/* FormPositivityBounds() for call-back: tell SNESVI (variational inequality)
that we want positive solutions for both W and P */
PetscErrorCode FormPositivityBounds(SNES snes, Vec Xl, Vec Xu) {
VecStrideSet(Xl,0,0.0); /* W >= 0 */
VecStrideSet(Xl,1,0.0); /* P >= 0 */
VecStrideSet(Xu,0,SNES_VI_INF);
VecStrideSet(Xu,1,SNES_VI_INF);
PetscFunctionReturn(0);
}
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)
{
TS ts; /* nonlinear solver */
Vec x,r; /* solution, residual vectors */
Mat J; /* Jacobian matrix */
PetscInt steps,Mx,maxsteps = 10000000;
PetscErrorCode ierr;
DM da;
MatFDColoring matfdcoloring;
ISColoring iscoloring;
PetscReal dt;
PetscReal vbounds[] = {-100000,100000,-1.1,1.1};
PetscBool wait;
Vec ul,uh;
SNES snes;
UserCtx ctx;
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Initialize program
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
ctx.kappa = 1.0;
ierr = PetscOptionsGetReal(NULL,"-kappa",&ctx.kappa,NULL);CHKERRQ(ierr);
ctx.cahnhillard = PETSC_FALSE;
ierr = PetscOptionsGetBool(NULL,NULL,"-cahn-hillard",&ctx.cahnhillard,NULL);CHKERRQ(ierr);
ierr = PetscViewerDrawSetBounds(PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD),2,vbounds);CHKERRQ(ierr);
ierr = PetscViewerDrawResize(PETSC_VIEWER_DRAW_(PETSC_COMM_WORLD),600,600);CHKERRQ(ierr);
ctx.energy = 1;
/* ierr = PetscOptionsGetInt(NULL,NULL,"-energy",&ctx.energy,NULL);CHKERRQ(ierr); */
ierr = PetscOptionsGetInt(NULL,NULL,"-energy",&ctx.energy,NULL);CHKERRQ(ierr);
ctx.tol = 1.0e-8;
ierr = PetscOptionsGetReal(NULL,"-tol",&ctx.tol,NULL);CHKERRQ(ierr);
ctx.theta = .001;
ctx.theta_c = 1.0;
ierr = PetscOptionsGetReal(NULL,"-theta",&ctx.theta,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetReal(NULL,"-theta_c",&ctx.theta_c,NULL);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create distributed array (DMDA) to manage parallel grid and vectors
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_PERIODIC, -10,2,2,NULL,&da);CHKERRQ(ierr);
ierr = DMSetFromOptions(da);CHKERRQ(ierr);
ierr = DMSetUp(da);CHKERRQ(ierr);
ierr = DMDASetFieldName(da,0,"Biharmonic heat equation: w = -kappa*u_xx");CHKERRQ(ierr);
ierr = DMDASetFieldName(da,1,"Biharmonic heat equation: u");CHKERRQ(ierr);
ierr = DMDAGetInfo(da,0,&Mx,0,0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
dt = 1.0/(10.*ctx.kappa*Mx*Mx*Mx*Mx);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Extract global vectors from DMDA; then duplicate for remaining
vectors that are the same types
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = DMCreateGlobalVector(da,&x);CHKERRQ(ierr);
ierr = VecDuplicate(x,&r);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create timestepping solver context
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
ierr = TSSetDM(ts,da);CHKERRQ(ierr);
ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr);
ierr = TSSetIFunction(ts,NULL,FormFunction,&ctx);CHKERRQ(ierr);
ierr = TSSetDuration(ts,maxsteps,.02);CHKERRQ(ierr);
ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create matrix data structure; set Jacobian evaluation routine
< Set Jacobian matrix data structure and default Jacobian evaluation
routine. User can override with:
-snes_mf : matrix-free Newton-Krylov method with no preconditioning
(unless user explicitly sets preconditioner)
-snes_mf_operator : form preconditioning matrix as set by the user,
but use matrix-free approx for Jacobian-vector
products within Newton-Krylov method
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
ierr = DMCreateColoring(da,IS_COLORING_GLOBAL,&iscoloring);CHKERRQ(ierr);
ierr = DMSetMatType(da,MATAIJ);CHKERRQ(ierr);
ierr = DMCreateMatrix(da,&J);CHKERRQ(ierr);
ierr = MatFDColoringCreate(J,iscoloring,&matfdcoloring);CHKERRQ(ierr);
ierr = ISColoringDestroy(&iscoloring);CHKERRQ(ierr);
ierr = MatFDColoringSetFunction(matfdcoloring,(PetscErrorCode (*)(void))SNESTSFormFunction,ts);CHKERRQ(ierr);
ierr = MatFDColoringSetFromOptions(matfdcoloring);CHKERRQ(ierr);
ierr = MatFDColoringSetUp(J,iscoloring,matfdcoloring);CHKERRQ(ierr);
ierr = SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor,matfdcoloring);CHKERRQ(ierr);
{
ierr = VecDuplicate(x,&ul);CHKERRQ(ierr);
ierr = VecDuplicate(x,&uh);CHKERRQ(ierr);
ierr = VecStrideSet(ul,0,PETSC_NINFINITY);CHKERRQ(ierr);
ierr = VecStrideSet(ul,1,-1.0);CHKERRQ(ierr);
ierr = VecStrideSet(uh,0,PETSC_INFINITY);CHKERRQ(ierr);
ierr = VecStrideSet(uh,1,1.0);CHKERRQ(ierr);
ierr = TSVISetVariableBounds(ts,ul,uh);CHKERRQ(ierr);
}
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Customize nonlinear solver
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetType(ts,TSBEULER);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set initial conditions
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = FormInitialSolution(da,x,ctx.kappa);CHKERRQ(ierr);
ierr = TSSetInitialTimeStep(ts,0.0,dt);CHKERRQ(ierr);
ierr = TSSetSolution(ts,x);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Set runtime options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve nonlinear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = TSSolve(ts,x);CHKERRQ(ierr);
wait = PETSC_FALSE;
ierr = PetscOptionsGetBool(NULL,NULL,"-wait",&wait,NULL);CHKERRQ(ierr);
if (wait) {
ierr = PetscSleep(-1);CHKERRQ(ierr);
}
ierr = TSGetTimeStepNumber(ts,&steps);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Free work space. All PETSc objects should be destroyed when they
are no longer needed.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
{
ierr = VecDestroy(&ul);CHKERRQ(ierr);
ierr = VecDestroy(&uh);CHKERRQ(ierr);
}
ierr = MatDestroy(&J);CHKERRQ(ierr);
ierr = MatFDColoringDestroy(&matfdcoloring);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&r);CHKERRQ(ierr);
ierr = TSDestroy(&ts);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
ierr = PetscFinalize();
PetscFunctionReturn(0);
}
