int main(int argc,char **argv)
{
TS ts; /* time integration context */
Vec X; /* solution, residual vectors */
Mat J; /* Jacobian matrix */
PetscErrorCode ierr;
PetscScalar *x;
PetscReal ftime;
PetscInt i,steps,nits,lits;
PetscBool view_final;
Ctx ctx;
PetscInitialize(&argc,&argv,(char *)0,help);
ctx.n = 3;
ierr = PetscOptionsGetInt(PETSC_NULL,"-n",&ctx.n,PETSC_NULL);CHKERRQ(ierr);
if (ctx.n < 2) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_ARG_OUTOFRANGE,"The dimension specified with -n must be at least 2");
view_final = PETSC_FALSE;
ierr = PetscOptionsGetBool(PETSC_NULL,"-view_final",&view_final,PETSC_NULL);CHKERRQ(ierr);
ctx.monitor_short = PETSC_FALSE;
ierr = PetscOptionsGetBool(PETSC_NULL,"-monitor_short",&ctx.monitor_short,PETSC_NULL);CHKERRQ(ierr);
/*
Create Jacobian matrix data structure and state vector
*/
ierr = MatCreate(PETSC_COMM_WORLD,&J);CHKERRQ(ierr);
ierr = MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,ctx.n,ctx.n);CHKERRQ(ierr);
ierr = MatSetFromOptions(J);CHKERRQ(ierr);
ierr = MatSetUp(J);CHKERRQ(ierr);
ierr = MatGetVecs(J,&X,PETSC_NULL);CHKERRQ(ierr);
/* Create time integration context */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
ierr = TSSetType(ts,TSPSEUDO);CHKERRQ(ierr);
ierr = TSSetIFunction(ts,PETSC_NULL,FormIFunction,&ctx);CHKERRQ(ierr);
ierr = TSSetIJacobian(ts,J,J,FormIJacobian,&ctx);CHKERRQ(ierr);
ierr = TSSetDuration(ts,1000,1e14);CHKERRQ(ierr);
ierr = TSSetInitialTimeStep(ts,0.0,1e-3);CHKERRQ(ierr);
ierr = TSMonitorSet(ts,MonitorObjective,&ctx,PETSC_NULL);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Customize time integrator; set runtime options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Evaluate initial guess; then solve nonlinear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = VecSet(X,0.0);CHKERRQ(ierr);
ierr = VecGetArray(X,&x);CHKERRQ(ierr);
#if 1
x[0] = 5.;
x[1] = -5.;
for (i=2; i<ctx.n; i++) x[i] = 5.;
#else
x[0] = 1.0;
x[1] = 15.0;
for (i=2; i<ctx.n; i++) x[i] = 10.0;
#endif
ierr = VecRestoreArray(X,&x);CHKERRQ(ierr);
ierr = TSSolve(ts,X);CHKERRQ(ierr);
ierr = TSGetSolveTime(ts,&ftime);CHKERRQ(ierr);
ierr = TSGetTimeStepNumber(ts,&steps);CHKERRQ(ierr);
ierr = TSGetSNESIterations(ts,&nits);CHKERRQ(ierr);
ierr = TSGetKSPIterations(ts,&lits);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Time integrator took (%D,%D,%D) iterations to reach final time %G\n",steps,nits,lits,ftime);CHKERRQ(ierr);
if (view_final) {
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 = VecDestroy(&X);CHKERRQ(ierr);
ierr = MatDestroy(&J);CHKERRQ(ierr);
ierr = TSDestroy(&ts);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 */
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!");
/* 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,"-imex",&user.imex,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,"-monitor",&monitor,NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-mu","Stiffness parameter","<1.0e6>",user.mu,&user.mu,NULL);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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 = MatGetVecs(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);
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);
}
PetscErrorCode Brusselator(int argc,char **argv,PetscInt cycle)
{
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,xmax,xmin;
struct _User user; /* user-defined work context */
TSConvergedReason reason;
ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create distributed array (DMDA) to manage parallel grid and vectors
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = DMDACreate1d(PETSC_COMM_WORLD,DM_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 = 0.1;
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 = DMSetMatType(da,MATAIJ);CHKERRQ(ierr);
ierr = DMCreateMatrix(da,&J);CHKERRQ(ierr);
ierr = TSSetIJacobian(ts,J,J,FormIJacobian,&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);
ierr = VecGetSize(X,&mx);CHKERRQ(ierr);
hx = 1.0/(PetscReal)(mx/2-1);
dt = 0.4 * PetscSqr(hx) / user.alpha; /* Diffusive stability limit */
dt *= PetscPowRealInt(0.2,cycle); /* Shrink the time step in convergence study. */
ierr = TSSetInitialTimeStep(ts,0.0,dt);CHKERRQ(ierr);
ierr = TSSetTolerances(ts,1e-3*PetscPowRealInt(0.5,cycle),NULL,1e-3*PetscPowRealInt(0.5,cycle),NULL);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 = VecMin(X,NULL,&xmin);CHKERRQ(ierr);
ierr = VecMax(X,NULL,&xmax);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"%s at time %g after % 3D steps. Range [%6.4f,%6.4f]\n",TSConvergedReasons[reason],(double)ftime,steps,(double)xmin,(double)xmax);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 ierr;
}
int main(int argc, char *argv[])
{
PetscMPIInt size;
TS ts;
Vec R;
Mat J;
Vec U,V;
PetscScalar *u,*v;
UserParams user = {/*Omega=*/ 1, /*Xi=*/ 0, /*u0=*/ 1, /*,v0=*/ 0};
PetscErrorCode ierr;
ierr = PetscInitialize(&argc,&argv,NULL,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");
ierr = PetscOptionsBegin(PETSC_COMM_SELF,"","ex43 options","");CHKERRQ(ierr);
ierr = PetscOptionsReal("-frequency","Natual frequency",__FILE__,user.Omega,&user.Omega,NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-damping","Damping coefficient",__FILE__,user.Xi,&user.Xi,NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-initial_u","Initial displacement",__FILE__,user.u0,&user.u0,NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-initial_v","Initial velocity",__FILE__,user.v0,&user.v0,NULL);CHKERRQ(ierr);
ierr = PetscOptionsEnd();CHKERRQ(ierr);
ierr = TSCreate(PETSC_COMM_SELF,&ts);CHKERRQ(ierr);
ierr = TSSetType(ts,TSALPHA2);CHKERRQ(ierr);
ierr = TSSetMaxTime(ts,5*(2*PETSC_PI));CHKERRQ(ierr);
ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);CHKERRQ(ierr);
ierr = TSSetTimeStep(ts,0.01);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF,1,&R);CHKERRQ(ierr);
ierr = VecSetUp(R);CHKERRQ(ierr);
ierr = MatCreateSeqDense(PETSC_COMM_SELF,1,1,NULL,&J);CHKERRQ(ierr);
ierr = MatSetUp(J);CHKERRQ(ierr);
if (user.Xi) {
ierr = TSSetI2Function(ts,R,Residual2,&user);CHKERRQ(ierr);
ierr = TSSetI2Jacobian(ts,J,J,Tangent2,&user);CHKERRQ(ierr);
} else {
ierr = TSSetIFunction(ts,R,Residual1,&user);CHKERRQ(ierr);
ierr = TSSetIJacobian(ts,J,J,Tangent1,&user);CHKERRQ(ierr);
}
ierr = VecDestroy(&R);CHKERRQ(ierr);
ierr = MatDestroy(&J);CHKERRQ(ierr);
ierr = TSSetSolutionFunction(ts,Solution,&user);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF,1,&U);CHKERRQ(ierr);
ierr = VecCreateSeq(PETSC_COMM_SELF,1,&V);CHKERRQ(ierr);
ierr = VecGetArray(U,&u);CHKERRQ(ierr);
ierr = VecGetArray(V,&v);CHKERRQ(ierr);
u[0] = user.u0;
v[0] = user.v0;
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; /* nonlinear solver */
Vec u; /* solution, residual vectors */
Mat J; /* Jacobian matrix */
PetscInt maxsteps = 1000; /* iterations for convergence */
PetscInt nsteps;
PetscReal vmin,vmax,norm;
PetscErrorCode ierr;
DM da;
PetscReal ftime,dt;
AppCtx user; /* user-defined work context */
JacobianType jacType;
PetscInitialize(&argc,&argv,(char*)0,help);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create distributed array (DMDA) to manage parallel grid and vectors
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = DMDACreate1d(PETSC_COMM_WORLD,DMDA_BOUNDARY_NONE,-11,1,1,NULL,&da);
CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Extract global vectors from DMDA;
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = DMCreateGlobalVector(da,&u);
CHKERRQ(ierr);
/* Initialize user application context */
user.c = -30.0;
user.boundary = 0; /* 0: Dirichlet BC; 1: Neumann BC */
user.viewJacobian = PETSC_FALSE;
ierr = PetscOptionsGetInt(NULL,"-boundary",&user.boundary,NULL);
CHKERRQ(ierr);
ierr = PetscOptionsHasName(NULL,"-viewJacobian",&user.viewJacobian);
CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create timestepping solver context
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);
CHKERRQ(ierr);
ierr = TSSetProblemType(ts,TS_NONLINEAR);
CHKERRQ(ierr);
ierr = TSSetType(ts,TSTHETA);
CHKERRQ(ierr);
ierr = TSThetaSetTheta(ts,1.0);
CHKERRQ(ierr); /* Make the Theta method behave like backward Euler */
ierr = TSSetIFunction(ts,NULL,FormIFunction,&user);
CHKERRQ(ierr);
ierr = DMSetMatType(da,MATAIJ);
CHKERRQ(ierr);
ierr = DMCreateMatrix(da,&J);
CHKERRQ(ierr);
jacType = JACOBIAN_ANALYTIC; /* use user-provide Jacobian */
ierr = TSSetDM(ts,da);
CHKERRQ(ierr); /* Use TSGetDM() to access. Setting here allows easy use of geometric multigrid. */
ftime = 1.0;
ierr = TSSetDuration(ts,maxsteps,ftime);
CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set initial conditions
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = FormInitialSolution(ts,u,&user);
CHKERRQ(ierr);
ierr = TSSetSolution(ts,u);
CHKERRQ(ierr);
dt = .01;
ierr = TSSetInitialTimeStep(ts,0.0,dt);
CHKERRQ(ierr);
/* Use slow fd Jacobian or fast fd Jacobian with colorings.
Note: this requirs snes which is not created until TSSetUp()/TSSetFromOptions() is called */
ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Options for Jacobian evaluation",NULL);
CHKERRQ(ierr);
ierr = PetscOptionsEnum("-jac_type","Type of Jacobian","",JacobianTypes,(PetscEnum)jacType,(PetscEnum*)&jacType,0);
CHKERRQ(ierr);
ierr = PetscOptionsEnd();
CHKERRQ(ierr);
if (jacType == JACOBIAN_ANALYTIC) {
ierr = TSSetIJacobian(ts,J,J,FormIJacobian,&user);
CHKERRQ(ierr);
} else if (jacType == JACOBIAN_FD_COLORING) {
SNES snes;
ierr = TSGetSNES(ts,&snes);
CHKERRQ(ierr);
ierr = SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor,0);
CHKERRQ(ierr);
} else if (jacType == JACOBIAN_FD_FULL) {
SNES snes;
ierr = TSGetSNES(ts,&snes);
CHKERRQ(ierr);
ierr = SNESSetJacobian(snes,J,J,SNESComputeJacobianDefault,&user);
CHKERRQ(ierr);
}
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set runtime options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetFromOptions(ts);
CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Integrate ODE system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSolve(ts,u);
CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Compute diagnostics of the solution
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = VecNorm(u,NORM_1,&norm);
CHKERRQ(ierr);
ierr = VecMax(u,NULL,&vmax);
CHKERRQ(ierr);
ierr = VecMin(u,NULL,&vmin);
CHKERRQ(ierr);
ierr = TSGetTimeStepNumber(ts,&nsteps);
CHKERRQ(ierr);
ierr = TSGetTime(ts,&ftime);
CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"timestep %D: time %G, solution norm %G, max %G, min %G\n",nsteps,ftime,norm,vmax,vmin);
CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Free work space.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = MatDestroy(&J);
CHKERRQ(ierr);
ierr = VecDestroy(&u);
CHKERRQ(ierr);
ierr = TSDestroy(&ts);
CHKERRQ(ierr);
ierr = DMDestroy(&da);
CHKERRQ(ierr);
ierr = PetscFinalize();
PetscFunctionReturn(0);
}
int main(int argc, char **argv)
{
TS ts;
Vec x; /*solution vector*/
Mat A; /*Jacobian*/
PetscInt steps,maxsteps,mx;
PetscErrorCode ierr;
PetscReal ftime;
AppCtx user; /* user-defined work context */
PetscInitialize(&argc,&argv,NULL,help);
/* Initialize user application context */
ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Allen-Cahn equation","");
user.param = 9e-4;
user.xleft = -1.;
user.xright = 2.;
user.mx = 400;
ierr = PetscOptionsReal("-eps","parameter","",user.param,&user.param,NULL);CHKERRQ(ierr);
ierr = PetscOptionsEnd();CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set runtime options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
* 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,user.mx,user.mx);CHKERRQ(ierr);
ierr = MatSetFromOptions(A);CHKERRQ(ierr);
ierr = MatSetUp(A);CHKERRQ(ierr);
ierr = MatGetVecs(A,&x,NULL);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create time stepping solver context
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
ierr = TSSetType(ts,TSEIMEX);CHKERRQ(ierr);
ierr = TSSetRHSFunction(ts,NULL,RHSFunction,&user);CHKERRQ(ierr);
ierr = TSSetIFunction(ts,NULL,FormIFunction,&user);CHKERRQ(ierr);
ierr = TSSetIJacobian(ts,A,A,FormIJacobian,&user);CHKERRQ(ierr);
ftime = 142;
maxsteps = 100000;
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);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set runtime options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve nonlinear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSolve(ts,x);CHKERRQ(ierr);
ierr = TSGetTime(ts,&ftime);CHKERRQ(ierr);
ierr = TSGetTimeStepNumber(ts,&steps);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"eps %G, steps %D, ftime %G\n",user.param,steps,ftime);CHKERRQ(ierr);
/* ierr = VecView(x,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);*/
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Free work space.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
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 u,r; /* solution, residual vectors */
Mat J,Jmf = 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 = NULL;
user.nstencilpts = 5;
user.c = -30.0;
user.boundary = 0; /* 0: Drichlet BC; 1: Neumann BC */
user.viewJacobian = PETSC_FALSE;
ierr = PetscOptionsGetInt(NULL,"-nstencilpts",&user.nstencilpts,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-boundary",&user.boundary,NULL);CHKERRQ(ierr);
ierr = PetscOptionsHasName(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, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,-11,-11,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);CHKERRQ(ierr);
} else if (user.nstencilpts == 9) {
ierr = DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_BOX,-11,-11,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,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 = DMSetMatType(da,MATAIJ);CHKERRQ(ierr);
ierr = DMCreateMatrix(da,&J);CHKERRQ(ierr);
Jtype = 0;
ierr = PetscOptionsGetInt(NULL, "-Jtype",&Jtype,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,SNESComputeJacobianDefault,NULL);CHKERRQ(ierr);
} else if (Jtype == 2) { /* Use coloring to compute finite difference J efficiently */
ierr = SNESSetJacobian(snes,Jmf,J,SNESComputeJacobianDefaultColor,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);
}
