/* 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); }