int main(int argc,char **argv) {
PetscErrorCode ierr;
SNES snes;
KSP ksp;
Vec u, uexact;
FishCtx user;
DMDALocalInfo info;
double errnorm;
PetscInitialize(&argc,&argv,NULL,help);
user.printevals = PETSC_FALSE;
ierr = PetscOptionsBegin(PETSC_COMM_WORLD, "f3_", "options for fish3", ""); CHKERRQ(ierr);
ierr = PetscOptionsBool("-printevals","residual and Jacobian routines report grid",
"fish3.c",user.printevals,&user.printevals,NULL);CHKERRQ(ierr);
ierr = PetscOptionsEnd(); CHKERRQ(ierr);
ierr = DMDACreate3d(COMM,
DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,
DMDA_STENCIL_STAR,
3,3,3,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,
1,1,
NULL,NULL,NULL,&(user.da)); CHKERRQ(ierr);
ierr = DMSetFromOptions(user.da); CHKERRQ(ierr);
ierr = DMSetUp(user.da); CHKERRQ(ierr);
ierr = DMSetApplicationContext(user.da,&user);CHKERRQ(ierr);
ierr = DMDAGetLocalInfo(user.da,&info); CHKERRQ(ierr);
ierr = DMCreateGlobalVector(user.da,&u);CHKERRQ(ierr);
ierr = VecDuplicate(u,&uexact);CHKERRQ(ierr);
ierr = VecDuplicate(u,&(user.b));CHKERRQ(ierr);
ierr = formExactRHS(&info,uexact,user.b,&user); CHKERRQ(ierr);
ierr = SNESCreate(COMM,&snes); CHKERRQ(ierr);
ierr = SNESSetDM(snes,user.da); CHKERRQ(ierr);
ierr = DMDASNESSetFunctionLocal(user.da,INSERT_VALUES,
(DMDASNESFunction)FormFunctionLocal,&user); CHKERRQ(ierr);
ierr = DMDASNESSetJacobianLocal(user.da,
(DMDASNESJacobian)FormJacobianLocal,&user); CHKERRQ(ierr);
ierr = SNESGetKSP(snes,&ksp); CHKERRQ(ierr);
ierr = KSPSetType(ksp,KSPCG); CHKERRQ(ierr);
ierr = SNESSetFromOptions(snes); CHKERRQ(ierr);
ierr = VecSet(u,0.0); CHKERRQ(ierr);
ierr = SNESSolve(snes,NULL,u); CHKERRQ(ierr);
ierr = VecAXPY(u,-1.0,uexact); CHKERRQ(ierr); // u <- u + (-1.0) uexact
ierr = VecNorm(u,NORM_INFINITY,&errnorm); CHKERRQ(ierr);
ierr = PetscPrintf(COMM,"on %d x %d x %d grid: error |u-uexact|_inf = %g\n",
info.mx,info.my,info.mz,errnorm); CHKERRQ(ierr);
VecDestroy(&u); VecDestroy(&uexact); VecDestroy(&(user.b));
SNESDestroy(&snes); DMDestroy(&(user.da));
PetscFinalize();
return 0;
}
int main(int argc,char **argv) {
PetscErrorCode ierr;
SNES snes;
Vec u;
DMDALocalInfo info;
Ctx user;
PetscInitialize(&argc,&argv,(char*)0,help);
ierr = configureCtx(&user); CHKERRQ(ierr);
ierr = DMDACreate2d(PETSC_COMM_WORLD,
DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,
DMDA_STENCIL_STAR,
-3,-3,
PETSC_DECIDE,PETSC_DECIDE,
1,1,
NULL,NULL,
&user.da); CHKERRQ(ierr);
ierr = DMDASetUniformCoordinates(user.da,-1.0,1.0,-1.0,1.0,0.0,1.0); CHKERRQ(ierr);
ierr = DMSetApplicationContext(user.da,&user); CHKERRQ(ierr);
ierr = DMDAGetLocalInfo(user.da,&info); CHKERRQ(ierr);
if ((info.mx < 2) || (info.my < 2)) {
SETERRQ(PETSC_COMM_WORLD,1,"grid too coarse ... require (mx,my) > (2,2)");
}
ierr = DMCreateGlobalVector(user.da,&u); CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject)u,"u_vec");CHKERRQ(ierr);
ierr = formInitial(&info,&user,u); CHKERRQ(ierr);
ierr = SNESCreate(PETSC_COMM_WORLD,&snes);CHKERRQ(ierr);
ierr = SNESSetDM(snes,user.da);CHKERRQ(ierr);
ierr = DMDASNESSetFunctionLocal(user.da,INSERT_VALUES,
(DMDASNESFunction)FormFunctionLocal,&user);CHKERRQ(ierr);
ierr = DMDASNESSetJacobianLocal(user.da,
(DMDASNESJacobian)FormJacobianLocal,&user);CHKERRQ(ierr);
ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
ierr = SNESSolve(snes,NULL,u); CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,
"done on %d x %d x %d grid with eps=%g ...\n",
info.mx,info.my,info.mz,user.eps); CHKERRQ(ierr);
VecDestroy(&u);
SNESDestroy(&snes); DMDestroy(&user.da);
ierr = PetscFinalize(); CHKERRQ(ierr);
return 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;
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, uexact;
double err, uexnorm;
DMDALocalInfo info;
Ctx user;
PetscInitialize(&argc,&argv,(char*)0,help);
ierr = configureCtx(&user);
CHKERRQ(ierr);
//STARTDMDA
ierr = DMDACreate3d(PETSC_COMM_WORLD,
DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_PERIODIC,
DMDA_STENCIL_STAR, 3,3,3, PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,
1, 1, NULL,NULL,NULL,
&user.da);
CHKERRQ(ierr);
//ENDDMDA
ierr = DMSetFromOptions(user.da);
CHKERRQ(ierr);
ierr = DMSetUp(user.da);
CHKERRQ(ierr);
ierr = DMDASetUniformCoordinates(user.da,-1.0,1.0,-1.0,1.0,-1.0,1.0);
CHKERRQ(ierr);
ierr = DMSetApplicationContext(user.da,&user);
CHKERRQ(ierr);
ierr = DMDAGetLocalInfo(user.da,&info);
CHKERRQ(ierr);
if ((info.mx < 2) || (info.my < 2) || (info.mz < 3)) {
SETERRQ(PETSC_COMM_WORLD,1,"grid too coarse: require (mx,my,mz) > (2,2,3)");
}
ierr = DMCreateGlobalVector(user.da,&uexact);
CHKERRQ(ierr);
ierr = VecDuplicate(uexact,&user.f);
CHKERRQ(ierr);
ierr = VecDuplicate(uexact,&user.g);
CHKERRQ(ierr);
ierr = formUexFG(&info,&user,uexact);
CHKERRQ(ierr);
ierr = SNESCreate(PETSC_COMM_WORLD,&snes);
CHKERRQ(ierr);
ierr = SNESSetDM(snes,user.da);
CHKERRQ(ierr);
ierr = DMDASNESSetFunctionLocal(user.da,INSERT_VALUES,
(DMDASNESFunction)FormFunctionLocal,&user);
CHKERRQ(ierr);
ierr = DMDASNESSetJacobianLocal(user.da,
(DMDASNESJacobian)FormJacobianLocal,&user);
CHKERRQ(ierr);
ierr = SNESSetFromOptions(snes);
CHKERRQ(ierr);
ierr = VecDuplicate(uexact,&u);
CHKERRQ(ierr);
ierr = VecCopy(user.g,u);
CHKERRQ(ierr); // g has zeros except at bdry
ierr = SNESSolve(snes,NULL,u);
CHKERRQ(ierr);
ierr = VecAXPY(u,-1.0,uexact);
CHKERRQ(ierr); // u <- u + (-1.0) uxact
ierr = VecNorm(u,NORM_2,&err);
CHKERRQ(ierr);
ierr = VecNorm(uexact,NORM_2,&uexnorm);
CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,
"done on %d x %d x %d grid with eps=%g: error |u-uexact|_2/|uexact|_2 = %g\n",
info.mx,info.my,info.mz,user.eps,err/uexnorm);
CHKERRQ(ierr);
VecDestroy(&u);
VecDestroy(&uexact);
VecDestroy(&user.f);
VecDestroy(&user.g);
SNESDestroy(&snes);
DMDestroy(&user.da);
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)
{
AppCtx user; /* user-defined work context */
PetscInt mx,my,its;
PetscErrorCode ierr;
MPI_Comm comm;
SNES snes;
DM da;
Vec x,X,b;
PetscBool youngflg,poissonflg,muflg,lambdaflg,view=PETSC_FALSE,viewline=PETSC_FALSE;
PetscReal poisson=0.2,young=4e4;
char filename[PETSC_MAX_PATH_LEN] = "ex16.vts";
char filename_def[PETSC_MAX_PATH_LEN] = "ex16_def.vts";
ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
ierr = FormElements();CHKERRQ(ierr);
comm = PETSC_COMM_WORLD;
ierr = SNESCreate(comm,&snes);CHKERRQ(ierr);
ierr = DMDACreate3d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_BOX,11,2,2,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,3,1,NULL,NULL,NULL,&da);CHKERRQ(ierr);
ierr = DMSetFromOptions(da);CHKERRQ(ierr);
ierr = DMSetUp(da);CHKERRQ(ierr);
ierr = SNESSetDM(snes,(DM)da);CHKERRQ(ierr);
ierr = SNESSetNGS(snes,NonlinearGS,&user);CHKERRQ(ierr);
ierr = DMDAGetInfo(da,0,&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.loading = 0.0;
user.arc = PETSC_PI/3.;
user.mu = 4.0;
user.lambda = 1.0;
user.rad = 100.0;
user.height = 3.;
user.width = 1.;
user.ploading = -5e3;
ierr = PetscOptionsGetReal(NULL,NULL,"-arc",&user.arc,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetReal(NULL,NULL,"-mu",&user.mu,&muflg);CHKERRQ(ierr);
ierr = PetscOptionsGetReal(NULL,NULL,"-lambda",&user.lambda,&lambdaflg);CHKERRQ(ierr);
ierr = PetscOptionsGetReal(NULL,NULL,"-rad",&user.rad,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetReal(NULL,NULL,"-height",&user.height,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetReal(NULL,NULL,"-width",&user.width,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetReal(NULL,NULL,"-loading",&user.loading,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetReal(NULL,NULL,"-ploading",&user.ploading,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetReal(NULL,NULL,"-poisson",&poisson,&poissonflg);CHKERRQ(ierr);
ierr = PetscOptionsGetReal(NULL,NULL,"-young",&young,&youngflg);CHKERRQ(ierr);
if ((youngflg || poissonflg) || !(muflg || lambdaflg)) {
/* set the lame' parameters based upon the poisson ratio and young's modulus */
user.lambda = poisson*young / ((1. + poisson)*(1. - 2.*poisson));
user.mu = young/(2.*(1. + poisson));
}
ierr = PetscOptionsGetBool(NULL,NULL,"-view",&view,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,NULL,"-view_line",&viewline,NULL);CHKERRQ(ierr);
ierr = DMDASetFieldName(da,0,"x_disp");CHKERRQ(ierr);
ierr = DMDASetFieldName(da,1,"y_disp");CHKERRQ(ierr);
ierr = DMDASetFieldName(da,2,"z_disp");CHKERRQ(ierr);
ierr = DMSetApplicationContext(da,&user);CHKERRQ(ierr);
ierr = DMDASNESSetFunctionLocal(da,INSERT_VALUES,(PetscErrorCode (*)(DMDALocalInfo*,void*,void*,void*))FormFunctionLocal,&user);CHKERRQ(ierr);
ierr = DMDASNESSetJacobianLocal(da,(DMDASNESJacobian)FormJacobianLocal,&user);CHKERRQ(ierr);
ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
ierr = FormCoordinates(da,&user);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da,&x);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da,&b);CHKERRQ(ierr);
ierr = InitialGuess(da,&user,x);CHKERRQ(ierr);
ierr = FormRHS(da,&user,b);CHKERRQ(ierr);
ierr = PetscPrintf(comm,"lambda: %f mu: %f\n",(double)user.lambda,(double)user.mu);CHKERRQ(ierr);
/* show a cross-section of the initial state */
if (viewline) {
ierr = DisplayLine(snes,x);CHKERRQ(ierr);
}
/* get the loaded configuration */
ierr = SNESSolve(snes,b,x);CHKERRQ(ierr);
ierr = SNESGetIterationNumber(snes,&its);CHKERRQ(ierr);
ierr = PetscPrintf(comm,"Number of SNES iterations = %D\n", its);CHKERRQ(ierr);
ierr = SNESGetSolution(snes,&X);CHKERRQ(ierr);
/* show a cross-section of the final state */
if (viewline) {
ierr = DisplayLine(snes,X);CHKERRQ(ierr);
}
if (view) {
PetscViewer viewer;
Vec coords;
ierr = PetscViewerVTKOpen(PETSC_COMM_WORLD,filename,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr);
ierr = VecView(x,viewer);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
ierr = DMGetCoordinates(da,&coords);CHKERRQ(ierr);
ierr = VecAXPY(coords,1.0,x);CHKERRQ(ierr);
ierr = PetscViewerVTKOpen(PETSC_COMM_WORLD,filename_def,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr);
ierr = VecView(x,viewer);CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
}
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
ierr = SNESDestroy(&snes);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
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;
}
int main(int argc,char **argv)
{
PetscErrorCode ierr;
SNES snes; /* nonlinear solver */
Vec Hu; /* solution vector */
AppCtx user; /* user-defined work context */
ExactCtx exact;
PetscInt its; /* snes reports iteration count */
SNESConvergedReason reason; /* snes reports convergence */
PetscReal tmp1, tmp2, tmp3,
errnorms[2], scaleNode[2], descaleNode[2];
PetscInt i;
char dumpfile[80],dxdocstr[80];
PetscBool eps_set = PETSC_FALSE,
dump = PETSC_FALSE,
exactinitial = PETSC_FALSE,
snes_mf_set, snes_fd_set, dx_set;
PetscInitialize(&argc,&argv,(char *)0,help);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD, &user.rank); CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,
"MARINE solves for thickness and velocity in 1D, steady marine ice sheet\n"
" [run with -help for info and options]\n");CHKERRQ(ierr);
user.n = 3.0; /* Glen flow law exponent */
user.secpera = 31556926.0;
user.rho = 910.0; /* kg m^-3 */
user.rhow = 1028.0; /* kg m^-3 */
user.omega = 1.0 - user.rho / user.rhow;
user.g = 9.81; /* m s^-2 */
/* get parameters of exact solution */
ierr = params_exactBod(&tmp1, &(exact.L0), &(exact.xg), &tmp2, &tmp3, &(user.k)); CHKERRQ(ierr);
ierr = exactBod(exact.xg,&(exact.Hg),&tmp2,&(exact.Mg)); CHKERRQ(ierr);
ierr = exactBodBueler(exact.xg,&tmp1,&(exact.Bg)); CHKERRQ(ierr);
user.zocean = user.rho * exact.Hg / user.rhow;
/* see ../marineshoot.py: */
#define xa_default 0.2
#define xc_default 0.98
/* define interval [xa,xc] */
user.xa = xa_default * exact.L0;
user.xc = xc_default * exact.L0;
/* get Dirichlet boundary conditions, and mass balance on shelf */
ierr = exactBod(user.xa, &(user.Ha), &(user.ua), &tmp1); CHKERRQ(ierr);
/* regularize using strain rate of 1/(length) per year */
user.epsilon = (1.0 / user.secpera) / (user.xc - user.xa);
/*user.epsilon = 0.0;*/
user.Hscale = 1000.0;
user.uscale = 100.0 / user.secpera;
user.noscale = PETSC_FALSE;
user.dx = 10000.0; /* default to coarse 10 km grid */
ierr = PetscOptionsBegin(PETSC_COMM_WORLD,
"","options to marine (steady marine ice sheet solver)","");CHKERRQ(ierr);
{
ierr = PetscOptionsBool("-snes_mf","","",PETSC_FALSE,&snes_mf_set,NULL);CHKERRQ(ierr);
ierr = PetscOptionsBool("-snes_fd","","",PETSC_FALSE,&snes_fd_set,NULL);CHKERRQ(ierr);
ierr = PetscOptionsBool("-noscale","","",PETSC_FALSE,&user.noscale,NULL);CHKERRQ(ierr);
snprintf(dxdocstr,80,"target grid spacing (m) on interval of length %.0f m",
user.xc-user.xa);
ierr = PetscOptionsReal("-dx",dxdocstr,"",user.dx,&user.dx,&dx_set);CHKERRQ(ierr);
ierr = PetscOptionsBool("-exactinit",
"initialize using exact solution instead of default linear function","",
PETSC_FALSE,&exactinitial,NULL);CHKERRQ(ierr);
ierr = PetscOptionsString("-dump",
"dump approx and exact solution into given file (as ascii matlab format)","",
NULL,dumpfile,80,&dump);CHKERRQ(ierr);
ierr = PetscOptionsReal("-epsilon","regularizing strain rate for stress computation (a-1)","",
user.epsilon * user.secpera,&user.epsilon,&eps_set);CHKERRQ(ierr);
if (eps_set) user.epsilon *= 1.0 / user.secpera;
}
ierr = PetscOptionsEnd();CHKERRQ(ierr);
if (snes_fd_set) {
ierr = PetscPrintf(PETSC_COMM_WORLD,
" using approximate Jacobian; finite-differencing using coloring\n");
CHKERRQ(ierr);
} else if (snes_mf_set) {
ierr = PetscPrintf(PETSC_COMM_WORLD,
" matrix free; no preconditioner\n"); CHKERRQ(ierr);
} else {
ierr = PetscPrintf(PETSC_COMM_WORLD,
" true Jacobian\n"); CHKERRQ(ierr);
}
if (dx_set && (user.dx <= 0.0)) {
PetscPrintf(PETSC_COMM_WORLD,
"\n***ERROR: -dx value must be positive ... USAGE FOLLOWS ...\n\n%s",help);
PetscEnd();
}
user.N = (int)ceil( ((user.xc - user.xa) / user.dx) - 0.5 );
user.Mx = user.N + 2;
user.dx = (user.xc - user.xa) / ((PetscReal)(user.N) + 0.5); /* recompute so dx * (N+1/2) = xc - xa */
if (dx_set && (user.dx < 1.0)) {
PetscPrintf(PETSC_COMM_WORLD,
"\n***WARNING: '-dx %.3f' meters is below one meter and creates grid of %d points\n"
" ... probably uncomputable!\n\n",
user.dx,user.Mx);
}
/* residual scaling coeffs; motivation at right */
user.rscHa = 1.0 / user.Hscale, /* Dirichlet cond for H */
user.rscua = 1.0 / user.uscale, /* Dirichlet cond for u */
user.rscuH = user.dx / (user.Hscale * user.uscale), /* flux derivative d(uH)/dx */
user.rscstress = 1.0 / (user.k * user.rho * user.g * user.Hscale * user.uscale), /* beta term in SSA */
user.rsccalv = 1.0 / (0.025 * user.rho * user.g * user.Hscale); /* 0.5 * omega * overburden */
/* Create machinery for parallel grid management (DMDA), nonlinear solver (SNES),
and Vecs for fields (solution, RHS). Degrees of freedom = 2 (thickness and
velocity at each point). */
ierr = DMDACreate1d(PETSC_COMM_WORLD,DMDA_BOUNDARY_NONE,user.Mx,2,1,PETSC_NULL,&user.da);
CHKERRQ(ierr);
ierr = DMSetApplicationContext(user.da,&user);CHKERRQ(ierr);
ierr = DMDASetFieldName(user.da,0,"ice thickness [non-dimensional]"); CHKERRQ(ierr);
ierr = DMDASetFieldName(user.da,1,"ice velocity [non-dimensional]"); CHKERRQ(ierr);
ierr = DMSetFromOptions(user.da); CHKERRQ(ierr);
ierr = DMDAGetInfo(user.da,PETSC_IGNORE,&user.Mx,PETSC_IGNORE,
PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);CHKERRQ(ierr);
ierr = DMDAGetCorners(user.da,&user.xs,PETSC_NULL,PETSC_NULL,&user.xm,PETSC_NULL,PETSC_NULL);
CHKERRQ(ierr);
/* another DMDA for scalar staggered parameters; one fewer point */
ierr = DMDACreate1d(PETSC_COMM_WORLD,DMDA_BOUNDARY_NONE,user.Mx-1,1,1,PETSC_NULL,&user.stagda);
CHKERRQ(ierr);
/* establish geometry on grid; note xa = x_0 and xc = x_{N+1/2} */
ierr = DMDASetUniformCoordinates(user.da, user.xa, user.xc+0.5*user.dx,
0.0,1.0,0.0,1.0);CHKERRQ(ierr);
ierr = DMDASetUniformCoordinates(user.stagda,user.xa+0.5*user.dx,user.xc,
0.0,1.0,0.0,1.0);CHKERRQ(ierr);
/* report on current grid */
ierr = PetscPrintf(PETSC_COMM_WORLD,
" grid: Mx = N+2 = %D regular points, dx = %.3f m, xa = %.2f km, xc = %.2f km\n",
user.Mx, user.dx, user.xa/1000.0, user.xc/1000.0);CHKERRQ(ierr);
/* Extract/allocate global vectors from DMDAs and duplicate for remaining same types */
ierr = DMCreateGlobalVector(user.da,&Hu);CHKERRQ(ierr);
ierr = VecSetBlockSize(Hu,2);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject)Hu,"Hu");CHKERRQ(ierr);
ierr = VecDuplicate(Hu,&exact.Hu);CHKERRQ(ierr); /* inherits block size */
ierr = PetscObjectSetName((PetscObject)exact.Hu,"exactHu");CHKERRQ(ierr);
ierr = DMCreateGlobalVector(user.stagda,&user.Mstag);CHKERRQ(ierr);
ierr = VecDuplicate(user.Mstag,&user.Bstag);CHKERRQ(ierr);
/* set up snes */
ierr = SNESCreate(PETSC_COMM_WORLD,&snes);CHKERRQ(ierr);
ierr = SNESSetDM(snes,user.da);CHKERRQ(ierr);
ierr = DMDASNESSetFunctionLocal(user.da,INSERT_VALUES,(DMDASNESFunction)scshell,&user);CHKERRQ(ierr);
ierr = DMDASNESSetJacobianLocal(user.da,(DMDASNESJacobian)JacobianMatrixLocal,&user);CHKERRQ(ierr);
ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
/* the exact thickness and exact ice velocity (user.uHexact) are known */
ierr = FillExactSoln(&exact, &user); CHKERRQ(ierr);
/* the exact solution allows setting M(x), B(x) */
ierr = FillDistributedParams(&exact, &user);CHKERRQ(ierr);
if (exactinitial) {
ierr = PetscPrintf(PETSC_COMM_WORLD," using exact solution as initial guess\n"); CHKERRQ(ierr);
/* the initial guess is the exact continuum solution */
ierr = VecCopy(exact.Hu,Hu); CHKERRQ(ierr);
} else {
/* the initial guess is a linear solution */
ierr = FillInitial(&user, &Hu); CHKERRQ(ierr);
}
/************ SOLVE NONLINEAR SYSTEM ************/
/* recall that RHS r is used internally by KSP, and is set by the SNES */
if (user.noscale) {
user.Hscale = 1.0;
user.uscale = 1.0;
}
scaleNode[0] = user.Hscale;
scaleNode[1] = user.uscale;
for (i = 0; i < 2; i++) descaleNode[i] = 1.0 / scaleNode[i];
ierr = VecStrideScaleAll(Hu,descaleNode); CHKERRQ(ierr); /* de-dimensionalize initial guess */
ierr = SNESSolve(snes,PETSC_NULL,Hu);CHKERRQ(ierr);
ierr = VecStrideScaleAll(Hu,scaleNode); CHKERRQ(ierr); /* put back in "real" scale */
/* minimal report on solve */
ierr = SNESGetIterationNumber(snes,&its);CHKERRQ(ierr);
ierr = SNESGetConvergedReason(snes,&reason);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,
" %s Number of Newton iterations = %D\n",
SNESConvergedReasons[reason],its);CHKERRQ(ierr);
if (dump) {
ierr = PetscPrintf(PETSC_COMM_WORLD,
"dumping results in ascii matlab format to file '%s' ...\n",dumpfile);CHKERRQ(ierr);
PetscViewer viewer;
ierr = PetscViewerASCIIOpen(PETSC_COMM_WORLD,dumpfile,&viewer);CHKERRQ(ierr);
ierr = PetscViewerSetFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);CHKERRQ(ierr);
DM coord_da;
Vec coord_x;
ierr = DMGetCoordinateDM(user.da, &coord_da); CHKERRQ(ierr);
ierr = DMGetCoordinates(user.da, &coord_x); CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"%% START MATLAB\n"); CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject)coord_x,"x");CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"%% viewing coordinate vector x \n");CHKERRQ(ierr);
ierr = VecView(coord_x,viewer); CHKERRQ(ierr);
ierr = VecView(Hu,viewer); CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"%% viewing combined result Hu\n");CHKERRQ(ierr);
ierr = VecView(Hu,viewer); CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"%% viewing combined exact result exactHu\n");CHKERRQ(ierr);
ierr = VecView(exact.Hu,viewer); CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,
"%% defining plottable variables and plotting in Matlab\n"
"Mx = %d; secpera = 31556926.0;\n"
"H = Hu(1:2:2*Mx-1);\n"
"u = Hu(2:2:2*Mx);\n"
"exactH = exactHu(1:2:2*Mx-1);\n"
"exactu = exactHu(2:2:2*Mx);\n"
"figure, plot(x,H,x,exactH);\n"
"legend('numerical','exact'), xlabel x, ylabel('H (m)')\n"
"figure, plot(x,u*secpera,x,exactu*secpera);\n"
"legend('numerical','exact'), xlabel x, ylabel('u (m/a)')\n"
"figure, subplot(2,1,1), semilogy(x,abs(H-exactH));\n"
"ylabel('H error (m)'), grid\n"
"subplot(2,1,2), semilogy(x,abs(u-exactu)*secpera);\n"
"xlabel x, ylabel('u error (m/a)'), grid\n",
user.Mx); CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(viewer,"%% END MATLAB\n"); CHKERRQ(ierr);
ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
}
/* evaluate error relative to exact solution */
ierr = VecAXPY(Hu,-1.0,exact.Hu); CHKERRQ(ierr); /* Hu = - Huexact + Hu */
ierr = VecStrideNormAll(Hu,NORM_INFINITY,errnorms); CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,
"(dx,errHinf,erruinf) %.3f %.4e %.4e\n",
user.dx,errnorms[0],errnorms[1]*user.secpera);CHKERRQ(ierr);
ierr = VecDestroy(&Hu);CHKERRQ(ierr);
ierr = VecDestroy(&(exact.Hu));CHKERRQ(ierr);
ierr = VecDestroy(&(user.Mstag));CHKERRQ(ierr);
ierr = VecDestroy(&(user.Bstag));CHKERRQ(ierr);
ierr = SNESDestroy(&snes);CHKERRQ(ierr);
ierr = DMDestroy(&(user.da));CHKERRQ(ierr);
ierr = DMDestroy(&(user.stagda));CHKERRQ(ierr);
ierr = PetscFinalize();CHKERRQ(ierr);
return 0;
}
int main(int argc,char **argv)
{
DM da;
SNES snes; /* nonlinear solver */
AppCtx *user; /* user-defined work context */
PetscBag bag;
PetscInt its; /* iterations for convergence */
PetscMPIInt size;
SNESConvergedReason reason;
PetscErrorCode ierr;
PetscReal lambda_max = 6.81, lambda_min = 0.0, error;
Vec x;
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
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,"Example only works for one process.");
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Initialize problem parameters
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PetscBagCreate(PETSC_COMM_WORLD, sizeof(AppCtx), &bag);CHKERRQ(ierr);
ierr = PetscBagGetData(bag, (void**) &user);CHKERRQ(ierr);
ierr = PetscBagSetName(bag, "params", "Parameters for SNES example 4");CHKERRQ(ierr);
ierr = PetscBagRegisterReal(bag, &user->alpha, 1.0, "alpha", "Linear coefficient");CHKERRQ(ierr);
ierr = PetscBagRegisterReal(bag, &user->lambda, 6.0, "lambda", "Nonlinear coefficient");CHKERRQ(ierr);
ierr = PetscBagSetFromOptions(bag);CHKERRQ(ierr);
ierr = PetscOptionsGetReal(NULL,"-alpha",&user->alpha,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetReal(NULL,"-lambda",&user->lambda,NULL);CHKERRQ(ierr);
if (user->lambda > lambda_max || user->lambda < lambda_min) SETERRQ3(PETSC_COMM_SELF,1,"Lambda %g is out of range [%g, %g]", (double)user->lambda, (double)lambda_min, (double)lambda_max);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create multilevel DM data structure (SNES) to manage hierarchical solvers
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = SNESCreate(PETSC_COMM_WORLD,&snes);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create distributed array (DMDA) to manage parallel grid and vectors
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_BOX,-3,-3,PETSC_DECIDE,PETSC_DECIDE,3,1,NULL,NULL,&da);CHKERRQ(ierr);
ierr = DMDASetFieldName(da, 0, "ooblek");CHKERRQ(ierr);
ierr = DMSetApplicationContext(da,user);CHKERRQ(ierr);
ierr = SNESSetDM(snes, (DM) da);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set the discretization functions
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
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);
ierr = SNESSetComputeInitialGuess(snes, FormInitialGuess,NULL);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve nonlinear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = SNESSolve(snes,NULL,NULL);CHKERRQ(ierr);
ierr = SNESGetIterationNumber(snes,&its);CHKERRQ(ierr);
ierr = SNESGetConvergedReason(snes, &reason);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PetscPrintf(PETSC_COMM_WORLD,"Number of SNES iterations = %D, %s\n",its,SNESConvergedReasons[reason]);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
ierr = SNESGetDM(snes,&da);CHKERRQ(ierr);
ierr = SNESGetSolution(snes,&x);CHKERRQ(ierr);
ierr = L_2Error(da, x, &error, user);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"L_2 error in the solution: %g\n", (double)error);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Free work space. All PETSc objects should be destroyed when they
are no longer needed.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = SNESDestroy(&snes);CHKERRQ(ierr);
ierr = PetscBagDestroy(&bag);CHKERRQ(ierr);
ierr = PetscFinalize();
PetscFunctionReturn(0);
}