static const char help[] = "Time-dependent PDE in 1d. Simplified from ex15.c for illustrating how to solve DAEs. \n"; /* u_t = uxx 0 < x < 1; At t=0: u(x) = exp(c*r*r*r), if r=PetscSqrtReal((x-.5)*(x-.5)) < .125 u(x) = 0.0 if r >= .125 Boundary conditions: Dirichlet BC: At x=0, x=1, u = 0.0 Neumann BC: At x=0, x=1: du(x,t)/dx = 0 mpiexec -n 2 ./ex17 -da_grid_x 40 -ts_max_steps 2 -snes_monitor -ksp_monitor ./ex17 -da_grid_x 40 -monitor_solution ./ex17 -da_grid_x 100 -ts_type theta -ts_theta_theta 0.5 # Midpoint is not L-stable ./ex17 -jac_type fd_coloring -da_grid_x 500 -boundary 1 ./ex17 -da_grid_x 100 -ts_type gl -ts_adapt_type none -ts_max_steps 2 */ #include #include #include typedef enum {JACOBIAN_ANALYTIC,JACOBIAN_FD_COLORING,JACOBIAN_FD_FULL} JacobianType; static const char *const JacobianTypes[] = {"analytic","fd_coloring","fd_full","JacobianType","fd_",0}; /* User-defined data structures and routines */ typedef struct { PetscReal c; PetscInt boundary; /* Type of boundary condition */ PetscBool viewJacobian; } AppCtx; static PetscErrorCode FormIFunction(TS,PetscReal,Vec,Vec,Vec,void*); static PetscErrorCode FormIJacobian(TS,PetscReal,Vec,Vec,PetscReal,Mat,Mat,void*); static PetscErrorCode FormInitialSolution(TS,Vec,void*); int main(int argc,char **argv) { TS ts; /* nonlinear solver */ Vec u; /* solution, residual vectors */ Mat J; /* Jacobian matrix */ PetscInt nsteps; PetscReal vmin,vmax,norm; PetscErrorCode ierr; DM da; PetscReal ftime,dt; AppCtx user; /* user-defined work context */ JacobianType jacType; PetscCall(PetscInitialize(&argc,&argv,(char*)0,help)); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Create distributed array (DMDA) to manage parallel grid and vectors - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,11,1,1,NULL,&da)); PetscCall(DMSetFromOptions(da)); PetscCall(DMSetUp(da)); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Extract global vectors from DMDA; - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(DMCreateGlobalVector(da,&u)); /* Initialize user application context */ user.c = -30.0; user.boundary = 0; /* 0: Dirichlet BC; 1: Neumann BC */ user.viewJacobian = PETSC_FALSE; PetscCall(PetscOptionsGetInt(NULL,NULL,"-boundary",&user.boundary,NULL)); PetscCall(PetscOptionsHasName(NULL,NULL,"-viewJacobian",&user.viewJacobian)); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Create timestepping solver context - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(TSCreate(PETSC_COMM_WORLD,&ts)); PetscCall(TSSetProblemType(ts,TS_NONLINEAR)); PetscCall(TSSetType(ts,TSTHETA)); PetscCall(TSThetaSetTheta(ts,1.0)); /* Make the Theta method behave like backward Euler */ PetscCall(TSSetIFunction(ts,NULL,FormIFunction,&user)); PetscCall(DMSetMatType(da,MATAIJ)); PetscCall(DMCreateMatrix(da,&J)); jacType = JACOBIAN_ANALYTIC; /* use user-provide Jacobian */ PetscCall(TSSetDM(ts,da)); /* Use TSGetDM() to access. Setting here allows easy use of geometric multigrid. */ ftime = 1.0; PetscCall(TSSetMaxTime(ts,ftime)); PetscCall(TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER)); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Set initial conditions - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(FormInitialSolution(ts,u,&user)); PetscCall(TSSetSolution(ts,u)); dt = .01; PetscCall(TSSetTimeStep(ts,dt)); /* Use slow fd Jacobian or fast fd Jacobian with colorings. Note: this requirs snes which is not created until TSSetUp()/TSSetFromOptions() is called */ ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Options for Jacobian evaluation",NULL);PetscCall(ierr); PetscCall(PetscOptionsEnum("-jac_type","Type of Jacobian","",JacobianTypes,(PetscEnum)jacType,(PetscEnum*)&jacType,0)); ierr = PetscOptionsEnd();PetscCall(ierr); if (jacType == JACOBIAN_ANALYTIC) { PetscCall(TSSetIJacobian(ts,J,J,FormIJacobian,&user)); } else if (jacType == JACOBIAN_FD_COLORING) { SNES snes; PetscCall(TSGetSNES(ts,&snes)); PetscCall(SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor,0)); } else if (jacType == JACOBIAN_FD_FULL) { SNES snes; PetscCall(TSGetSNES(ts,&snes)); PetscCall(SNESSetJacobian(snes,J,J,SNESComputeJacobianDefault,&user)); } /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Set runtime options - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(TSSetFromOptions(ts)); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Integrate ODE system - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(TSSolve(ts,u)); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Compute diagnostics of the solution - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(VecNorm(u,NORM_1,&norm)); PetscCall(VecMax(u,NULL,&vmax)); PetscCall(VecMin(u,NULL,&vmin)); PetscCall(TSGetStepNumber(ts,&nsteps)); PetscCall(TSGetTime(ts,&ftime)); PetscCall(PetscPrintf(PETSC_COMM_WORLD,"timestep %D: time %g, solution norm %g, max %g, min %g\n",nsteps,(double)ftime,(double)norm,(double)vmax,(double)vmin)); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Free work space. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscCall(MatDestroy(&J)); PetscCall(VecDestroy(&u)); PetscCall(TSDestroy(&ts)); PetscCall(DMDestroy(&da)); PetscCall(PetscFinalize()); return 0; } /* ------------------------------------------------------------------- */ static PetscErrorCode FormIFunction(TS ts,PetscReal ftime,Vec U,Vec Udot,Vec F,void *ptr) { AppCtx *user=(AppCtx*)ptr; DM da; PetscInt i,Mx,xs,xm; PetscReal hx,sx; PetscScalar *u,*udot,*f; Vec localU; PetscFunctionBeginUser; PetscCall(TSGetDM(ts,&da)); PetscCall(DMGetLocalVector(da,&localU)); PetscCall(DMDAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE)); hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx); /* Scatter ghost points to local vector,using the 2-step process DMGlobalToLocalBegin(),DMGlobalToLocalEnd(). By placing code between these two statements, computations can be done while messages are in transition. */ PetscCall(DMGlobalToLocalBegin(da,U,INSERT_VALUES,localU)); PetscCall(DMGlobalToLocalEnd(da,U,INSERT_VALUES,localU)); /* Get pointers to vector data */ PetscCall(DMDAVecGetArrayRead(da,localU,&u)); PetscCall(DMDAVecGetArrayRead(da,Udot,&udot)); PetscCall(DMDAVecGetArray(da,F,&f)); /* Get local grid boundaries */ PetscCall(DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL)); /* Compute function over the locally owned part of the grid */ for (i=xs; iboundary == 0) { /* Dirichlet BC */ if (i == 0 || i == Mx-1) f[i] = u[i]; /* F = U */ else f[i] = udot[i] + (2.*u[i] - u[i-1] - u[i+1])*sx; } else { /* Neumann BC */ if (i == 0) f[i] = u[0] - u[1]; else if (i == Mx-1) f[i] = u[i] - u[i-1]; else f[i] = udot[i] + (2.*u[i] - u[i-1] - u[i+1])*sx; } } /* Restore vectors */ PetscCall(DMDAVecRestoreArrayRead(da,localU,&u)); PetscCall(DMDAVecRestoreArrayRead(da,Udot,&udot)); PetscCall(DMDAVecRestoreArray(da,F,&f)); PetscCall(DMRestoreLocalVector(da,&localU)); PetscFunctionReturn(0); } /* --------------------------------------------------------------------- */ /* IJacobian - Compute IJacobian = dF/dU + a dF/dUdot */ PetscErrorCode FormIJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat J,Mat Jpre,void *ctx) { PetscInt i,rstart,rend,Mx; PetscReal hx,sx; AppCtx *user = (AppCtx*)ctx; DM da; MatStencil col[3],row; PetscInt nc; PetscScalar vals[3]; PetscFunctionBeginUser; PetscCall(TSGetDM(ts,&da)); PetscCall(MatGetOwnershipRange(Jpre,&rstart,&rend)); PetscCall(DMDAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE)); hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx); for (i=rstart; iboundary == 0 && (i == 0 || i == Mx-1)) { col[nc].i = i; vals[nc++] = 1.0; } else if (user->boundary > 0 && i == 0) { /* Left Neumann */ col[nc].i = i; vals[nc++] = 1.0; col[nc].i = i+1; vals[nc++] = -1.0; } else if (user->boundary > 0 && i == Mx-1) { /* Right Neumann */ col[nc].i = i-1; vals[nc++] = -1.0; col[nc].i = i; vals[nc++] = 1.0; } else { /* Interior */ col[nc].i = i-1; vals[nc++] = -1.0*sx; col[nc].i = i; vals[nc++] = 2.0*sx + a; col[nc].i = i+1; vals[nc++] = -1.0*sx; } PetscCall(MatSetValuesStencil(Jpre,1,&row,nc,col,vals,INSERT_VALUES)); } PetscCall(MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY)); PetscCall(MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY)); if (J != Jpre) { PetscCall(MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY)); PetscCall(MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY)); } if (user->viewJacobian) { PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Jpre:\n")); PetscCall(MatView(Jpre,PETSC_VIEWER_STDOUT_WORLD)); } PetscFunctionReturn(0); } /* ------------------------------------------------------------------- */ PetscErrorCode FormInitialSolution(TS ts,Vec U,void *ptr) { AppCtx *user=(AppCtx*)ptr; PetscReal c =user->c; DM da; PetscInt i,xs,xm,Mx; PetscScalar *u; PetscReal hx,x,r; PetscFunctionBeginUser; PetscCall(TSGetDM(ts,&da)); PetscCall(DMDAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE)); hx = 1.0/(PetscReal)(Mx-1); /* Get pointers to vector data */ PetscCall(DMDAVecGetArray(da,U,&u)); /* Get local grid boundaries */ PetscCall(DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL)); /* Compute function over the locally owned part of the grid */ for (i=xs; i