int main(int argc,char **argv)
{
PetscErrorCode ierr;
SNES snes; /* nonlinear solver */
Vec Hu,r; /* solution, residual vectors */
Mat J; /* Jacobian matrix */
AppCtx user; /* user-defined work context */
PetscInt its, i, tmpxs, tmpxm; /* iteration count, index, etc. */
PetscReal tmp1, tmp2, tmp3, tmp4, tmp5,
errnorms[2], descaleNode[2];
PetscTruth eps_set = PETSC_FALSE, dump = PETSC_FALSE, exactinitial = PETSC_FALSE,
snes_mf_set, snes_fd_set;
MatFDColoring matfdcoloring = 0;
ISColoring iscoloring;
SNESConvergedReason reason; /* Check convergence */
PetscInitialize(&argc,&argv,(char *)0,help);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD, &user.rank); CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,
"BODVARDSSON solves for thickness and velocity in 1D, steady ice stream\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.g = 9.81; /* m s^-2 */
/* ask Test N for its parameters, but only those we need to solve */
ierr = params_exactN(&(user.H0), &tmp1, &(user.xc), &tmp2, &tmp3, &tmp4, &tmp5,
&(user.Txc)); CHKERRQ(ierr);
/* regularize using strain rate of 1/xc per year */
user.epsilon = (1.0 / user.secpera) / user.xc;
/* tools for non-dimensionalizing to improve equation scaling */
user.scaleNode[0] = 1000.0; user.scaleNode[1] = 100.0 / user.secpera;
ierr = PetscOptionsTruth("-snes_mf","","",PETSC_FALSE,&snes_mf_set,NULL);CHKERRQ(ierr);
ierr = PetscOptionsTruth("-snes_fd","","",PETSC_FALSE,&snes_fd_set,NULL);CHKERRQ(ierr);
if (!snes_mf_set && !snes_fd_set) {
PetscPrintf(PETSC_COMM_WORLD,
"\n***ERROR: bodvardsson needs one or zero of '-snes_mf', '-snes_fd'***\n\n"
"USAGE FOLLOWS ...\n\n%s",help);
PetscEnd();
}
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);
}
ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,
"bodvardsson program options",__FILE__);CHKERRQ(ierr);
{
ierr = PetscOptionsTruth("-bod_up_one","","",PETSC_FALSE,&user.upwind1,NULL);CHKERRQ(ierr);
ierr = PetscOptionsTruth("-bod_exact_init","","",PETSC_FALSE,&exactinitial,NULL);CHKERRQ(ierr);
ierr = PetscOptionsTruth("-bod_dump",
"dump out exact and approximate solution and residual, as asci","",
dump,&dump,NULL);CHKERRQ(ierr);
ierr = PetscOptionsReal("-bod_epsilon","regularization (a strain rate in units of 1/a)","",
user.epsilon * user.secpera,&user.epsilon,&eps_set);CHKERRQ(ierr);
if (eps_set) user.epsilon *= 1.0 / user.secpera;
}
ierr = PetscOptionsEnd();CHKERRQ(ierr);
/* Create machinery for parallel grid management (DA), nonlinear solver (SNES),
and Vecs for fields (solution, RHS). Note default Mx=46 grid points means
dx=10 km. Also degrees of freedom = 2 (thickness and velocity
at each point) and stencil radius = ghost width = 2 for 2nd-order upwinding. */
user.solnghostwidth = 2;
ierr = DACreate1d(PETSC_COMM_WORLD,DA_NONPERIODIC,-46,2,user.solnghostwidth,PETSC_NULL,&user.da);
CHKERRQ(ierr);
ierr = DASetUniformCoordinates(user.da,0.0,user.xc,
PETSC_NULL,PETSC_NULL,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
ierr = DASetFieldName(user.da,0,"ice thickness [non-dimensional]"); CHKERRQ(ierr);
ierr = DASetFieldName(user.da,1,"ice velocity [non-dimensional]"); CHKERRQ(ierr);
ierr = DAGetInfo(user.da,PETSC_IGNORE,&user.Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
ierr = DAGetCorners(user.da,&user.xs,PETSC_NULL,PETSC_NULL,&user.xm,PETSC_NULL,PETSC_NULL);
CHKERRQ(ierr);
user.dx = user.xc / (PetscReal)(user.Mx-1);
/* another DA for scalar parameters, with same length */
ierr = DACreate1d(PETSC_COMM_WORLD,DA_NONPERIODIC,user.Mx,1,1,PETSC_NULL,&user.scalarda);CHKERRQ(ierr);
ierr = DASetUniformCoordinates(user.scalarda,0.0,user.xc,
PETSC_NULL,PETSC_NULL,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
/* check that parallel layout of scalar DA is same as dof=2 DA */
ierr = DAGetCorners(user.scalarda,&tmpxs,PETSC_NULL,PETSC_NULL,&tmpxm,PETSC_NULL,PETSC_NULL);
CHKERRQ(ierr);
if ((tmpxs != user.xs) || (tmpxm != user.xm)) {
PetscPrintf(PETSC_COMM_SELF,
"\n***ERROR: rank %d gets different ownership range for the two DAs! ENDING ...***\n\n",
user.rank);
PetscEnd();
}
ierr = PetscPrintf(PETSC_COMM_WORLD,
" Mx = %D points, dx = %.3f m\n H0 = %.2f m, xc = %.2f km, Txc = %.5e Pa m\n",
user.Mx, user.dx, user.H0, user.xc/1000.0, user.Txc);CHKERRQ(ierr);
/* Extract/allocate global vectors from DAs and duplicate for remaining same types */
ierr = DACreateGlobalVector(user.da,&Hu);CHKERRQ(ierr);
ierr = VecSetBlockSize(Hu,2);CHKERRQ(ierr);
ierr = VecDuplicate(Hu,&r);CHKERRQ(ierr); /* inherits block size */
ierr = VecDuplicate(Hu,&user.Huexact);CHKERRQ(ierr); /* ditto */
ierr = DACreateGlobalVector(user.scalarda,&user.M);CHKERRQ(ierr);
ierr = VecDuplicate(user.M,&user.Bstag);CHKERRQ(ierr);
ierr = VecDuplicate(user.M,&user.beta);CHKERRQ(ierr);
ierr = DASetLocalFunction(user.da,(DALocalFunction1)scshell);CHKERRQ(ierr);
ierr = DASetLocalJacobian(user.da,(DALocalFunction1)BodJacobianMatrixLocal);CHKERRQ(ierr);
ierr = SNESCreate(PETSC_COMM_WORLD,&snes);CHKERRQ(ierr);
ierr = SNESSetFunction(snes,r,SNESDAFormFunction,&user);CHKERRQ(ierr);
/* setting up a matrix is only actually needed for -snes_fd case */
ierr = DAGetMatrix(user.da,MATAIJ,&J);CHKERRQ(ierr);
if (snes_fd_set) {
/* tools needed so DA can use sparse matrix for its F.D. Jacobian approx */
ierr = DAGetColoring(user.da,IS_COLORING_GLOBAL,MATAIJ,&iscoloring);CHKERRQ(ierr);
ierr = MatFDColoringCreate(J,iscoloring,&matfdcoloring);CHKERRQ(ierr);
ierr = ISColoringDestroy(iscoloring);CHKERRQ(ierr);
ierr = MatFDColoringSetFunction(matfdcoloring,
(PetscErrorCode (*)(void))SNESDAFormFunction,&user);CHKERRQ(ierr);
ierr = MatFDColoringSetFromOptions(matfdcoloring);CHKERRQ(ierr);
ierr = SNESSetJacobian(snes,J,J,SNESDefaultComputeJacobianColor,matfdcoloring);CHKERRQ(ierr);
} else {
ierr = SNESSetJacobian(snes,J,J,SNESDAComputeJacobian,&user);CHKERRQ(ierr);
}
ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
/* the the Bodvardsson (1955) exact solution allows setting M(x), B(x), beta(x), T(xc) */
ierr = FillDistributedParams(&user);CHKERRQ(ierr);
/* the exact thickness and exact ice velocity (user.uHexact) are known from Bodvardsson (1955) */
ierr = FillExactSoln(&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(user.Huexact,Hu); CHKERRQ(ierr);
} else {
ierr = FillInitial(&user, &Hu); CHKERRQ(ierr);
}
/************ SOLVE NONLINEAR SYSTEM ************/
/* recall that RHS r is used internally by KSP, and is set by the SNES */
for (i = 0; i < 2; i++) descaleNode[i] = 1.0 / user.scaleNode[i];
ierr = VecStrideScaleAll(Hu,descaleNode); CHKERRQ(ierr); /* de-dimensionalize initial guess */
ierr = SNESSolve(snes,PETSC_NULL,Hu);CHKERRQ(ierr);
ierr = VecStrideScaleAll(Hu,user.scaleNode); CHKERRQ(ierr); /* put back in "real" scale */
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,
" viewing combined result Hu\n");CHKERRQ(ierr);
ierr = VecView(Hu,PETSC_VIEWER_STDOUT_WORLD); CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,
" viewing combined exact result Huexact\n");CHKERRQ(ierr);
ierr = VecView(user.Huexact,PETSC_VIEWER_STDOUT_WORLD); CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,
" viewing final combined residual at Hu\n");CHKERRQ(ierr);
ierr = VecView(r,PETSC_VIEWER_STDOUT_WORLD); CHKERRQ(ierr);
}
/* evaluate error relative to exact solution */
ierr = VecAXPY(Hu,-1.0,user.Huexact); 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(r);CHKERRQ(ierr);
ierr = VecDestroy(user.Huexact);CHKERRQ(ierr);
ierr = VecDestroy(user.M);CHKERRQ(ierr);
ierr = VecDestroy(user.Bstag);CHKERRQ(ierr);
ierr = VecDestroy(user.beta);CHKERRQ(ierr);
ierr = MatDestroy(J); CHKERRQ(ierr);
ierr = SNESDestroy(snes);CHKERRQ(ierr);
ierr = DADestroy(user.da);CHKERRQ(ierr);
ierr = DADestroy(user.scalarda);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;
}