = (data.m)*(data.n);
ierr = PetscOptionsGetInt(NULL,"-time",&time_steps,NULL);CHKERRQ(ierr);
/* set initial conditions */
ierr = VecCreate(PETSC_COMM_WORLD,&global);CHKERRQ(ierr);
ierr = VecSetSizes(global,PETSC_DECIDE,mn);CHKERRQ(ierr);
ierr = VecSetFromOptions(global);CHKERRQ(ierr);
ierr = Initial(global,&data);CHKERRQ(ierr);
ierr = VecDuplicate(global,&x);CHKERRQ(ierr);
/* create timestep context */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
ierr = TSMonitorSet(ts,Monitor,&data,NULL);CHKERRQ(ierr);
#if defined(PETSC_HAVE_SUNDIALS)
ierr = TSSetType(ts,TSSUNDIALS);CHKERRQ(ierr);
#else
ierr = TSSetType(ts,TSEULER);CHKERRQ(ierr);
#endif
dt = 0.1;
ftime_original = data.tfinal = 1.0;
ierr = TSSetInitialTimeStep(ts,0.0,dt);CHKERRQ(ierr);
ierr = TSSetDuration(ts,time_steps,ftime_original);CHKERRQ(ierr);
ierr = TSSetSolution(ts,global);CHKERRQ(ierr);
/* set user provided RHSFunction and RHSJacobian */
ierr = TSSetRHSFunction(ts,NULL,RHSFunction,&data);CHKERRQ(ierr);
ierr = MatCreate(PETSC_COMM_WORLD,&J);CHKERRQ(ierr);
ierr = MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,mn,mn);CHKERRQ(ierr);
ierr = MatSetFromOptions(J);CHKERRQ(ierr);
ierr = MatSeqAIJSetPreallocation(J,5,NULL);CHKERRQ(ierr);
ierr = MatMPIAIJSetPreallocation(J,5,NULL,5,NULL);CHKERRQ(ierr);
ierr = PetscOptionsHasName(NULL,"-ts_fd",&flg);CHKERRQ(ierr);
if (!flg) {
ierr = TSSetRHSJacobian(ts,J,J,RHSJacobian,&data);CHKERRQ(ierr);
} else {
ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
ierr = PetscOptionsHasName(NULL,"-fd_color",&fd_jacobian_coloring);CHKERRQ(ierr);
if (fd_jacobian_coloring) { /* Use finite differences with coloring */
/* Get data structure of J */
PetscBool pc_diagonal;
ierr = PetscOptionsHasName(NULL,"-pc_diagonal",&pc_diagonal);CHKERRQ(ierr);
if (pc_diagonal) { /* the preconditioner of J is a diagonal matrix */
PetscInt rstart,rend,i;
PetscScalar zero=0.0;
ierr = MatGetOwnershipRange(J,&rstart,&rend);CHKERRQ(ierr);
for (i=rstart; i<rend; i++) {
ierr = MatSetValues(J,1,&i,1,&i,&zero,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
} else {
/* Fill the structure using the expensive SNESComputeJacobianDefault. Temporarily set up the TS so we can call this function */
ierr = TSSetType(ts,TSBEULER);CHKERRQ(ierr);
ierr = TSSetUp(ts);CHKERRQ(ierr);
ierr = SNESComputeJacobianDefault(snes,x,J,J,ts);CHKERRQ(ierr);
}
/* create coloring context */
ierr = MatColoringCreate(J,&mc);CHKERRQ(ierr);
ierr = MatColoringSetType(mc,MATCOLORINGSL);CHKERRQ(ierr);
ierr = MatColoringSetFromOptions(mc);CHKERRQ(ierr);
ierr = MatColoringApply(mc,&iscoloring);CHKERRQ(ierr);
ierr = MatColoringDestroy(&mc);CHKERRQ(ierr);
ierr = MatFDColoringCreate(J,iscoloring,&matfdcoloring);CHKERRQ(ierr);
ierr = MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode (*)(void))SNESTSFormFunction,ts);CHKERRQ(ierr);
ierr = MatFDColoringSetFromOptions(matfdcoloring);CHKERRQ(ierr);
ierr = MatFDColoringSetUp(J,iscoloring,matfdcoloring);CHKERRQ(ierr);
ierr = SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor,matfdcoloring);CHKERRQ(ierr);
ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
} else { /* Use finite differences (slow) */
ierr = SNESSetJacobian(snes,J,J,SNESComputeJacobianDefault,NULL);CHKERRQ(ierr);
}
}
/* Pick up a Petsc preconditioner */
/* one can always set method or preconditioner during the run time */
ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
ierr = SNESGetKSP(snes,&ksp);CHKERRQ(ierr);
ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
ierr = PCSetType(pc,PCJACOBI);CHKERRQ(ierr);
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
ierr = TSSetUp(ts);CHKERRQ(ierr);
/* Test TSSetPostStep() */
ierr = PetscOptionsHasName(NULL,"-test_PostStep",&flg);CHKERRQ(ierr);
if (flg) {
ierr = TSSetPostStep(ts,PostStep);CHKERRQ(ierr);
}
ierr = PetscOptionsGetInt(NULL,"-NOUT",&NOUT,NULL);CHKERRQ(ierr);
for (iout=1; iout<=NOUT; iout++) {
ierr = TSSetDuration(ts,time_steps,iout*ftime_original/NOUT);CHKERRQ(ierr);
ierr = TSSolve(ts,global);CHKERRQ(ierr);
ierr = TSGetSolveTime(ts,&ftime);CHKERRQ(ierr);
ierr = TSSetInitialTimeStep(ts,ftime,dt);CHKERRQ(ierr);
}
/* Interpolate solution at tfinal */
ierr = TSGetSolution(ts,&global);CHKERRQ(ierr);
ierr = TSInterpolate(ts,ftime_original,global);CHKERRQ(ierr);
ierr = PetscOptionsHasName(NULL,"-matlab_view",&flg);CHKERRQ(ierr);
if (flg) { /* print solution into a MATLAB file */
ierr = PetscViewerASCIIOpen(PETSC_COMM_WORLD,"out.m",&viewfile);CHKERRQ(ierr);
ierr = PetscViewerSetFormat(viewfile,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
ierr = VecView(global,viewfile);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewfile);CHKERRQ(ierr);
}
/* display solver info for Sundials */
ierr = TSGetType(ts,&tstype);CHKERRQ(ierr);
ierr = PetscObjectTypeCompare((PetscObject)ts,TSSUNDIALS,&sundials);CHKERRQ(ierr);
if (sundials) {
ierr = PetscViewerStringOpen(PETSC_COMM_WORLD,tsinfo,120,&viewer);CHKERRQ(ierr);
ierr = TSView(ts,viewer);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
ierr = PetscViewerStringOpen(PETSC_COMM_WORLD,pcinfo,120,&viewer);CHKERRQ(ierr);
ierr = PCView(pc,viewer);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"%d Procs,%s TSType, %s Preconditioner\n",size,tsinfo,pcinfo);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
}
/* free the memories */
ierr = TSDestroy(&ts);CHKERRQ(ierr);
ierr = VecDestroy(&global);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = MatDestroy(&J);CHKERRQ(ierr);
if (fd_jacobian_coloring) {ierr = MatFDColoringDestroy(&matfdcoloring);CHKERRQ(ierr);}
ierr = PetscFinalize();
return 0;
}
