/*
Monitor - User-provided routine to monitor the solution computed at
each timestep. This example plots the solution and computes the
error in two different norms.
Input Parameters:
ts - the timestep context
step - the count of the current step (with 0 meaning the
initial condition)
time - the current time
u - the solution at this timestep
ctx - the user-provided context for this monitoring routine.
In this case we use the application context which contains
information about the problem size, workspace and the exact
solution.
*/
PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal time,Vec u,void *ctx)
{
AppCtx *appctx = (AppCtx*) ctx; /* user-defined application context */
PetscErrorCode ierr;
PetscReal en2,en2s,enmax;
PetscDraw draw;
/*
We use the default X windows viewer
PETSC_VIEWER_DRAW_(appctx->comm)
that is associated with the current communicator. This saves
the effort of calling PetscViewerDrawOpen() to create the window.
Note that if we wished to plot several items in separate windows we
would create each viewer with PetscViewerDrawOpen() and store them in
the application context, appctx.
PetscReal buffering makes graphics look better.
*/
ierr = PetscViewerDrawGetDraw(PETSC_VIEWER_DRAW_(appctx->comm),0,&draw);CHKERRQ(ierr);
ierr = PetscDrawSetDoubleBuffer(draw);CHKERRQ(ierr);
ierr = VecView(u,PETSC_VIEWER_DRAW_(appctx->comm));CHKERRQ(ierr);
/*
Compute the exact solution at this timestep
*/
ierr = ExactSolution(time,appctx->solution,appctx);CHKERRQ(ierr);
/*
Print debugging information if desired
*/
if (appctx->debug) {
ierr = PetscPrintf(appctx->comm,"Computed solution vector\n");CHKERRQ(ierr);
ierr = VecView(u,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscPrintf(appctx->comm,"Exact solution vector\n");CHKERRQ(ierr);
ierr = VecView(appctx->solution,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
/*
Compute the 2-norm and max-norm of the error
*/
ierr = VecAXPY(appctx->solution,-1.0,u);CHKERRQ(ierr);
ierr = VecNorm(appctx->solution,NORM_2,&en2);CHKERRQ(ierr);
en2s = PetscSqrtReal(appctx->h)*en2; /* scale the 2-norm by the grid spacing */
ierr = VecNorm(appctx->solution,NORM_MAX,&enmax);CHKERRQ(ierr);
/*
PetscPrintf() causes only the first processor in this
communicator to print the timestep information.
*/
ierr = PetscPrintf(appctx->comm,"Timestep %D: time = %g,2-norm error = %g, max norm error = %g\n",step,(double)time,(double)en2s,(double)enmax);CHKERRQ(ierr);
/*
Print debugging information if desired
*/
/* if (appctx->debug) {
ierr = PetscPrintf(appctx->comm,"Error vector\n");CHKERRQ(ierr);
ierr = VecView(appctx->solution,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
} */
return 0;
}
PetscErrorCode ComputeExactSolution(DM dm, PetscReal time, Vec X, User user)
{
DM dmCell;
const PetscScalar *cellgeom;
PetscScalar *x;
PetscInt cStart, cEnd, cEndInterior = user->cEndInterior, c;
PetscErrorCode ierr;
PetscFunctionBeginUser;
ierr = VecGetDM(user->cellgeom, &dmCell);CHKERRQ(ierr);
ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd);CHKERRQ(ierr);
ierr = VecGetArrayRead(user->cellgeom, &cellgeom);CHKERRQ(ierr);
ierr = VecGetArray(X, &x);CHKERRQ(ierr);
for (c = cStart; c < cEndInterior; ++c) {
const CellGeom *cg;
PetscScalar *xc;
ierr = DMPlexPointLocalRead(dmCell,c,cellgeom,&cg);CHKERRQ(ierr);
ierr = DMPlexPointGlobalRef(dm,c,x,&xc);CHKERRQ(ierr);
if (xc) {ierr = ExactSolution(time, cg->centroid, xc, user);CHKERRQ(ierr);}
}
ierr = VecRestoreArrayRead(user->cellgeom, &cellgeom);CHKERRQ(ierr);
ierr = VecRestoreArray(X, &x);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode InitialCondition(PetscReal time, const PetscReal *x, PetscScalar *u, User user)
{
PetscInt i;
PetscFunctionBeginUser;
if (time != 0.0) SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"No solution known for time %g",time);
if(user->benchmark_couette){
PetscScalar U, H, T;
U = 0.3; H = 10;
T = user->T0 + x[1]/H*(user->T1 - user->T0) + user->viscosity*U*U/(2*user->k)*x[1]/H*(1.0 - x[1]/H);
u[0] = 1.0/T; /*Density*/
u[1] = u[0]*x[1]/H*U + 0.001; /*Velocity u (the x-direction)*/
u[2] = 0.0; /*Velocity v (the y-direction)*/
u[3] = 0.0; /*Velocity w (the z-direction)*/
u[4] = 1.0; /*Energy*/
PetscErrorCode ierr;
ierr = ExactSolution(time, x, u, user);CHKERRQ(ierr);
}else{
u[0] = 1.0; /* Density */
u[DIM+1] = 1.0; /* Energy */
for (i=1; i<DIM+1; i++) u[i] = 0.0; /* Momentum */
}
PetscFunctionReturn(0);
}
/*
Monitor - User-provided routine to monitor the solution computed at
each timestep. This example plots the solution and computes the
error in two different norms.
Input Parameters:
ts - the timestep context
step - the count of the current step (with 0 meaning the
initial condition)
time - the current time
u - the solution at this timestep
ctx - the user-provided context for this monitoring routine.
In this case we use the application context which contains
information about the problem size, workspace and the exact
solution.
*/
PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal time,Vec u,void *ctx)
{
AppCtx *appctx = (AppCtx*) ctx; /* user-defined application context */
PetscErrorCode ierr;
PetscReal norm_2,norm_max;
/*
View a graph of the current iterate
*/
ierr = VecView(u,appctx->viewer2);CHKERRQ(ierr);
/*
Compute the exact solution
*/
ierr = ExactSolution(time,appctx->solution,appctx);CHKERRQ(ierr);
/*
Print debugging information if desired
*/
if (appctx->debug) {
ierr = PetscPrintf(appctx->comm,"Computed solution vector\n");CHKERRQ(ierr);
ierr = VecView(u,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscPrintf(appctx->comm,"Exact solution vector\n");CHKERRQ(ierr);
ierr = VecView(appctx->solution,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
/*
Compute the 2-norm and max-norm of the error
*/
ierr = VecAXPY(appctx->solution,-1.0,u);CHKERRQ(ierr);
ierr = VecNorm(appctx->solution,NORM_2,&norm_2);CHKERRQ(ierr);
norm_2 = PetscSqrtReal(appctx->h)*norm_2;
ierr = VecNorm(appctx->solution,NORM_MAX,&norm_max);CHKERRQ(ierr);
if (norm_2 < 1e-14) norm_2 = 0;
if (norm_max < 1e-14) norm_max = 0;
/*
PetscPrintf() causes only the first processor in this
communicator to print the timestep information.
*/
ierr = PetscPrintf(appctx->comm,"Timestep %D: time = %g 2-norm error = %g max norm error = %g\n",step,(double)time,(double)norm_2,(double)norm_max);CHKERRQ(ierr);
appctx->norm_2 += norm_2;
appctx->norm_max += norm_max;
/*
View a graph of the error
*/
ierr = VecView(appctx->solution,appctx->viewer1);CHKERRQ(ierr);
/*
Print debugging information if desired
*/
if (appctx->debug) {
ierr = PetscPrintf(appctx->comm,"Error vector\n");CHKERRQ(ierr);
ierr = VecView(appctx->solution,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
return 0;
}
/*
Monitor - User-provided routine to monitor the solution computed at
each timestep. This example plots the solution and computes the
error in two different norms.
Input Parameters:
ts - the timestep context
step - the count of the current step (with 0 meaning the
initial condition)
time - the current time
u - the solution at this timestep
ctx - the user-provided context for this monitoring routine.
In this case we use the application context which contains
information about the problem size, workspace and the exact
solution.
*/
PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal time,Vec u,void *ctx)
{
AppCtx *appctx = (AppCtx*) ctx; /* user-defined application context */
PetscErrorCode ierr;
PetscReal norm_2,norm_max;
/*
View a graph of the current iterate
*/
ierr = VecView(u,appctx->viewer2);CHKERRQ(ierr);
/*
Compute the exact solution
*/
ierr = ExactSolution(time,appctx->solution,appctx);CHKERRQ(ierr);
/*
Print debugging information if desired
*/
if (appctx->debug) {
printf("Computed solution vector\n");
ierr = VecView(u,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
printf("Exact solution vector\n");
ierr = VecView(appctx->solution,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
}
/*
Compute the 2-norm and max-norm of the error
*/
ierr = VecAXPY(appctx->solution,-1.0,u);CHKERRQ(ierr);
ierr = VecNorm(appctx->solution,NORM_2,&norm_2);CHKERRQ(ierr);
norm_2 = sqrt(appctx->h)*norm_2;
ierr = VecNorm(appctx->solution,NORM_MAX,&norm_max);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"Timestep %D: time = %G, 2-norm error = %G, max norm error = %G\n",
step,time,norm_2,norm_max);CHKERRQ(ierr);
appctx->norm_2 += norm_2;
appctx->norm_max += norm_max;
/*
View a graph of the error
*/
ierr = VecView(appctx->solution,appctx->viewer1);CHKERRQ(ierr);
/*
Print debugging information if desired
*/
if (appctx->debug) {
printf("Error vector\n");
ierr = VecView(appctx->solution,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
}
return 0;
}
PetscErrorCode BoundaryWallflow(PetscReal time, const PetscReal *c, const PetscReal *n, const PetscScalar *xI, PetscScalar *xG, User user)
{
PetscErrorCode ierr;
PetscFunctionBeginUser;
if(user->benchmark_couette){
ierr = ExactSolution(time, c, xG, user);CHKERRQ(ierr);
}else{
xG[0] = 1.0; /*Density*/
xG[1] = 0.0; /*Velocity u (the x-direction)*/
xG[2] = 0.0; /*Velocity v (the y-direction)*/
xG[3] = 0.0; /*Velocity w (the z-direction)*/
xG[4] = 1.0; /*Energy*/
}
//printf("wall: (%f, %f, %f)\n", c[0], c[1], c[2]);
PetscFunctionReturn(0);
}
PetscErrorCode Monitor(SNES snes,PetscInt its,PetscReal rnorm,void *dummy)
{
UserCtx *user;
PetscErrorCode ierr;
PetscInt m,N;
PetscScalar *w,*dw;
Vec u_lambda,U,F,Uexact;
DM packer;
PetscReal norm;
DM da;
PetscFunctionBeginUser;
ierr = SNESGetDM(snes,&packer);CHKERRQ(ierr);
ierr = DMGetApplicationContext(packer,&user);CHKERRQ(ierr);
ierr = SNESGetSolution(snes,&U);CHKERRQ(ierr);
ierr = DMCompositeGetAccess(packer,U,&w,&u_lambda);CHKERRQ(ierr);
ierr = VecView(u_lambda,user->u_lambda_viewer);CHKERRQ(ierr);
ierr = DMCompositeRestoreAccess(packer,U,&w,&u_lambda);CHKERRQ(ierr);
ierr = SNESGetFunction(snes,&F,0,0);CHKERRQ(ierr);
ierr = DMCompositeGetAccess(packer,F,&w,&u_lambda);CHKERRQ(ierr);
/* ierr = VecView(u_lambda,user->fu_lambda_viewer); */
ierr = DMCompositeRestoreAccess(packer,U,&w,&u_lambda);CHKERRQ(ierr);
ierr = DMCompositeGetEntries(packer,&m,&da);CHKERRQ(ierr);
ierr = DMDAGetInfo(da,0,&N,0,0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
ierr = VecDuplicate(U,&Uexact);CHKERRQ(ierr);
ierr = ExactSolution(packer,Uexact);CHKERRQ(ierr);
ierr = VecAXPY(Uexact,-1.0,U);CHKERRQ(ierr);
ierr = DMCompositeGetAccess(packer,Uexact,&dw,&u_lambda);CHKERRQ(ierr);
ierr = VecStrideNorm(u_lambda,0,NORM_2,&norm);CHKERRQ(ierr);
norm = norm/PetscSqrtReal((PetscReal)N-1.);
if (dw) ierr = PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g Error at x = 0 %g\n",(double)norm,(double)PetscRealPart(dw[0]));CHKERRQ(ierr);
ierr = VecView(u_lambda,user->fu_lambda_viewer);CHKERRQ(ierr);
ierr = DMCompositeRestoreAccess(packer,Uexact,&dw,&u_lambda);CHKERRQ(ierr);
ierr = VecDestroy(&Uexact);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
Monitor - User-provided routine to monitor the solution computed at
each timestep. This example plots the solution and computes the
error in two different norms.
This example also demonstrates changing the timestep via TSSetTimeStep().
Input Parameters:
ts - the timestep context
step - the count of the current step (with 0 meaning the
initial condition)
crtime - the current time
u - the solution at this timestep
ctx - the user-provided context for this monitoring routine.
In this case we use the application context which contains
information about the problem size, workspace and the exact
solution.
*/
PetscErrorCode Monitor(TS ts,PetscInt step,PetscReal crtime,Vec u,void *ctx)
{
AppCtx *appctx = (AppCtx*) ctx; /* user-defined application context */
PetscErrorCode ierr;
PetscReal norm_2, norm_max, dt, dttol;
PetscBool flg;
/*
View a graph of the current iterate
*/
ierr = VecView(u,appctx->viewer2);CHKERRQ(ierr);
/*
Compute the exact solution
*/
ierr = ExactSolution(crtime,appctx->solution,appctx);CHKERRQ(ierr);
/*
Print debugging information if desired
*/
if (appctx->debug) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Computed solution vector\n");CHKERRQ(ierr);
ierr = VecView(u,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF,"Exact solution vector\n");CHKERRQ(ierr);
ierr = VecView(appctx->solution,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
}
/*
Compute the 2-norm and max-norm of the error
*/
ierr = VecAXPY(appctx->solution,-1.0,u);CHKERRQ(ierr);
ierr = VecNorm(appctx->solution,NORM_2,&norm_2);CHKERRQ(ierr);
norm_2 = PetscSqrtReal(appctx->h)*norm_2;
ierr = VecNorm(appctx->solution,NORM_MAX,&norm_max);CHKERRQ(ierr);
ierr = TSGetTimeStep(ts,&dt);CHKERRQ(ierr);
if (norm_2 > 1.e-2) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Timestep %D: step size = %G, time = %G, 2-norm error = %G, max norm error = %G\n",step,dt,crtime,norm_2,norm_max);CHKERRQ(ierr);
}
appctx->norm_2 += norm_2;
appctx->norm_max += norm_max;
dttol = .0001;
ierr = PetscOptionsGetReal(NULL,"-dttol",&dttol,&flg);CHKERRQ(ierr);
if (dt < dttol) {
dt *= .999;
ierr = TSSetTimeStep(ts,dt);CHKERRQ(ierr);
}
/*
View a graph of the error
*/
ierr = VecView(appctx->solution,appctx->viewer1);CHKERRQ(ierr);
/*
Print debugging information if desired
*/
if (appctx->debug) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error vector\n");CHKERRQ(ierr);
ierr = VecView(appctx->solution,PETSC_VIEWER_STDOUT_SELF);CHKERRQ(ierr);
}
return 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);
}
/*
L_2Error - Integrate the L_2 error of our solution over each face
*/
PetscErrorCode L_2Error(DM da, Vec fVec, PetscReal *error, AppCtx *user)
{
DMDALocalInfo info;
Vec fLocalVec;
Field **f;
Field u, uExact, uLocal[4];
PetscScalar hx, hy, hxhy, x, y, phi[3];
PetscInt i, j, q;
PetscErrorCode ierr;
PetscFunctionBeginUser;
ierr = DMDAGetLocalInfo(da, &info);CHKERRQ(ierr);
ierr = DMGetLocalVector(da, &fLocalVec);CHKERRQ(ierr);
ierr = DMGlobalToLocalBegin(da,fVec, INSERT_VALUES, fLocalVec);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(da,fVec, INSERT_VALUES, fLocalVec);CHKERRQ(ierr);
ierr = DMDAVecGetArray(da, fLocalVec, &f);CHKERRQ(ierr);
*error = 0.0;
hx = 1.0/(PetscReal)(info.mx-1);
hy = 1.0/(PetscReal)(info.my-1);
hxhy = hx*hy;
for (j = info.ys; j < info.ys+info.ym-1; j++) {
for (i = info.xs; i < info.xs+info.xm-1; i++) {
uLocal[0] = f[j][i];
uLocal[1] = f[j][i+1];
uLocal[2] = f[j+1][i+1];
uLocal[3] = f[j+1][i];
/* Lower element */
for (q = 0; q < 4; q++) {
phi[0] = 1.0 - quadPoints[q*2] - quadPoints[q*2+1];
phi[1] = quadPoints[q*2];
phi[2] = quadPoints[q*2+1];
u.u = uLocal[0].u*phi[0]+ uLocal[1].u*phi[1] + uLocal[3].u*phi[2];
u.v = uLocal[0].v*phi[0]+ uLocal[1].v*phi[1] + uLocal[3].v*phi[2];
u.p = uLocal[0].p*phi[0]+ uLocal[1].p*phi[1] + uLocal[3].p*phi[2];
x = (quadPoints[q*2] + (PetscReal)i)*hx;
y = (quadPoints[q*2+1] + (PetscReal)j)*hy;
ierr = ExactSolution(PetscAbsScalar(x), PetscAbsScalar(y), &uExact);CHKERRQ(ierr);
*error += PetscAbsScalar(hxhy*quadWeights[q]*((u.u - uExact.u)*(u.u - uExact.u) + (u.v - uExact.v)*(u.v - uExact.v) + (u.p - uExact.p)*(u.p - uExact.p)));
}
/* Upper element */
/*
The affine map from the lower to the upper is
/ x_U \ = / -1 0 \ / x_L \ + / hx \
\ y_U / \ 0 -1 / \ y_L / \ hy /
*/
for (q = 0; q < 4; q++) {
phi[0] = 1.0 - quadPoints[q*2] - quadPoints[q*2+1];
phi[1] = quadPoints[q*2];
phi[2] = quadPoints[q*2+1];
u.u = uLocal[2].u*phi[0]+ uLocal[3].u*phi[1] + uLocal[1].u*phi[2];
u.v = uLocal[2].v*phi[0]+ uLocal[3].v*phi[1] + uLocal[1].v*phi[2];
u.p = uLocal[0].p*phi[0]+ uLocal[1].p*phi[1] + uLocal[3].p*phi[2];
x = (1.0 - quadPoints[q*2] + (PetscReal)i)*hx;
y = (1.0 - quadPoints[q*2+1] + (PetscReal)j)*hy;
ierr = ExactSolution(PetscAbsScalar(x), PetscAbsScalar(y), &uExact);CHKERRQ(ierr);
*error += PetscAbsScalar(hxhy*quadWeights[q]*((u.u - uExact.u)*(u.u - uExact.u) + (u.v - uExact.v)*(u.v - uExact.v) + (u.p - uExact.p)*(u.p - uExact.p)));
}
}
}
ierr = DMDAVecRestoreArray(da, fLocalVec, &f);CHKERRQ(ierr);
/* ierr = DMLocalToGlobalBegin(da,xLocalVec,ADD_VALUES,xVec);CHKERRQ(ierr); */
/* ierr = DMLocalToGlobalEnd(da,xLocalVec,ADD_VALUES,xVec);CHKERRQ(ierr); */
ierr = DMRestoreLocalVector(da, &fLocalVec);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
FormFunctionLocal - Evaluates nonlinear function, F(x).
*/
PetscErrorCode FormFunctionLocal(DMDALocalInfo *info, Field **x, Field **f, AppCtx *user)
{
Field uLocal[3];
Field rLocal[3];
PetscScalar G[4];
Field uExact;
PetscReal alpha,lambda,hx,hy,hxhy,sc,detJInv;
PetscInt i,j,k,l;
PetscErrorCode ierr;
PetscFunctionBeginUser;
/* Naive Jacobian calculation:
J = / 1/hx 0 \ J^{-1} = / hx 0 \ 1/|J| = hx*hy = |J^{-1}|
\ 0 1/hy / \ 0 hy /
*/
alpha = user->alpha;
lambda = user->lambda;
hx = 1.0/(PetscReal)(info->mx-1);
hy = 1.0/(PetscReal)(info->my-1);
sc = hx*hy*lambda;
hxhy = hx*hy;
detJInv = hxhy;
G[0] = (1.0/(hx*hx)) * detJInv;
G[1] = 0.0;
G[2] = G[1];
G[3] = (1.0/(hy*hy)) * detJInv;
for (k = 0; k < 4; k++) {
/* printf("G[%d] = %g\n", k, G[k]);*/
}
/* Zero the vector */
ierr = PetscMemzero((void*) &(f[info->xs][info->ys]), info->xm*info->ym*sizeof(Field));CHKERRQ(ierr);
/* Compute function over the locally owned part of the grid. For each
vertex (i,j), we consider the element below:
2 (1) (0)
i,j+1 --- i+1,j+1
| \ |
| \ |
| \ |
| \ |
| \ |
i,j --- i+1,j
0 1 (2)
and therefore we do not loop over the last vertex in each dimension.
*/
for (j = info->ys; j < info->ys+info->ym-1; j++) {
for (i = info->xs; i < info->xs+info->xm-1; i++) {
/* Lower element */
uLocal[0] = x[j][i];
uLocal[1] = x[j][i+1];
uLocal[2] = x[j+1][i];
/* printf("Lower Solution ElementVector for (%d, %d)\n", i, j);*/
for (k = 0; k < 3; k++) {
/* printf(" uLocal[%d] = (%g, %g, %g)\n", k, uLocal[k].u, uLocal[k].v, uLocal[k].p);*/
}
for (k = 0; k < 3; k++) {
rLocal[k].u = 0.0;
rLocal[k].v = 0.0;
rLocal[k].p = 0.0;
for (l = 0; l < 3; l++) {
rLocal[k].u += alpha*(G[0]*Kref[(k*2*3 + l)*2]+G[1]*Kref[(k*2*3 + l)*2+1]+G[2]*Kref[((k*2+1)*3 + l)*2]+G[3]*Kref[((k*2+1)*3 + l)*2+1])*uLocal[l].u;
rLocal[k].v += alpha*(G[0]*Kref[(k*2*3 + l)*2]+G[1]*Kref[(k*2*3 + l)*2+1]+G[2]*Kref[((k*2+1)*3 + l)*2]+G[3]*Kref[((k*2+1)*3 + l)*2+1])*uLocal[l].v;
/* rLocal[k].u += hxhy*Identity[k*3+l]*uLocal[l].u; */
/* rLocal[k].p += hxhy*Identity[k*3+l]*uLocal[l].p; */
/* Gradient */
rLocal[k].u += hx*Gradient[(k*2+0)*3 + l]*uLocal[l].p;
rLocal[k].v += hy*Gradient[(k*2+1)*3 + l]*uLocal[l].p;
/* Divergence */
rLocal[k].p += hx*Divergence[(k*2+0)*3 + l]*uLocal[l].u + hy*Divergence[(k*2+1)*3 + l]*uLocal[l].v;
}
}
/* printf("Lower Laplacian ElementVector for (%d, %d)\n", i, j);*/
for (k = 0; k < 3; k++) {
/* printf(" rLocal[%d] = (%g, %g, %g)\n", k, rLocal[k].u, rLocal[k].v, rLocal[k].p);*/
}
ierr = constantResidual(1.0, PETSC_TRUE, i, j, hx, hy, rLocal);CHKERRQ(ierr);
/* printf("Lower Laplacian+Constant ElementVector for (%d, %d)\n", i, j);*/
for (k = 0; k < 3; k++) {
/* printf(" rLocal[%d] = (%g, %g, %g)\n", k, rLocal[k].u, rLocal[k].v, rLocal[k].p);*/
}
ierr = nonlinearResidual(0.0*sc, uLocal, rLocal);CHKERRQ(ierr);
/* printf("Lower Full nonlinear ElementVector for (%d, %d)\n", i, j);*/
for (k = 0; k < 3; k++) {
/* printf(" rLocal[%d] = (%g, %g, %g)\n", k, rLocal[k].u, rLocal[k].v, rLocal[k].p);*/
}
f[j][i].u += rLocal[0].u;
f[j][i].v += rLocal[0].v;
f[j][i].p += rLocal[0].p;
f[j][i+1].u += rLocal[1].u;
f[j][i+1].v += rLocal[1].v;
f[j][i+1].p += rLocal[1].p;
f[j+1][i].u += rLocal[2].u;
f[j+1][i].v += rLocal[2].v;
f[j+1][i].p += rLocal[2].p;
/* Upper element */
uLocal[0] = x[j+1][i+1];
uLocal[1] = x[j+1][i];
uLocal[2] = x[j][i+1];
/* printf("Upper Solution ElementVector for (%d, %d)\n", i, j);*/
for (k = 0; k < 3; k++) {
/* printf(" uLocal[%d] = (%g, %g, %g)\n", k, uLocal[k].u, uLocal[k].v, uLocal[k].p);*/
}
for (k = 0; k < 3; k++) {
rLocal[k].u = 0.0;
rLocal[k].v = 0.0;
rLocal[k].p = 0.0;
for (l = 0; l < 3; l++) {
rLocal[k].u += alpha*(G[0]*Kref[(k*2*3 + l)*2]+G[1]*Kref[(k*2*3 + l)*2+1]+G[2]*Kref[((k*2+1)*3 + l)*2]+G[3]*Kref[((k*2+1)*3 + l)*2+1])*uLocal[l].u;
rLocal[k].v += alpha*(G[0]*Kref[(k*2*3 + l)*2]+G[1]*Kref[(k*2*3 + l)*2+1]+G[2]*Kref[((k*2+1)*3 + l)*2]+G[3]*Kref[((k*2+1)*3 + l)*2+1])*uLocal[l].v;
/* rLocal[k].p += Identity[k*3+l]*uLocal[l].p; */
/* Gradient */
rLocal[k].u += hx*Gradient[(k*2+0)*3 + l]*uLocal[l].p;
rLocal[k].v += hy*Gradient[(k*2+1)*3 + l]*uLocal[l].p;
/* Divergence */
rLocal[k].p += hx*Divergence[(k*2+0)*3 + l]*uLocal[l].u + hy*Divergence[(k*2+1)*3 + l]*uLocal[l].v;
}
}
/* printf("Upper Laplacian ElementVector for (%d, %d)\n", i, j);*/
for (k = 0; k < 3; k++) {
/* printf(" rLocal[%d] = (%g, %g, %g)\n", k, rLocal[k].u, rLocal[k].v, rLocal[k].p);*/
}
ierr = constantResidual(1.0, PETSC_TRUE, i, j, hx, hy, rLocal);CHKERRQ(ierr);
/* printf("Upper Laplacian+Constant ElementVector for (%d, %d)\n", i, j);*/
for (k = 0; k < 3; k++) {
/* printf(" rLocal[%d] = (%g, %g, %g)\n", k, rLocal[k].u, rLocal[k].v, rLocal[k].p);*/
}
ierr = nonlinearResidual(0.0*sc, uLocal, rLocal);CHKERRQ(ierr);
/* printf("Upper Full nonlinear ElementVector for (%d, %d)\n", i, j);*/
for (k = 0; k < 3; k++) {
/* printf(" rLocal[%d] = (%g, %g, %g)\n", k, rLocal[k].u, rLocal[k].v, rLocal[k].p);*/
}
f[j+1][i+1].u += rLocal[0].u;
f[j+1][i+1].v += rLocal[0].v;
f[j+1][i+1].p += rLocal[0].p;
f[j+1][i].u += rLocal[1].u;
f[j+1][i].v += rLocal[1].v;
f[j+1][i].p += rLocal[1].p;
f[j][i+1].u += rLocal[2].u;
f[j][i+1].v += rLocal[2].v;
f[j][i+1].p += rLocal[2].p;
/* Boundary conditions */
if (i == 0 || j == 0) {
ierr = ExactSolution(i*hx, j*hy, &uExact);CHKERRQ(ierr);
f[j][i].u = x[j][i].u - uExact.u;
f[j][i].v = x[j][i].v - uExact.v;
f[j][i].p = x[j][i].p - uExact.p;
}
if ((i == info->mx-2) || (j == 0)) {
ierr = ExactSolution((i+1)*hx, j*hy, &uExact);CHKERRQ(ierr);
f[j][i+1].u = x[j][i+1].u - uExact.u;
f[j][i+1].v = x[j][i+1].v - uExact.v;
f[j][i+1].p = x[j][i+1].p - uExact.p;
}
if ((i == info->mx-2) || (j == info->my-2)) {
ierr = ExactSolution((i+1)*hx, (j+1)*hy, &uExact);CHKERRQ(ierr);
f[j+1][i+1].u = x[j+1][i+1].u - uExact.u;
f[j+1][i+1].v = x[j+1][i+1].v - uExact.v;
f[j+1][i+1].p = x[j+1][i+1].p - uExact.p;
}
if ((i == 0) || (j == info->my-2)) {
ierr = ExactSolution(i*hx, (j+1)*hy, &uExact);CHKERRQ(ierr);
f[j+1][i].u = x[j+1][i].u - uExact.u;
f[j+1][i].v = x[j+1][i].v - uExact.v;
f[j+1][i].p = x[j+1][i].p - uExact.p;
}
}
}
for (j = info->ys+info->ym-1; j >= info->ys; j--) {
for (i = info->xs; i < info->xs+info->xm; i++) {
/* printf("f[%d][%d] = (%g, %g, %g) ", j, i, f[j][i].u, f[j][i].v, f[j][i].p);*/
}
/*printf("\n");*/
}
ierr = PetscLogFlops(68.0*(info->ym-1)*(info->xm-1));CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
FormInitialGuess - Forms initial approximation.
Input Parameters:
dm - The DM context
X - vector
Output Parameter:
X - vector
*/
PetscErrorCode FormInitialGuess(SNES snes,Vec X,void *ctx)
{
AppCtx *user;
PetscInt i,j,Mx,My,xs,ys,xm,ym;
PetscErrorCode ierr;
PetscReal lambda,hx,hy;
PETSC_UNUSED PetscReal temp1;
Field **x;
DM da;
PetscFunctionBeginUser;
ierr = SNESGetDM(snes,&da);CHKERRQ(ierr);
ierr = DMGetApplicationContext(da,&user);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);
lambda = user->lambda;
hx = 1.0/(PetscReal)(Mx-1);
hy = 1.0/(PetscReal)(My-1);
if (lambda == 0.0) temp1 = 0.0;
else temp1 = lambda/(lambda + 1.0);
/*
Get a pointer to vector data.
- For default PETSc vectors, VecGetArray() returns a pointer to
the data array. Otherwise, the routine is implementation dependent.
- You MUST call VecRestoreArray() when you no longer need access to
the array.
*/
ierr = DMDAVecGetArray(da,X,&x);CHKERRQ(ierr);
/*
Get local grid boundaries (for 2-dimensional DMDA):
xs, ys - starting grid indices (no ghost points)
xm, ym - widths of local grid (no ghost points)
*/
ierr = DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);CHKERRQ(ierr);
/*
Compute initial guess over the locally owned part of the grid
*/
for (j=ys; j<ys+ym; j++) {
for (i=xs; i<xs+xm; i++) {
#define CHECK_SOLUTION
#if defined(CHECK_SOLUTION)
ierr = ExactSolution(i*hx, j*hy, &x[j][i]);CHKERRQ(ierr);
#else
if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
/* Boundary conditions are usually zero Dirichlet */
ierr = ExactSolution(i*hx, j*hy, &x[j][i]);CHKERRQ(ierr);
} else {
PetscReal temp = (PetscReal)(PetscMin(j,My-j-1))*hy;
x[j][i].u = temp1*PetscSqrtReal(PetscMin((PetscReal)(PetscMin(i,Mx-i-1))*hx,temp));
x[j][i].v = temp1*PetscSqrtReal(PetscMin((PetscReal)(PetscMin(i,Mx-i-1))*hx,temp));
x[j][i].p = 1.0;
}
#endif
}
}
/*
Restore vector
*/
ierr = DMDAVecRestoreArray(da,X,&x);CHKERRQ(ierr);
PetscFunctionReturn(0);
}