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;
}
