int main(int argc,char **argv) { TS ts; /* time integration context */ Vec X; /* solution, residual vectors */ Mat J; /* Jacobian matrix */ PetscErrorCode ierr; PetscScalar *x; PetscReal ftime; PetscInt i,steps,nits,lits; PetscBool view_final; Ctx ctx; PetscInitialize(&argc,&argv,(char *)0,help); ctx.n = 3; ierr = PetscOptionsGetInt(PETSC_NULL,"-n",&ctx.n,PETSC_NULL);CHKERRQ(ierr); if (ctx.n < 2) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_ARG_OUTOFRANGE,"The dimension specified with -n must be at least 2"); view_final = PETSC_FALSE; ierr = PetscOptionsGetBool(PETSC_NULL,"-view_final",&view_final,PETSC_NULL);CHKERRQ(ierr); ctx.monitor_short = PETSC_FALSE; ierr = PetscOptionsGetBool(PETSC_NULL,"-monitor_short",&ctx.monitor_short,PETSC_NULL);CHKERRQ(ierr); /* Create Jacobian matrix data structure and state vector */ ierr = MatCreate(PETSC_COMM_WORLD,&J);CHKERRQ(ierr); ierr = MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,ctx.n,ctx.n);CHKERRQ(ierr); ierr = MatSetFromOptions(J);CHKERRQ(ierr); ierr = MatSetUp(J);CHKERRQ(ierr); ierr = MatGetVecs(J,&X,PETSC_NULL);CHKERRQ(ierr); /* Create time integration context */ ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr); ierr = TSSetType(ts,TSPSEUDO);CHKERRQ(ierr); ierr = TSSetIFunction(ts,PETSC_NULL,FormIFunction,&ctx);CHKERRQ(ierr); ierr = TSSetIJacobian(ts,J,J,FormIJacobian,&ctx);CHKERRQ(ierr); ierr = TSSetDuration(ts,1000,1e14);CHKERRQ(ierr); ierr = TSSetInitialTimeStep(ts,0.0,1e-3);CHKERRQ(ierr); ierr = TSMonitorSet(ts,MonitorObjective,&ctx,PETSC_NULL);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Customize time integrator; set runtime options - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = TSSetFromOptions(ts);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Evaluate initial guess; then solve nonlinear system - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = VecSet(X,0.0);CHKERRQ(ierr); ierr = VecGetArray(X,&x);CHKERRQ(ierr); #if 1 x[0] = 5.; x[1] = -5.; for (i=2; i<ctx.n; i++) x[i] = 5.; #else x[0] = 1.0; x[1] = 15.0; for (i=2; i<ctx.n; i++) x[i] = 10.0; #endif ierr = VecRestoreArray(X,&x);CHKERRQ(ierr); ierr = TSSolve(ts,X);CHKERRQ(ierr); ierr = TSGetSolveTime(ts,&ftime);CHKERRQ(ierr); ierr = TSGetTimeStepNumber(ts,&steps);CHKERRQ(ierr); ierr = TSGetSNESIterations(ts,&nits);CHKERRQ(ierr); ierr = TSGetKSPIterations(ts,&lits);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD,"Time integrator took (%D,%D,%D) iterations to reach final time %G\n",steps,nits,lits,ftime);CHKERRQ(ierr); if (view_final) { ierr = VecView(X,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr); } /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Free work space. All PETSc objects should be destroyed when they are no longer needed. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = VecDestroy(&X);CHKERRQ(ierr); ierr = MatDestroy(&J);CHKERRQ(ierr); ierr = TSDestroy(&ts);CHKERRQ(ierr); ierr = PetscFinalize(); return 0; }
int main(int argc,char **argv) { TS ts; /* nonlinear solver */ Vec x; /* solution, residual vectors */ Mat A; /* Jacobian matrix */ PetscInt steps; PetscReal ftime = 0.5; PetscBool monitor = PETSC_FALSE; PetscScalar *x_ptr; PetscMPIInt size; struct _n_User user; PetscErrorCode ierr; /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Initialize program - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ PetscInitialize(&argc,&argv,NULL,help); ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr); if (size != 1) SETERRQ(PETSC_COMM_SELF,1,"This is a uniprocessor example only!"); /* Register user-specified ARKIMEX method */ ierr = RegisterMyARK2();CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Set runtime options - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ user.imex = PETSC_TRUE; user.next_output = 0.0; user.mu = 1.0e6; ierr = PetscOptionsGetBool(NULL,"-imex",&user.imex,NULL);CHKERRQ(ierr); ierr = PetscOptionsGetBool(NULL,"-monitor",&monitor,NULL);CHKERRQ(ierr); ierr = PetscOptionsReal("-mu","Stiffness parameter","<1.0e6>",user.mu,&user.mu,NULL); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Create necessary matrix and vectors, solve same ODE on every process - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr); ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,2,2);CHKERRQ(ierr); ierr = MatSetFromOptions(A);CHKERRQ(ierr); ierr = MatSetUp(A);CHKERRQ(ierr); ierr = MatGetVecs(A,&x,NULL);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Create timestepping solver context - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr); ierr = TSSetType(ts,TSBEULER);CHKERRQ(ierr); ierr = TSSetRHSFunction(ts,NULL,RHSFunction,&user);CHKERRQ(ierr); ierr = TSSetIFunction(ts,NULL,IFunction,&user);CHKERRQ(ierr); ierr = TSSetIJacobian(ts,A,A,IJacobian,&user);CHKERRQ(ierr); ierr = TSSetDuration(ts,PETSC_DEFAULT,ftime);CHKERRQ(ierr); if (monitor) { ierr = TSMonitorSet(ts,Monitor,&user,NULL);CHKERRQ(ierr); } /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Set initial conditions - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = VecGetArray(x,&x_ptr);CHKERRQ(ierr); x_ptr[0] = 2.0; x_ptr[1] = -6.666665432100101e-01; ierr = VecRestoreArray(x,&x_ptr);CHKERRQ(ierr); ierr = TSSetInitialTimeStep(ts,0.0,.001);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Set runtime options - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = TSSetFromOptions(ts);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Solve nonlinear system - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = TSSolve(ts,x);CHKERRQ(ierr); ierr = TSGetSolveTime(ts,&ftime);CHKERRQ(ierr); ierr = TSGetTimeStepNumber(ts,&steps);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD,"steps %D, ftime %g\n",steps,(double)ftime);CHKERRQ(ierr); ierr = VecView(x,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Free work space. All PETSc objects should be destroyed when they are no longer needed. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = MatDestroy(&A);CHKERRQ(ierr); ierr = VecDestroy(&x);CHKERRQ(ierr); ierr = TSDestroy(&ts);CHKERRQ(ierr); ierr = PetscFinalize(); PetscFunctionReturn(0); }
PetscErrorCode Brusselator(int argc,char **argv,PetscInt cycle) { TS ts; /* nonlinear solver */ Vec X; /* solution, residual vectors */ Mat J; /* Jacobian matrix */ PetscInt steps,maxsteps,mx; PetscErrorCode ierr; DM da; PetscReal ftime,hx,dt,xmax,xmin; struct _User user; /* user-defined work context */ TSConvergedReason reason; ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr; /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Create distributed array (DMDA) to manage parallel grid and vectors - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,-11,2,2,NULL,&da);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Extract global vectors from DMDA; - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = DMCreateGlobalVector(da,&X);CHKERRQ(ierr); /* Initialize user application context */ ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Advection-reaction options",""); { user.A = 1; user.B = 3; user.alpha = 0.1; user.uleft = 1; user.uright = 1; user.vleft = 3; user.vright = 3; ierr = PetscOptionsReal("-A","Reaction rate","",user.A,&user.A,NULL);CHKERRQ(ierr); ierr = PetscOptionsReal("-B","Reaction rate","",user.B,&user.B,NULL);CHKERRQ(ierr); ierr = PetscOptionsReal("-alpha","Diffusion coefficient","",user.alpha,&user.alpha,NULL);CHKERRQ(ierr); ierr = PetscOptionsReal("-uleft","Dirichlet boundary condition","",user.uleft,&user.uleft,NULL);CHKERRQ(ierr); ierr = PetscOptionsReal("-uright","Dirichlet boundary condition","",user.uright,&user.uright,NULL);CHKERRQ(ierr); ierr = PetscOptionsReal("-vleft","Dirichlet boundary condition","",user.vleft,&user.vleft,NULL);CHKERRQ(ierr); ierr = PetscOptionsReal("-vright","Dirichlet boundary condition","",user.vright,&user.vright,NULL);CHKERRQ(ierr); } ierr = PetscOptionsEnd();CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Create timestepping solver context - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr); ierr = TSSetDM(ts,da);CHKERRQ(ierr); ierr = TSSetType(ts,TSARKIMEX);CHKERRQ(ierr); ierr = TSSetRHSFunction(ts,NULL,FormRHSFunction,&user);CHKERRQ(ierr); ierr = TSSetIFunction(ts,NULL,FormIFunction,&user);CHKERRQ(ierr); ierr = DMSetMatType(da,MATAIJ);CHKERRQ(ierr); ierr = DMCreateMatrix(da,&J);CHKERRQ(ierr); ierr = TSSetIJacobian(ts,J,J,FormIJacobian,&user);CHKERRQ(ierr); ftime = 1.0; maxsteps = 10000; ierr = TSSetDuration(ts,maxsteps,ftime);CHKERRQ(ierr); ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Set initial conditions - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = FormInitialSolution(ts,X,&user);CHKERRQ(ierr); ierr = TSSetSolution(ts,X);CHKERRQ(ierr); ierr = VecGetSize(X,&mx);CHKERRQ(ierr); hx = 1.0/(PetscReal)(mx/2-1); dt = 0.4 * PetscSqr(hx) / user.alpha; /* Diffusive stability limit */ dt *= PetscPowRealInt(0.2,cycle); /* Shrink the time step in convergence study. */ ierr = TSSetInitialTimeStep(ts,0.0,dt);CHKERRQ(ierr); ierr = TSSetTolerances(ts,1e-3*PetscPowRealInt(0.5,cycle),NULL,1e-3*PetscPowRealInt(0.5,cycle),NULL);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Set runtime options - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = TSSetFromOptions(ts);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Solve nonlinear system - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = TSSolve(ts,X);CHKERRQ(ierr); ierr = TSGetSolveTime(ts,&ftime);CHKERRQ(ierr); ierr = TSGetTimeStepNumber(ts,&steps);CHKERRQ(ierr); ierr = TSGetConvergedReason(ts,&reason);CHKERRQ(ierr); ierr = VecMin(X,NULL,&xmin);CHKERRQ(ierr); ierr = VecMax(X,NULL,&xmax);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD,"%s at time %g after % 3D steps. Range [%6.4f,%6.4f]\n",TSConvergedReasons[reason],(double)ftime,steps,(double)xmin,(double)xmax);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Free work space. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = MatDestroy(&J);CHKERRQ(ierr); ierr = VecDestroy(&X);CHKERRQ(ierr); ierr = TSDestroy(&ts);CHKERRQ(ierr); ierr = DMDestroy(&da);CHKERRQ(ierr); ierr = PetscFinalize(); return ierr; }
int main(int argc, char *argv[]) { PetscMPIInt size; TS ts; Vec R; Mat J; Vec U,V; PetscScalar *u,*v; UserParams user = {/*Omega=*/ 1, /*Xi=*/ 0, /*u0=*/ 1, /*,v0=*/ 0}; PetscErrorCode ierr; ierr = PetscInitialize(&argc,&argv,NULL,help);CHKERRQ(ierr); ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr); if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs"); ierr = PetscOptionsBegin(PETSC_COMM_SELF,"","ex43 options","");CHKERRQ(ierr); ierr = PetscOptionsReal("-frequency","Natual frequency",__FILE__,user.Omega,&user.Omega,NULL);CHKERRQ(ierr); ierr = PetscOptionsReal("-damping","Damping coefficient",__FILE__,user.Xi,&user.Xi,NULL);CHKERRQ(ierr); ierr = PetscOptionsReal("-initial_u","Initial displacement",__FILE__,user.u0,&user.u0,NULL);CHKERRQ(ierr); ierr = PetscOptionsReal("-initial_v","Initial velocity",__FILE__,user.v0,&user.v0,NULL);CHKERRQ(ierr); ierr = PetscOptionsEnd();CHKERRQ(ierr); ierr = TSCreate(PETSC_COMM_SELF,&ts);CHKERRQ(ierr); ierr = TSSetType(ts,TSALPHA2);CHKERRQ(ierr); ierr = TSSetMaxTime(ts,5*(2*PETSC_PI));CHKERRQ(ierr); ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);CHKERRQ(ierr); ierr = TSSetTimeStep(ts,0.01);CHKERRQ(ierr); ierr = VecCreateSeq(PETSC_COMM_SELF,1,&R);CHKERRQ(ierr); ierr = VecSetUp(R);CHKERRQ(ierr); ierr = MatCreateSeqDense(PETSC_COMM_SELF,1,1,NULL,&J);CHKERRQ(ierr); ierr = MatSetUp(J);CHKERRQ(ierr); if (user.Xi) { ierr = TSSetI2Function(ts,R,Residual2,&user);CHKERRQ(ierr); ierr = TSSetI2Jacobian(ts,J,J,Tangent2,&user);CHKERRQ(ierr); } else { ierr = TSSetIFunction(ts,R,Residual1,&user);CHKERRQ(ierr); ierr = TSSetIJacobian(ts,J,J,Tangent1,&user);CHKERRQ(ierr); } ierr = VecDestroy(&R);CHKERRQ(ierr); ierr = MatDestroy(&J);CHKERRQ(ierr); ierr = TSSetSolutionFunction(ts,Solution,&user);CHKERRQ(ierr); ierr = VecCreateSeq(PETSC_COMM_SELF,1,&U);CHKERRQ(ierr); ierr = VecCreateSeq(PETSC_COMM_SELF,1,&V);CHKERRQ(ierr); ierr = VecGetArray(U,&u);CHKERRQ(ierr); ierr = VecGetArray(V,&v);CHKERRQ(ierr); u[0] = user.u0; v[0] = user.v0; ierr = VecRestoreArray(U,&u);CHKERRQ(ierr); ierr = VecRestoreArray(V,&v);CHKERRQ(ierr); ierr = TS2SetSolution(ts,U,V);CHKERRQ(ierr); ierr = TSSetFromOptions(ts);CHKERRQ(ierr); ierr = TSSolve(ts,NULL);CHKERRQ(ierr); ierr = VecDestroy(&U);CHKERRQ(ierr); ierr = VecDestroy(&V);CHKERRQ(ierr); ierr = TSDestroy(&ts);CHKERRQ(ierr); ierr = PetscFinalize(); return ierr; }
int main(int argc,char **argv) { TS ts; /* nonlinear solver */ Vec u; /* solution, residual vectors */ Mat J; /* Jacobian matrix */ PetscInt maxsteps = 1000; /* iterations for convergence */ PetscInt nsteps; PetscReal vmin,vmax,norm; PetscErrorCode ierr; DM da; PetscReal ftime,dt; AppCtx user; /* user-defined work context */ JacobianType jacType; PetscInitialize(&argc,&argv,(char*)0,help); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Create distributed array (DMDA) to manage parallel grid and vectors - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = DMDACreate1d(PETSC_COMM_WORLD,DMDA_BOUNDARY_NONE,-11,1,1,NULL,&da); CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Extract global vectors from DMDA; - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = DMCreateGlobalVector(da,&u); CHKERRQ(ierr); /* Initialize user application context */ user.c = -30.0; user.boundary = 0; /* 0: Dirichlet BC; 1: Neumann BC */ user.viewJacobian = PETSC_FALSE; ierr = PetscOptionsGetInt(NULL,"-boundary",&user.boundary,NULL); CHKERRQ(ierr); ierr = PetscOptionsHasName(NULL,"-viewJacobian",&user.viewJacobian); CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Create timestepping solver context - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = TSCreate(PETSC_COMM_WORLD,&ts); CHKERRQ(ierr); ierr = TSSetProblemType(ts,TS_NONLINEAR); CHKERRQ(ierr); ierr = TSSetType(ts,TSTHETA); CHKERRQ(ierr); ierr = TSThetaSetTheta(ts,1.0); CHKERRQ(ierr); /* Make the Theta method behave like backward Euler */ ierr = TSSetIFunction(ts,NULL,FormIFunction,&user); CHKERRQ(ierr); ierr = DMSetMatType(da,MATAIJ); CHKERRQ(ierr); ierr = DMCreateMatrix(da,&J); CHKERRQ(ierr); jacType = JACOBIAN_ANALYTIC; /* use user-provide Jacobian */ ierr = TSSetDM(ts,da); CHKERRQ(ierr); /* Use TSGetDM() to access. Setting here allows easy use of geometric multigrid. */ ftime = 1.0; ierr = TSSetDuration(ts,maxsteps,ftime); CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Set initial conditions - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = FormInitialSolution(ts,u,&user); CHKERRQ(ierr); ierr = TSSetSolution(ts,u); CHKERRQ(ierr); dt = .01; ierr = TSSetInitialTimeStep(ts,0.0,dt); CHKERRQ(ierr); /* 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); CHKERRQ(ierr); ierr = PetscOptionsEnum("-jac_type","Type of Jacobian","",JacobianTypes,(PetscEnum)jacType,(PetscEnum*)&jacType,0); CHKERRQ(ierr); ierr = PetscOptionsEnd(); CHKERRQ(ierr); if (jacType == JACOBIAN_ANALYTIC) { ierr = TSSetIJacobian(ts,J,J,FormIJacobian,&user); CHKERRQ(ierr); } else if (jacType == JACOBIAN_FD_COLORING) { SNES snes; ierr = TSGetSNES(ts,&snes); CHKERRQ(ierr); ierr = SNESSetJacobian(snes,J,J,SNESComputeJacobianDefaultColor,0); CHKERRQ(ierr); } else if (jacType == JACOBIAN_FD_FULL) { SNES snes; ierr = TSGetSNES(ts,&snes); CHKERRQ(ierr); ierr = SNESSetJacobian(snes,J,J,SNESComputeJacobianDefault,&user); CHKERRQ(ierr); } /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Set runtime options - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = TSSetFromOptions(ts); CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Integrate ODE system - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = TSSolve(ts,u); CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Compute diagnostics of the solution - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = VecNorm(u,NORM_1,&norm); CHKERRQ(ierr); ierr = VecMax(u,NULL,&vmax); CHKERRQ(ierr); ierr = VecMin(u,NULL,&vmin); CHKERRQ(ierr); ierr = TSGetTimeStepNumber(ts,&nsteps); CHKERRQ(ierr); ierr = TSGetTime(ts,&ftime); CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD,"timestep %D: time %G, solution norm %G, max %G, min %G\n",nsteps,ftime,norm,vmax,vmin); CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Free work space. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = MatDestroy(&J); CHKERRQ(ierr); ierr = VecDestroy(&u); CHKERRQ(ierr); ierr = TSDestroy(&ts); CHKERRQ(ierr); ierr = DMDestroy(&da); CHKERRQ(ierr); ierr = PetscFinalize(); PetscFunctionReturn(0); }
int main(int argc, char **argv) { TS ts; Vec x; /*solution vector*/ Mat A; /*Jacobian*/ PetscInt steps,maxsteps,mx; PetscErrorCode ierr; PetscReal ftime; AppCtx user; /* user-defined work context */ PetscInitialize(&argc,&argv,NULL,help); /* Initialize user application context */ ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Allen-Cahn equation",""); user.param = 9e-4; user.xleft = -1.; user.xright = 2.; user.mx = 400; ierr = PetscOptionsReal("-eps","parameter","",user.param,&user.param,NULL);CHKERRQ(ierr); ierr = PetscOptionsEnd();CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Set runtime options - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ /* * ierr = PetscOptionsGetBool(NULL,"-monitor",&monitor,NULL);CHKERRQ(ierr); */ /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Create necessary matrix and vectors, solve same ODE on every process - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr); ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,user.mx,user.mx);CHKERRQ(ierr); ierr = MatSetFromOptions(A);CHKERRQ(ierr); ierr = MatSetUp(A);CHKERRQ(ierr); ierr = MatGetVecs(A,&x,NULL);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Create time stepping solver context - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr); ierr = TSSetType(ts,TSEIMEX);CHKERRQ(ierr); ierr = TSSetRHSFunction(ts,NULL,RHSFunction,&user);CHKERRQ(ierr); ierr = TSSetIFunction(ts,NULL,FormIFunction,&user);CHKERRQ(ierr); ierr = TSSetIJacobian(ts,A,A,FormIJacobian,&user);CHKERRQ(ierr); ftime = 142; maxsteps = 100000; ierr = TSSetDuration(ts,maxsteps,ftime);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Set initial conditions - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = FormInitialSolution(ts,x,&user);CHKERRQ(ierr); ierr = TSSetSolution(ts,x);CHKERRQ(ierr); ierr = VecGetSize(x,&mx);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Set runtime options - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = TSSetFromOptions(ts);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Solve nonlinear system - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = TSSolve(ts,x);CHKERRQ(ierr); ierr = TSGetTime(ts,&ftime);CHKERRQ(ierr); ierr = TSGetTimeStepNumber(ts,&steps);CHKERRQ(ierr); ierr = PetscPrintf(PETSC_COMM_WORLD,"eps %G, steps %D, ftime %G\n",user.param,steps,ftime);CHKERRQ(ierr); /* ierr = VecView(x,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);*/ /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Free work space. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = MatDestroy(&A);CHKERRQ(ierr); ierr = VecDestroy(&x);CHKERRQ(ierr); ierr = TSDestroy(&ts);CHKERRQ(ierr); ierr = PetscFinalize(); PetscFunctionReturn(0); }
int main(int argc,char **argv) { TS ts; /* nonlinear solver */ Vec u,r; /* solution, residual vectors */ Mat J,Jmf = NULL; /* Jacobian matrices */ PetscInt maxsteps = 1000; /* iterations for convergence */ PetscErrorCode ierr; DM da; PetscReal dt; AppCtx user; /* user-defined work context */ SNES snes; PetscInt Jtype; /* Jacobian type 0: user provide Jacobian; 1: slow finite difference; 2: fd with coloring; */ PetscInitialize(&argc,&argv,(char*)0,help); /* Initialize user application context */ user.da = NULL; user.nstencilpts = 5; user.c = -30.0; user.boundary = 0; /* 0: Drichlet BC; 1: Neumann BC */ user.viewJacobian = PETSC_FALSE; ierr = PetscOptionsGetInt(NULL,"-nstencilpts",&user.nstencilpts,NULL);CHKERRQ(ierr); ierr = PetscOptionsGetInt(NULL,"-boundary",&user.boundary,NULL);CHKERRQ(ierr); ierr = PetscOptionsHasName(NULL,"-viewJacobian",&user.viewJacobian);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Create distributed array (DMDA) to manage parallel grid and vectors - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ if (user.nstencilpts == 5) { ierr = DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,-11,-11,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);CHKERRQ(ierr); } else if (user.nstencilpts == 9) { ierr = DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_BOX,-11,-11,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);CHKERRQ(ierr); } else SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"nstencilpts %d is not supported",user.nstencilpts); user.da = da; /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Extract global vectors from DMDA; - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = DMCreateGlobalVector(da,&u);CHKERRQ(ierr); ierr = VecDuplicate(u,&r);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Create timestepping solver context - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr); ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr); ierr = TSSetType(ts,TSBEULER);CHKERRQ(ierr); ierr = TSSetDM(ts,da);CHKERRQ(ierr); ierr = TSSetIFunction(ts,r,FormIFunction,&user);CHKERRQ(ierr); ierr = TSSetDuration(ts,maxsteps,1.0);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Set initial conditions - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = FormInitialSolution(u,&user);CHKERRQ(ierr); ierr = TSSetSolution(ts,u);CHKERRQ(ierr); dt = .01; ierr = TSSetInitialTimeStep(ts,0.0,dt);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Set Jacobian evaluation routine - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = DMSetMatType(da,MATAIJ);CHKERRQ(ierr); ierr = DMCreateMatrix(da,&J);CHKERRQ(ierr); Jtype = 0; ierr = PetscOptionsGetInt(NULL, "-Jtype",&Jtype,NULL);CHKERRQ(ierr); if (Jtype == 0) { /* use user provided Jacobian evaluation routine */ if (user.nstencilpts != 5) SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"user Jacobian routine FormIJacobian() does not support nstencilpts=%D",user.nstencilpts); ierr = TSSetIJacobian(ts,J,J,FormIJacobian,&user);CHKERRQ(ierr); } else { /* use finite difference Jacobian J as preconditioner and '-snes_mf_operator' for Mat*vec */ ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr); ierr = MatCreateSNESMF(snes,&Jmf);CHKERRQ(ierr); if (Jtype == 1) { /* slow finite difference J; */ ierr = SNESSetJacobian(snes,Jmf,J,SNESComputeJacobianDefault,NULL);CHKERRQ(ierr); } else if (Jtype == 2) { /* Use coloring to compute finite difference J efficiently */ ierr = SNESSetJacobian(snes,Jmf,J,SNESComputeJacobianDefaultColor,0);CHKERRQ(ierr); } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Jtype is not supported"); } /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Sets various TS parameters from user options - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = TSSetFromOptions(ts);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Solve nonlinear system - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = TSSolve(ts,u);CHKERRQ(ierr); /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Free work space. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ ierr = MatDestroy(&J);CHKERRQ(ierr); ierr = MatDestroy(&Jmf);CHKERRQ(ierr); ierr = VecDestroy(&u);CHKERRQ(ierr); ierr = VecDestroy(&r);CHKERRQ(ierr); ierr = TSDestroy(&ts);CHKERRQ(ierr); ierr = DMDestroy(&da);CHKERRQ(ierr); ierr = PetscFinalize(); PetscFunctionReturn(0); }