static PetscErrorCode SNESSetUp_Composite(SNES snes)
{
PetscErrorCode ierr;
DM dm;
SNES_Composite *jac = (SNES_Composite*)snes->data;
SNES_CompositeLink next = jac->head;
PetscInt n=0,i;
Vec F;
PetscFunctionBegin;
ierr = SNESGetDM(snes,&dm);CHKERRQ(ierr);
if (snes->ops->computevariablebounds) {
/* SNESVI only ever calls computevariablebounds once, so calling it once here is justified */
if (!snes->xl) {ierr = VecDuplicate(snes->vec_sol,&snes->xl);CHKERRQ(ierr);}
if (!snes->xu) {ierr = VecDuplicate(snes->vec_sol,&snes->xu);CHKERRQ(ierr);}
ierr = (*snes->ops->computevariablebounds)(snes,snes->xl,snes->xu);CHKERRQ(ierr);
}
while (next) {
n++;
ierr = SNESSetDM(next->snes,dm);CHKERRQ(ierr);
ierr = SNESSetApplicationContext(next->snes, snes->user);CHKERRQ(ierr);
if (snes->xl && snes->xu) {
if (snes->ops->computevariablebounds) {
ierr = SNESVISetComputeVariableBounds(next->snes, snes->ops->computevariablebounds);CHKERRQ(ierr);
} else {
ierr = SNESVISetVariableBounds(next->snes,snes->xl,snes->xu);CHKERRQ(ierr);
}
}
next = next->next;
}
jac->nsnes = n;
ierr = SNESGetFunction(snes,&F,NULL,NULL);CHKERRQ(ierr);
if (jac->type == SNES_COMPOSITE_ADDITIVEOPTIMAL) {
ierr = VecDuplicateVecs(F,jac->nsnes,&jac->Xes);CHKERRQ(ierr);
ierr = PetscMalloc1(n,&jac->Fes);CHKERRQ(ierr);
ierr = PetscMalloc1(n,&jac->fnorms);CHKERRQ(ierr);
next = jac->head;
i = 0;
while (next) {
ierr = SNESGetFunction(next->snes,&F,NULL,NULL);CHKERRQ(ierr);
jac->Fes[i] = F;
ierr = PetscObjectReference((PetscObject)F);CHKERRQ(ierr);
next = next->next;
i++;
}
/* allocate the subspace direct solve area */
jac->nrhs = 1;
jac->lda = jac->nsnes;
jac->ldb = jac->nsnes;
jac->n = jac->nsnes;
ierr = PetscMalloc1(jac->n*jac->n,&jac->h);CHKERRQ(ierr);
ierr = PetscMalloc1(jac->n,&jac->beta);CHKERRQ(ierr);
ierr = PetscMalloc1(jac->n,&jac->s);CHKERRQ(ierr);
ierr = PetscMalloc1(jac->n,&jac->g);CHKERRQ(ierr);
jac->lwork = 12*jac->n;
#if PETSC_USE_COMPLEX
ierr = PetscMalloc1(jac->lwork,&jac->rwork);CHKERRQ(ierr);
#endif
ierr = PetscMalloc1(jac->lwork,&jac->work);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
int main(int argc,char **argv) {
PetscErrorCode ierr;
DM da, da_after;
SNES snes;
Vec u_initial, u;
PoissonCtx user;
SNESConvergedReason reason;
int snesits;
double lflops,flops;
DMDALocalInfo info;
PetscInitialize(&argc,&argv,NULL,help);
ierr = PetscOptionsBegin(PETSC_COMM_WORLD,"el_",
"elasto-plastic torsion solver options",""); CHKERRQ(ierr);
ierr = PetscOptionsReal("-C","f(x,y)=2C is source term",
"elasto.c",C,&C,NULL); CHKERRQ(ierr);
ierr = PetscOptionsEnd(); CHKERRQ(ierr);
ierr = DMDACreate2d(PETSC_COMM_WORLD,
DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DMDA_STENCIL_STAR,
3,3, // override with -da_grid_x,_y
PETSC_DECIDE,PETSC_DECIDE, // num of procs in each dim
1,1,NULL,NULL, // dof = 1 and stencil width = 1
&da);CHKERRQ(ierr);
ierr = DMSetFromOptions(da); CHKERRQ(ierr);
ierr = DMSetUp(da); CHKERRQ(ierr);
ierr = DMDASetUniformCoordinates(da,0.0,1.0,0.0,1.0,-1.0,-1.0);CHKERRQ(ierr);
user.cx = 1.0;
user.cy = 1.0;
user.cz = 1.0;
user.g_bdry = &zero;
user.f_rhs = &f_fcn;
user.addctx = NULL;
ierr = DMSetApplicationContext(da,&user);CHKERRQ(ierr);
ierr = SNESCreate(PETSC_COMM_WORLD,&snes);CHKERRQ(ierr);
ierr = SNESSetDM(snes,da);CHKERRQ(ierr);
ierr = SNESSetApplicationContext(snes,&user);CHKERRQ(ierr);
ierr = SNESSetType(snes,SNESVINEWTONRSLS);CHKERRQ(ierr);
ierr = SNESVISetComputeVariableBounds(snes,&FormBounds);CHKERRQ(ierr);
// reuse residual and jacobian from ch6/
ierr = DMDASNESSetFunctionLocal(da,INSERT_VALUES,
(DMDASNESFunction)Poisson2DFunctionLocal,&user); CHKERRQ(ierr);
ierr = DMDASNESSetJacobianLocal(da,
(DMDASNESJacobian)Poisson2DJacobianLocal,&user); CHKERRQ(ierr);
ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
// initial iterate is zero
ierr = DMCreateGlobalVector(da,&u_initial);CHKERRQ(ierr);
ierr = VecSet(u_initial,0.0); CHKERRQ(ierr);
/* solve; then get solution and DM after solution*/
ierr = SNESSolve(snes,NULL,u_initial);CHKERRQ(ierr);
ierr = VecDestroy(&u_initial); CHKERRQ(ierr);
ierr = DMDestroy(&da); CHKERRQ(ierr);
ierr = SNESGetDM(snes,&da_after); CHKERRQ(ierr);
ierr = SNESGetSolution(snes,&u); CHKERRQ(ierr); /* do not destroy u */
/* performance measures */
ierr = SNESGetConvergedReason(snes,&reason); CHKERRQ(ierr);
if (reason <= 0) {
ierr = PetscPrintf(PETSC_COMM_WORLD,
"WARNING: SNES not converged ... use -snes_converged_reason to check\n"); CHKERRQ(ierr);
}
ierr = SNESGetIterationNumber(snes,&snesits); CHKERRQ(ierr);
ierr = PetscGetFlops(&lflops); CHKERRQ(ierr);
ierr = MPI_Allreduce(&lflops,&flops,1,MPI_DOUBLE,MPI_SUM,PETSC_COMM_WORLD); CHKERRQ(ierr);
ierr = DMDAGetLocalInfo(da_after,&info); CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,
"done on %4d x %4d grid; total flops = %.3e; SNES iterations %d\n",
info.mx,info.my,flops,snesits); CHKERRQ(ierr);
SNESDestroy(&snes);
return PetscFinalize();
}
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;
ObsCtx user;
SNES snes;
DM da;
Vec u; /* solution */
DMDALocalInfo info;
PetscReal error1,errorinf;
PetscInitialize(&argc,&argv,(char*)0,help);
ierr = DMDACreate2d(PETSC_COMM_WORLD,
DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,
DMDA_STENCIL_STAR,
-11,-11, /* default to 10x10 grid */
PETSC_DECIDE,PETSC_DECIDE, /* number of processors in each dimension */
1, /* dof = 1 */
1, /* s = 1; stencil extends out one cell */
NULL,NULL, /* do not specify processor decomposition */
&da);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da,&u);CHKERRQ(ierr);
ierr = VecDuplicate(u,&(user.uexact));CHKERRQ(ierr);
ierr = VecDuplicate(u,&(user.psi));CHKERRQ(ierr);
ierr = DMDASetUniformCoordinates(da,-2.0,2.0,-2.0,2.0,0.0,1.0);CHKERRQ(ierr);
ierr = DMSetApplicationContext(da,&user);CHKERRQ(ierr);
ierr = FormPsiAndExactSoln(da);CHKERRQ(ierr);
ierr = VecSet(u,0.0);CHKERRQ(ierr);
ierr = SNESCreate(PETSC_COMM_WORLD,&snes);CHKERRQ(ierr);
ierr = SNESSetDM(snes,da);CHKERRQ(ierr);
ierr = SNESSetApplicationContext(snes,&user);CHKERRQ(ierr);
ierr = SNESSetType(snes,SNESVINEWTONRSLS);CHKERRQ(ierr);
ierr = SNESVISetComputeVariableBounds(snes,&FormBounds);CHKERRQ(ierr);
ierr = DMDASNESSetFunctionLocal(da,INSERT_VALUES,(PetscErrorCode (*)(DMDALocalInfo*,void*,void*,void*))FormFunctionLocal,&user);CHKERRQ(ierr);
ierr = DMDASNESSetJacobianLocal(da,(PetscErrorCode (*)(DMDALocalInfo*,void*,Mat,Mat,void*))FormJacobianLocal,&user);CHKERRQ(ierr);
ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
/* report on setup */
ierr = DMDAGetLocalInfo(da,&info); CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"setup done: grid Mx,My = %D,%D with spacing dx,dy = %.4f,%.4f\n",
info.mx,info.my,4.0/(PetscReal)(info.mx-1),4.0/(PetscReal)(info.my-1));CHKERRQ(ierr);
/* solve nonlinear system */
ierr = SNESSolve(snes,NULL,u);CHKERRQ(ierr);
/* compare to exact */
ierr = VecAXPY(u,-1.0,user.uexact);CHKERRQ(ierr); /* u <- u - uexact */
ierr = VecNorm(u,NORM_1,&error1);CHKERRQ(ierr);
error1 /= (PetscReal)info.mx * (PetscReal)info.my;
ierr = VecNorm(u,NORM_INFINITY,&errorinf);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"errors: av |u-uexact| = %.3e |u-uexact|_inf = %.3e\n",error1,errorinf);CHKERRQ(ierr);
/* Free work space. */
ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = VecDestroy(&(user.psi));CHKERRQ(ierr);
ierr = VecDestroy(&(user.uexact));CHKERRQ(ierr);
ierr = SNESDestroy(&snes);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
ierr = PetscFinalize();CHKERRQ(ierr);
return 0;
}
int main(int argc,char **argv)
{
PetscErrorCode ierr;
SNES snes;
Vec u, r; /* solution, residual vector */
PetscInt Mx,My,its;
SNESConvergedReason reason;
DM da;
ObsCtx user;
PetscReal dx,dy,error1,errorinf;
PetscBool feasible = PETSC_FALSE,fdflg = PETSC_FALSE;
PetscInitialize(&argc,&argv,(char *)0,help);
ierr = DMDACreate2d(PETSC_COMM_WORLD,
DMDA_BOUNDARY_NONE, DMDA_BOUNDARY_NONE,
DMDA_STENCIL_STAR, /* nonlinear diffusion but diffusivity depends on soln W not grad W */
-11,-11, /* default to 10x10 grid but override with -da_grid_x, -da_grid_y (or -da_refine) */
PETSC_DECIDE,PETSC_DECIDE, /* num of procs in each dim */
1, /* dof = 1 */
1, /* s = 1 (stencil extends out one cell) */
PETSC_NULL,PETSC_NULL, /* no specify proc decomposition */
&da);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da,&u);CHKERRQ(ierr);
ierr = VecDuplicate(u,&r);CHKERRQ(ierr);
ierr = VecDuplicate(u,&(user.uexact));CHKERRQ(ierr);
ierr = VecDuplicate(u,&(user.psi));CHKERRQ(ierr);
ierr = PetscOptionsBegin(PETSC_COMM_WORLD,"","options to obstacle problem","");CHKERRQ(ierr);
ierr = PetscOptionsBool("-fd","use coloring to compute Jacobian by finite differences",PETSC_NULL,fdflg,&fdflg,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsBool("-feasible","use feasible initial guess",PETSC_NULL,feasible,&feasible,PETSC_NULL);CHKERRQ(ierr);
ierr = PetscOptionsEnd();CHKERRQ(ierr);
ierr = DMDASetUniformCoordinates(da,-2.0,2.0,-2.0,2.0,0.0,1.0);CHKERRQ(ierr);
ierr = DMSetApplicationContext(da,&user);CHKERRQ(ierr);
ierr = FormPsiAndInitialGuess(da,u,feasible);CHKERRQ(ierr);
ierr = SNESCreate(PETSC_COMM_WORLD,&snes);CHKERRQ(ierr);
ierr = SNESSetDM(snes,da);CHKERRQ(ierr);
ierr = SNESSetApplicationContext(snes,&user);CHKERRQ(ierr);
ierr = SNESSetType(snes,SNESVINEWTONRSLS);CHKERRQ(ierr);
ierr = SNESVISetComputeVariableBounds(snes,&FormBounds);CHKERRQ(ierr);
ierr = DMDASNESSetFunctionLocal(da,INSERT_VALUES,(PetscErrorCode (*)(DMDALocalInfo*,void*,void*,void*))FormFunctionLocal,&user);CHKERRQ(ierr);
if (!fdflg) {
ierr = DMDASNESSetJacobianLocal(da,(PetscErrorCode (*)(DMDALocalInfo*,void*,Mat,Mat,MatStructure*,void*))FormJacobianLocal,&user);CHKERRQ(ierr);
}
ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
/* report on setup */
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);
dx = 4.0 / (PetscReal)(Mx-1);
dy = 4.0 / (PetscReal)(My-1);
ierr = PetscPrintf(PETSC_COMM_WORLD,
"setup done: square side length = %.3f\n"
" grid Mx,My = %D,%D\n"
" spacing dx,dy = %.3f,%.3f\n",
4.0, Mx, My, (double)dx, (double)dy);CHKERRQ(ierr);
/* solve nonlinear system */
ierr = SNESSolve(snes,PETSC_NULL,u);CHKERRQ(ierr);
ierr = SNESGetIterationNumber(snes,&its);CHKERRQ(ierr);
ierr = SNESGetConvergedReason(snes,&reason);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"number of Newton iterations = %D; result = %s\n",
its,SNESConvergedReasons[reason]);CHKERRQ(ierr);
/* compare to exact */
ierr = VecWAXPY(r,-1.0,user.uexact,u);CHKERRQ(ierr); /* r = W - Wexact */
ierr = VecNorm(r,NORM_1,&error1);CHKERRQ(ierr);
error1 /= (PetscReal)Mx * (PetscReal)My;
ierr = VecNorm(r,NORM_INFINITY,&errorinf);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"errors: av |u-uexact| = %.3e\n |u-uexact|_inf = %.3e\n",error1,errorinf);CHKERRQ(ierr);
/* Free work space. */
ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = VecDestroy(&r);CHKERRQ(ierr);
ierr = VecDestroy(&(user.psi));CHKERRQ(ierr);
ierr = VecDestroy(&(user.uexact));CHKERRQ(ierr);
ierr = SNESDestroy(&snes);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
ierr = PetscFinalize();CHKERRQ(ierr);
return 0;
}
int main(int argc,char **argv)
{
PetscErrorCode ierr;
SNES snes;
Vec u, r; /* solution, residual vector */
PetscInt its;
SNESConvergedReason reason;
DM da;
ObsCtx user;
PetscReal error1,errorinf;
PetscBool feasible = PETSC_FALSE,fdflg = PETSC_FALSE;
DMDALocalInfo info;
PetscInitialize(&argc,&argv,NULL,help);
//CREATE
ierr = DMDACreate2d(PETSC_COMM_WORLD,
DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DMDA_STENCIL_STAR,
11,11, // override with -da_grid_x,_y or -da_refine
PETSC_DECIDE,PETSC_DECIDE, // num of procs in each dim
1,1,NULL,NULL, // dof = 1 and stencil width = 1
&da);CHKERRQ(ierr);
ierr = DMSetFromOptions(da); CHKERRQ(ierr);
ierr = DMSetUp(da); CHKERRQ(ierr);
ierr = DMDASetUniformCoordinates(da,-2.0,2.0,-2.0,2.0,-1.0,-1.0);CHKERRQ(ierr);
ierr = DMSetApplicationContext(da,&user);CHKERRQ(ierr);
ierr = DMDAGetLocalInfo(da,&info); CHKERRQ(ierr);
user.dx = 4.0 / (PetscReal)(info.mx-1);
user.dy = 4.0 / (PetscReal)(info.my-1);
ierr = DMCreateGlobalVector(da,&u);CHKERRQ(ierr);
ierr = VecDuplicate(u,&r);CHKERRQ(ierr);
ierr = VecDuplicate(u,&(user.g));CHKERRQ(ierr);
ierr = VecDuplicate(u,&(user.psi));CHKERRQ(ierr);
ierr = PetscOptionsBegin(PETSC_COMM_WORLD,"","options to obstacle problem","");CHKERRQ(ierr);
ierr = PetscOptionsBool("-fd","use coloring to compute Jacobian by finite differences",
NULL,fdflg,&fdflg,NULL);CHKERRQ(ierr);
ierr = PetscOptionsBool("-feasible","use feasible initial guess",
NULL,feasible,&feasible,NULL);CHKERRQ(ierr);
ierr = PetscOptionsEnd();CHKERRQ(ierr);
//ENDCREATE
//SETUPSNES
ierr = FormPsiAndInitialGuess(da,u,feasible,&user);CHKERRQ(ierr);
ierr = SNESCreate(PETSC_COMM_WORLD,&snes);CHKERRQ(ierr);
ierr = SNESSetDM(snes,da);CHKERRQ(ierr);
ierr = SNESSetApplicationContext(snes,&user);CHKERRQ(ierr);
ierr = SNESSetType(snes,SNESVINEWTONRSLS);CHKERRQ(ierr);
ierr = SNESVISetComputeVariableBounds(snes,&FormBounds);CHKERRQ(ierr);
ierr = DMDASNESSetFunctionLocal(da,INSERT_VALUES,
(PetscErrorCode (*)(DMDALocalInfo*,void*,void*,void*))FormFunctionLocal,
&user);CHKERRQ(ierr);
if (!fdflg) {
ierr = DMDASNESSetJacobianLocal(da,
(PetscErrorCode (*)(DMDALocalInfo*,void*,Mat,Mat,void*))FormJacobianLocal,
&user);CHKERRQ(ierr);
}
ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
//ENDSETUPSNES
/* report on setup */
ierr = PetscPrintf(PETSC_COMM_WORLD,
"setup done: square side length = %.3f\n"
" grid Mx,My = %D,%D\n"
" spacing dx,dy = %.3f,%.3f\n",
4.0, info.mx, info.my, user.dx, user.dy);CHKERRQ(ierr);
//SOLVE
/* solve nonlinear system */
ierr = SNESSolve(snes,NULL,u);CHKERRQ(ierr);
ierr = SNESGetIterationNumber(snes,&its);CHKERRQ(ierr);
ierr = SNESGetConvergedReason(snes,&reason);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"number of Newton iterations = %D; result = %s\n",
its,SNESConvergedReasons[reason]);CHKERRQ(ierr);
/* compare to exact */
ierr = VecWAXPY(r,-1.0,user.g,u);CHKERRQ(ierr); /* r = u - g = u - uexact */
ierr = VecNorm(r,NORM_1,&error1);CHKERRQ(ierr);
error1 /= (PetscReal)info.mx * (PetscReal)info.my;
ierr = VecNorm(r,NORM_INFINITY,&errorinf);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,
"errors: av |u-uexact| = %.3e\n"
" |u-uexact|_inf = %.3e\n",
(double)error1,(double)errorinf);CHKERRQ(ierr);
//ENDSOLVE
/* Free work space. */
ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = VecDestroy(&r);CHKERRQ(ierr);
ierr = VecDestroy(&(user.psi));CHKERRQ(ierr);
ierr = VecDestroy(&(user.g));CHKERRQ(ierr);
ierr = SNESDestroy(&snes);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
ierr = PetscFinalize();CHKERRQ(ierr);
return 0;
}
