C++ PetscInitialize函数代码示例

/*******************************************************************************
 * For each run, the input filename and restart information (if needed) must   *
 * be given on the command line.  For non-restarted case, command line is:     *
 *                                                                             *
 *    executable <input file name>                                             *
 *                                                                             *
 * For restarted run, command line is:                                         *
 *                                                                             *
 *    executable <input file name> <restart directory> <restart number>        *
 *                                                                             *
 *******************************************************************************/
bool
run_example(int argc, char* argv[])
{
    // Initialize PETSc, MPI, and SAMRAI.
    PetscInitialize(&argc, &argv, NULL, NULL);
    SAMRAI_MPI::setCommunicator(PETSC_COMM_WORLD);
    SAMRAI_MPI::setCallAbortInSerialInsteadOfExit();
    SAMRAIManager::startup();

    { // cleanup dynamically allocated objects prior to shutdown

        // Parse command line options, set some standard options from the input
        // file, initialize the restart database (if this is a restarted run),
        // and enable file logging.
        Pointer<AppInitializer> app_initializer = new AppInitializer(argc, argv, "IB.log");
        Pointer<Database> input_db = app_initializer->getInputDatabase();

        // Get various standard options set in the input file.
        const bool dump_viz_data = app_initializer->dumpVizData();
        const int viz_dump_interval = app_initializer->getVizDumpInterval();
        const bool uses_visit = dump_viz_data && !app_initializer->getVisItDataWriter().isNull();

        const bool dump_restart_data = app_initializer->dumpRestartData();
        const int restart_dump_interval = app_initializer->getRestartDumpInterval();
        const string restart_dump_dirname = app_initializer->getRestartDumpDirectory();

        const bool dump_postproc_data = app_initializer->dumpPostProcessingData();
        const int postproc_data_dump_interval = app_initializer->getPostProcessingDataDumpInterval();
        const string postproc_data_dump_dirname = app_initializer->getPostProcessingDataDumpDirectory();
        if (dump_postproc_data && (postproc_data_dump_interval > 0) && !postproc_data_dump_dirname.empty())
        {
            Utilities::recursiveMkdir(postproc_data_dump_dirname);
        }

        const bool dump_timer_data = app_initializer->dumpTimerData();
        const int timer_dump_interval = app_initializer->getTimerDumpInterval();

        // Create major algorithm and data objects that comprise the
        // application.  These objects are configured from the input database
        // and, if this is a restarted run, from the restart database.
        Pointer<INSHierarchyIntegrator> navier_stokes_integrator = new INSStaggeredHierarchyIntegrator(
            "INSStaggeredHierarchyIntegrator",
            app_initializer->getComponentDatabase("INSStaggeredHierarchyIntegrator"));

        const int num_structures = input_db->getIntegerWithDefault("num_structures", 1);
        Pointer<ConstraintIBMethod> ib_method_ops = new ConstraintIBMethod(
            "ConstraintIBMethod", app_initializer->getComponentDatabase("ConstraintIBMethod"), num_structures);
        Pointer<IBHierarchyIntegrator> time_integrator =
            new IBExplicitHierarchyIntegrator("IBHierarchyIntegrator",
                                              app_initializer->getComponentDatabase("IBHierarchyIntegrator"),
                                              ib_method_ops,
                                              navier_stokes_integrator);

        Pointer<CartesianGridGeometry<NDIM> > grid_geometry = new CartesianGridGeometry<NDIM>(
            "CartesianGeometry", app_initializer->getComponentDatabase("CartesianGeometry"));
        Pointer<PatchHierarchy<NDIM> > patch_hierarchy = new PatchHierarchy<NDIM>("PatchHierarchy", grid_geometry);

        Pointer<StandardTagAndInitialize<NDIM> > error_detector =
            new StandardTagAndInitialize<NDIM>("StandardTagAndInitialize",
                                               time_integrator,
                                               app_initializer->getComponentDatabase("StandardTagAndInitialize"));
        Pointer<BergerRigoutsos<NDIM> > box_generator = new BergerRigoutsos<NDIM>();
        Pointer<LoadBalancer<NDIM> > load_balancer =
            new LoadBalancer<NDIM>("LoadBalancer", app_initializer->getComponentDatabase("LoadBalancer"));
        Pointer<GriddingAlgorithm<NDIM> > gridding_algorithm =
            new GriddingAlgorithm<NDIM>("GriddingAlgorithm",
                                        app_initializer->getComponentDatabase("GriddingAlgorithm"),
                                        error_detector,
                                        box_generator,
                                        load_balancer);

        // Configure the IB solver.
        Pointer<IBStandardInitializer> ib_initializer = new IBStandardInitializer(
            "IBStandardInitializer", app_initializer->getComponentDatabase("IBStandardInitializer"));
        ib_method_ops->registerLInitStrategy(ib_initializer);
        Pointer<IBStandardForceGen> ib_force_fcn = new IBStandardForceGen();
        ib_method_ops->registerIBLagrangianForceFunction(ib_force_fcn);

        // Create Eulerian initial condition specification objects.
        if (input_db->keyExists("VelocityInitialConditions"))
        {
            Pointer<CartGridFunction> u_init = new muParserCartGridFunction(
                "u_init", app_initializer->getComponentDatabase("VelocityInitialConditions"), grid_geometry);
            navier_stokes_integrator->registerVelocityInitialConditions(u_init);
        }

        if (input_db->keyExists("PressureInitialConditions"))
        {
            Pointer<CartGridFunction> p_init = new muParserCartGridFunction(
//.........这里部分代码省略.........

/*******************************************************************************
 * For each run, the input filename and restart information (if needed) must   *
 * be given on the command line.  For non-restarted case, command line is:     *
 *                                                                             *
 *    executable <input file name>                                             *
 *                                                                             *
 * For restarted run, command line is:                                         *
 *                                                                             *
 *    executable <input file name> <restart directory> <restart number>        *
 *                                                                             *
 *******************************************************************************/
int main(int argc, char* argv[])
{
    // Initialize PETSc, MPI, and SAMRAI.
    PetscInitialize(&argc, &argv, NULL, NULL);
    SAMRAI_MPI::setCommunicator(PETSC_COMM_WORLD);
    SAMRAI_MPI::setCallAbortInSerialInsteadOfExit();
    SAMRAIManager::startup();

    { // cleanup dynamically allocated objects prior to shutdown

        // Parse command line options, set some standard options from the input
        // file, initialize the restart database (if this is a restarted run),
        // and enable file logging.
        Pointer<AppInitializer> app_initializer = new AppInitializer(argc, argv, "INS.log");
        Pointer<Database> input_db = app_initializer->getInputDatabase();

        // Get various standard options set in the input file.
        const bool dump_viz_data = app_initializer->dumpVizData();
        const int viz_dump_interval = app_initializer->getVizDumpInterval();
        const bool uses_visit = dump_viz_data && app_initializer->getVisItDataWriter();

        const bool dump_restart_data = app_initializer->dumpRestartData();
        const int restart_dump_interval = app_initializer->getRestartDumpInterval();
        const string restart_dump_dirname = app_initializer->getRestartDumpDirectory();

        const bool dump_postproc_data = app_initializer->dumpPostProcessingData();
        const int postproc_data_dump_interval = app_initializer->getPostProcessingDataDumpInterval();
        const string postproc_data_dump_dirname = app_initializer->getPostProcessingDataDumpDirectory();

        const bool dump_timer_data = app_initializer->dumpTimerData();
        const int timer_dump_interval = app_initializer->getTimerDumpInterval();

        // Create major algorithm and data objects that comprise the
        // application.  These objects are configured from the input database
        // and, if this is a restarted run, from the restart database.
        Pointer<INSHierarchyIntegrator> time_integrator;
        const string solver_type =
            app_initializer->getComponentDatabase("Main")->getStringWithDefault("solver_type", "STAGGERED");
        if (solver_type == "STAGGERED")
        {
            time_integrator = new INSStaggeredHierarchyIntegrator(
                "INSStaggeredHierarchyIntegrator",
                app_initializer->getComponentDatabase("INSStaggeredHierarchyIntegrator"));
        }
        else if (solver_type == "COLLOCATED")
        {
            time_integrator = new INSCollocatedHierarchyIntegrator(
                "INSCollocatedHierarchyIntegrator",
                app_initializer->getComponentDatabase("INSCollocatedHierarchyIntegrator"));
        }
        else
        {
            TBOX_ERROR("Unsupported solver type: " << solver_type << "\n"
                                                   << "Valid options are: COLLOCATED, STAGGERED");
        }
        Pointer<CartesianGridGeometry<NDIM> > grid_geometry = new CartesianGridGeometry<NDIM>(
            "CartesianGeometry", app_initializer->getComponentDatabase("CartesianGeometry"));
        Pointer<PatchHierarchy<NDIM> > patch_hierarchy = new PatchHierarchy<NDIM>("PatchHierarchy", grid_geometry);
        Pointer<StandardTagAndInitialize<NDIM> > error_detector =
            new StandardTagAndInitialize<NDIM>("StandardTagAndInitialize", time_integrator,
                                               app_initializer->getComponentDatabase("StandardTagAndInitialize"));
        Pointer<BergerRigoutsos<NDIM> > box_generator = new BergerRigoutsos<NDIM>();
        Pointer<LoadBalancer<NDIM> > load_balancer =
            new LoadBalancer<NDIM>("LoadBalancer", app_initializer->getComponentDatabase("LoadBalancer"));
        Pointer<GriddingAlgorithm<NDIM> > gridding_algorithm =
            new GriddingAlgorithm<NDIM>("GriddingAlgorithm", app_initializer->getComponentDatabase("GriddingAlgorithm"),
                                        error_detector, box_generator, load_balancer);

        // Create initial condition specification objects.
        if (input_db->keyExists("VelocityInitialConditions"))
        {
            Pointer<CartGridFunction> u_init = new muParserCartGridFunction(
                "u_init", app_initializer->getComponentDatabase("VelocityInitialConditions"), grid_geometry);
            time_integrator->registerVelocityInitialConditions(u_init);
        }

        // Create boundary condition specification objects (when necessary).
        const IntVector<NDIM>& periodic_shift = grid_geometry->getPeriodicShift();
        vector<RobinBcCoefStrategy<NDIM>*> u_bc_coefs(NDIM);
        if (periodic_shift.min() > 0)
        {
            for (unsigned int d = 0; d < NDIM; ++d)
            {
                u_bc_coefs[d] = NULL;
            }
        }
        else
        {
            for (unsigned int d = 0; d < NDIM; ++d)
//.........这里部分代码省略.........

int main(int argc,char **argv)
{
  AppCtx         user;                /* user-defined work context */
  PetscInt       mx,my,its;
  PetscErrorCode ierr;
  MPI_Comm       comm;
  SNES           snes;
  DM             da;
  Vec            x,X,b;
  PetscBool      youngflg,poissonflg,muflg,lambdaflg,view=PETSC_FALSE,viewline=PETSC_FALSE;
  PetscReal      poisson=0.2,young=4e4;
  char           filename[PETSC_MAX_PATH_LEN] = "ex16.vts";
  char           filename_def[PETSC_MAX_PATH_LEN] = "ex16_def.vts";

  ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
  ierr = FormElements();CHKERRQ(ierr);
  comm = PETSC_COMM_WORLD;
  ierr = SNESCreate(comm,&snes);CHKERRQ(ierr);
  ierr = DMDACreate3d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_BOX,11,2,2,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,3,1,NULL,NULL,NULL,&da);CHKERRQ(ierr);
  ierr = DMSetFromOptions(da);CHKERRQ(ierr);
  ierr = DMSetUp(da);CHKERRQ(ierr);
  ierr = SNESSetDM(snes,(DM)da);CHKERRQ(ierr);

  ierr = SNESSetNGS(snes,NonlinearGS,&user);CHKERRQ(ierr);

  ierr = DMDAGetInfo(da,0,&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.loading     = 0.0;
  user.arc         = PETSC_PI/3.;
  user.mu          = 4.0;
  user.lambda      = 1.0;
  user.rad         = 100.0;
  user.height      = 3.;
  user.width       = 1.;
  user.ploading    = -5e3;

  ierr = PetscOptionsGetReal(NULL,NULL,"-arc",&user.arc,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetReal(NULL,NULL,"-mu",&user.mu,&muflg);CHKERRQ(ierr);
  ierr = PetscOptionsGetReal(NULL,NULL,"-lambda",&user.lambda,&lambdaflg);CHKERRQ(ierr);
  ierr = PetscOptionsGetReal(NULL,NULL,"-rad",&user.rad,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetReal(NULL,NULL,"-height",&user.height,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetReal(NULL,NULL,"-width",&user.width,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetReal(NULL,NULL,"-loading",&user.loading,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetReal(NULL,NULL,"-ploading",&user.ploading,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetReal(NULL,NULL,"-poisson",&poisson,&poissonflg);CHKERRQ(ierr);
  ierr = PetscOptionsGetReal(NULL,NULL,"-young",&young,&youngflg);CHKERRQ(ierr);
  if ((youngflg || poissonflg) || !(muflg || lambdaflg)) {
    /* set the lame' parameters based upon the poisson ratio and young's modulus */
    user.lambda = poisson*young / ((1. + poisson)*(1. - 2.*poisson));
    user.mu     = young/(2.*(1. + poisson));
  }
  ierr = PetscOptionsGetBool(NULL,NULL,"-view",&view,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetBool(NULL,NULL,"-view_line",&viewline,NULL);CHKERRQ(ierr);

  ierr = DMDASetFieldName(da,0,"x_disp");CHKERRQ(ierr);
  ierr = DMDASetFieldName(da,1,"y_disp");CHKERRQ(ierr);
  ierr = DMDASetFieldName(da,2,"z_disp");CHKERRQ(ierr);

  ierr = DMSetApplicationContext(da,&user);CHKERRQ(ierr);
  ierr = DMDASNESSetFunctionLocal(da,INSERT_VALUES,(PetscErrorCode (*)(DMDALocalInfo*,void*,void*,void*))FormFunctionLocal,&user);CHKERRQ(ierr);
  ierr = DMDASNESSetJacobianLocal(da,(DMDASNESJacobian)FormJacobianLocal,&user);CHKERRQ(ierr);
  ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);
  ierr = FormCoordinates(da,&user);CHKERRQ(ierr);

  ierr = DMCreateGlobalVector(da,&x);CHKERRQ(ierr);
  ierr = DMCreateGlobalVector(da,&b);CHKERRQ(ierr);
  ierr = InitialGuess(da,&user,x);CHKERRQ(ierr);
  ierr = FormRHS(da,&user,b);CHKERRQ(ierr);

  ierr = PetscPrintf(comm,"lambda: %f mu: %f\n",(double)user.lambda,(double)user.mu);CHKERRQ(ierr);

  /* show a cross-section of the initial state */
  if (viewline) {
    ierr = DisplayLine(snes,x);CHKERRQ(ierr);
  }

  /* get the loaded configuration */
  ierr = SNESSolve(snes,b,x);CHKERRQ(ierr);

  ierr = SNESGetIterationNumber(snes,&its);CHKERRQ(ierr);
  ierr = PetscPrintf(comm,"Number of SNES iterations = %D\n", its);CHKERRQ(ierr);
  ierr = SNESGetSolution(snes,&X);CHKERRQ(ierr);
  /* show a cross-section of the final state */
  if (viewline) {
    ierr = DisplayLine(snes,X);CHKERRQ(ierr);
  }

  if (view) {
    PetscViewer viewer;
    Vec         coords;
    ierr = PetscViewerVTKOpen(PETSC_COMM_WORLD,filename,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr);
    ierr = VecView(x,viewer);CHKERRQ(ierr);
    ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
    ierr = DMGetCoordinates(da,&coords);CHKERRQ(ierr);
    ierr = VecAXPY(coords,1.0,x);CHKERRQ(ierr);
    ierr = PetscViewerVTKOpen(PETSC_COMM_WORLD,filename_def,FILE_MODE_WRITE,&viewer);CHKERRQ(ierr);
    ierr = VecView(x,viewer);CHKERRQ(ierr);
    ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
  }

  ierr = VecDestroy(&x);CHKERRQ(ierr);
//.........这里部分代码省略.........

int main(int argc,char **args)
{
  Vec            x,y,u,s1,s2;
  Mat            A,sA,sB;
  PetscRandom    rctx;
  PetscReal      r1,r2,rnorm,tol=1.e-10;
  PetscScalar    one=1.0, neg_one=-1.0, value[3], four=4.0,alpha=0.1;
  PetscInt       n,col[3],n1,block,row,i,j,i2,j2,Ii,J,rstart,rend,bs=1,mbs=16,d_nz=3,o_nz=3,prob=2;
  PetscErrorCode ierr;
  PetscMPIInt    size,rank;
  PetscBool      flg;
  MatType        type;

  PetscInitialize(&argc,&args,(char*)0,help);
  ierr = PetscOptionsGetInt(NULL,"-mbs",&mbs,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetInt(NULL,"-bs",&bs,NULL);CHKERRQ(ierr);

  ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
  ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);

  n = mbs*bs;

  /* Assemble MPISBAIJ matrix sA */
  ierr = MatCreate(PETSC_COMM_WORLD,&sA);CHKERRQ(ierr);
  ierr = MatSetSizes(sA,PETSC_DECIDE,PETSC_DECIDE,n,n);CHKERRQ(ierr);
  ierr = MatSetType(sA,MATSBAIJ);CHKERRQ(ierr);
  ierr = MatSetFromOptions(sA);CHKERRQ(ierr);
  ierr = MatGetType(sA,&type);CHKERRQ(ierr);
  /* printf(" mattype: %s\n",type); */
  ierr = MatMPISBAIJSetPreallocation(sA,bs,d_nz,NULL,o_nz,NULL);CHKERRQ(ierr);
  ierr = MatSeqSBAIJSetPreallocation(sA,bs,d_nz,NULL);CHKERRQ(ierr);
  ierr = MatSetOption(sA,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);

  if (bs == 1) {
    if (prob == 1) { /* tridiagonal matrix */
      value[0] = -1.0; value[1] = 2.0; value[2] = -1.0;
      for (i=1; i<n-1; i++) {
        col[0] = i-1; col[1] = i; col[2] = i+1;
        ierr   = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
      }
      i       = n - 1; col[0]=0; col[1] = n - 2; col[2] = n - 1;
      value[0]= 0.1; value[1]=-1; value[2]=2;
      ierr    = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);

      i        = 0; col[0] = 0; col[1] = 1; col[2]=n-1;
      value[0] = 2.0; value[1] = -1.0; value[2]=0.1;
      ierr     = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
    } else if (prob ==2) { /* matrix for the five point stencil */
      n1 =  (int) PetscSqrtReal((PetscReal)n);
      if (n1*n1 != n) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"n must be a perfect square of n1");

      for (i=0; i<n1; i++) {
        for (j=0; j<n1; j++) {
          Ii = j + n1*i;
          if (i>0)    {J = Ii - n1; ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);}
          if (i<n1-1) {J = Ii + n1; ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);}
          if (j>0)    {J = Ii - 1;  ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);}
          if (j<n1-1) {J = Ii + 1;  ierr = MatSetValues(sA,1,&Ii,1,&J,&neg_one,INSERT_VALUES);CHKERRQ(ierr);}
          ierr = MatSetValues(sA,1,&Ii,1,&Ii,&four,INSERT_VALUES);CHKERRQ(ierr);
        }
      }
    }
    /* end of if (bs == 1) */
  } else {  /* bs > 1 */
    for (block=0; block<n/bs; block++) {
      /* diagonal blocks */
      value[0] = -1.0; value[1] = 4.0; value[2] = -1.0;
      for (i=1+block*bs; i<bs-1+block*bs; i++) {
        col[0] = i-1; col[1] = i; col[2] = i+1;
        ierr   = MatSetValues(sA,1,&i,3,col,value,INSERT_VALUES);CHKERRQ(ierr);
      }
      i       = bs - 1+block*bs; col[0] = bs - 2+block*bs; col[1] = bs - 1+block*bs;
      value[0]=-1.0; value[1]=4.0;
      ierr    = MatSetValues(sA,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);

      i       = 0+block*bs; col[0] = 0+block*bs; col[1] = 1+block*bs;
      value[0]=4.0; value[1] = -1.0;
      ierr    = MatSetValues(sA,1,&i,2,col,value,INSERT_VALUES);CHKERRQ(ierr);
    }
    /* off-diagonal blocks */
    value[0]=-1.0;
    for (i=0; i<(n/bs-1)*bs; i++) {
      col[0]=i+bs;
      ierr  = MatSetValues(sA,1,&i,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
      col[0]=i; row=i+bs;
      ierr  = MatSetValues(sA,1,&row,1,col,value,INSERT_VALUES);CHKERRQ(ierr);
    }
  }
  ierr = MatAssemblyBegin(sA,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(sA,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

  /* Test MatView() */
  /*
  ierr = MatView(sA, PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
  ierr = MatView(sA, PETSC_VIEWER_DRAW_WORLD);CHKERRQ(ierr);
  */
  /* Assemble MPIBAIJ matrix A */
  ierr = MatCreateBAIJ(PETSC_COMM_WORLD,bs,PETSC_DECIDE,PETSC_DECIDE,n,n,d_nz,NULL,o_nz,NULL,&A);CHKERRQ(ierr);
  ierr = MatSetOption(A,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);

//.........这里部分代码省略.........

int main(int argc,char **argv)
{
  PetscMPIInt      rank;
  PetscErrorCode   ierr;
  PetscInt         M = 10,N = 8,m = PETSC_DECIDE;
  PetscInt         s=2,w=2,n = PETSC_DECIDE,nloc,l,i,j,kk;
  PetscInt         Xs,Xm,Ys,Ym,iloc,*iglobal,*ltog;
  PetscInt         *lx = PETSC_NULL,*ly = PETSC_NULL;
  PetscBool        testorder = PETSC_FALSE,flg;
  DMDABoundaryType bx = DMDA_BOUNDARY_NONE,by= DMDA_BOUNDARY_NONE;
  DM               da;
  PetscViewer      viewer;
  Vec              local,global;
  PetscScalar      value;
  DMDAStencilType  st = DMDA_STENCIL_BOX;
  AO               ao;

  ierr = PetscInitialize(&argc,&argv,(char*)0,help);CHKERRQ(ierr);
  ierr = PetscViewerDrawOpen(PETSC_COMM_WORLD,0,"",300,0,400,400,&viewer);CHKERRQ(ierr);

  /* Readoptions */
  ierr = PetscOptionsGetInt(PETSC_NULL,"-NX",&M,PETSC_NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetInt(PETSC_NULL,"-NY",&N,PETSC_NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetInt(PETSC_NULL,"-m",&m,PETSC_NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetInt(PETSC_NULL,"-s",&s,PETSC_NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetInt(PETSC_NULL,"-w",&w,PETSC_NULL);CHKERRQ(ierr);

  flg  = PETSC_FALSE;
  ierr = PetscOptionsGetBool(PETSC_NULL,"-xperiodic",&flg,PETSC_NULL);CHKERRQ(ierr); if (flg) bx = DMDA_BOUNDARY_PERIODIC;
  flg  = PETSC_FALSE;
  ierr = PetscOptionsGetBool(PETSC_NULL,"-yperiodic",&flg,PETSC_NULL);CHKERRQ(ierr); if (flg) by = DMDA_BOUNDARY_PERIODIC;
  flg  = PETSC_FALSE;
  ierr = PetscOptionsGetBool(PETSC_NULL,"-xghosted",&flg,PETSC_NULL);CHKERRQ(ierr); if (flg) bx = DMDA_BOUNDARY_GHOSTED;
  flg  = PETSC_FALSE;
  ierr = PetscOptionsGetBool(PETSC_NULL,"-yghosted",&flg,PETSC_NULL);CHKERRQ(ierr); if (flg) by = DMDA_BOUNDARY_GHOSTED;
  flg  = PETSC_FALSE;
  ierr = PetscOptionsGetBool(PETSC_NULL,"-star",&flg,PETSC_NULL);CHKERRQ(ierr); if (flg) st = DMDA_STENCIL_STAR;
  flg  = PETSC_FALSE;
  ierr = PetscOptionsGetBool(PETSC_NULL,"-box",&flg,PETSC_NULL);CHKERRQ(ierr); if (flg) st = DMDA_STENCIL_BOX;
  flg  = PETSC_FALSE;
  ierr = PetscOptionsGetBool(PETSC_NULL,"-testorder",&testorder,PETSC_NULL);CHKERRQ(ierr);
  /*
      Test putting two nodes in x and y on each processor, exact last processor
      in x and y gets the rest.
  */
  flg  = PETSC_FALSE;
  ierr = PetscOptionsGetBool(PETSC_NULL,"-distribute",&flg,PETSC_NULL);CHKERRQ(ierr);
  if (flg) {
    if (m == PETSC_DECIDE) SETERRQ(PETSC_COMM_WORLD,1,"Must set -m option with -distribute option");
    ierr = PetscMalloc(m*sizeof(PetscInt),&lx);CHKERRQ(ierr);
    for (i=0; i<m-1; i++) { lx[i] = 4;}
    lx[m-1] = M - 4*(m-1);
    if (n == PETSC_DECIDE) SETERRQ(PETSC_COMM_WORLD,1,"Must set -n option with -distribute option");
    ierr = PetscMalloc(n*sizeof(PetscInt),&ly);CHKERRQ(ierr);
    for (i=0; i<n-1; i++) { ly[i] = 2;}
    ly[n-1] = N - 2*(n-1);
  }


  /* Create distributed array and get vectors */
  ierr = DMDACreate2d(PETSC_COMM_WORLD,bx,by,st,M,N,m,n,w,s,lx,ly,&da);CHKERRQ(ierr);
  ierr = PetscFree(lx);CHKERRQ(ierr);
  ierr = PetscFree(ly);CHKERRQ(ierr);

  ierr = DMView(da,viewer);CHKERRQ(ierr);
  ierr = DMCreateGlobalVector(da,&global);CHKERRQ(ierr);
  ierr = DMCreateLocalVector(da,&local);CHKERRQ(ierr);

  /* Set global vector; send ghost points to local vectors */
  value = 1;
  ierr = VecSet(global,value);CHKERRQ(ierr);
  ierr = DMGlobalToLocalBegin(da,global,INSERT_VALUES,local);CHKERRQ(ierr);
  ierr = DMGlobalToLocalEnd(da,global,INSERT_VALUES,local);CHKERRQ(ierr);

  /* Scale local vectors according to processor rank; pass to global vector */
  ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
  value = rank;
  ierr = VecScale(local,value);CHKERRQ(ierr);
  ierr = DMLocalToGlobalBegin(da,local,INSERT_VALUES,global);CHKERRQ(ierr);
  ierr = DMLocalToGlobalEnd(da,local,INSERT_VALUES,global);CHKERRQ(ierr);

  if (!testorder) { /* turn off printing when testing ordering mappings */
    ierr = PetscPrintf (PETSC_COMM_WORLD,"\nGlobal Vectors:\n");CHKERRQ(ierr);
    ierr = VecView(global,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
    ierr = PetscPrintf (PETSC_COMM_WORLD,"\n\n");CHKERRQ(ierr);
  }

  /* Send ghost points to local vectors */
  ierr = DMGlobalToLocalBegin(da,global,INSERT_VALUES,local);CHKERRQ(ierr);
  ierr = DMGlobalToLocalEnd(da,global,INSERT_VALUES,local);CHKERRQ(ierr);

  flg  = PETSC_FALSE;
  ierr = PetscOptionsGetBool(PETSC_NULL,"-local_print",&flg,PETSC_NULL);CHKERRQ(ierr);
  if (flg) {
    PetscViewer sviewer;
    ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"\nLocal Vector: processor %d\n",rank);CHKERRQ(ierr);
    ierr = PetscViewerGetSingleton(PETSC_VIEWER_STDOUT_WORLD,&sviewer);CHKERRQ(ierr);
    ierr = VecView(local,sviewer);CHKERRQ(ierr);
    ierr = PetscViewerRestoreSingleton(PETSC_VIEWER_STDOUT_WORLD,&sviewer);CHKERRQ(ierr);
//.........这里部分代码省略.........

int main(int argc,char **argv)
{
  TS             ts;            /* ODE integrator */
  Vec            U;             /* solution will be stored here */
  Mat            A;             /* Jacobian matrix */
  PetscErrorCode ierr;
  PetscMPIInt    size;
  PetscInt       n = 2,idx;
  AppCtx         user;
  PetscScalar    *u;
  SNES           snes;
  PetscScalar       *mat;
  const PetscScalar *x;
  Mat         B;
  PetscScalar *amat;
  PetscViewer viewer;



  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Initialize program
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = PetscInitialize(&argc,&argv,(char*)0,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");

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    Create necessary matrix and vectors
    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
  ierr = MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
  ierr = MatSetFromOptions(A);CHKERRQ(ierr);
  ierr = MatSetUp(A);CHKERRQ(ierr);

  ierr = MatCreateVecs(A,&U,NULL);CHKERRQ(ierr);

  /* Create wind speed data using Weibull distribution */
  ierr = WindSpeeds(&user);CHKERRQ(ierr);
  /* Set parameters for wind turbine and induction generator */
  ierr = SetWindTurbineParams(&user);CHKERRQ(ierr);
  ierr = SetInductionGeneratorParams(&user);CHKERRQ(ierr);

  ierr = VecGetArray(U,&u);CHKERRQ(ierr);
  u[0] = vwa;
  u[1] = s;
  ierr = VecRestoreArray(U,&u);CHKERRQ(ierr);

  /* Create matrix to save solutions at each time step */
  user.stepnum = 0;

  ierr = MatCreateSeqDense(PETSC_COMM_SELF,3,2010,NULL,&user.Sol);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 = TSSetIFunction(ts,NULL,(TSIFunction) IFunction,&user);CHKERRQ(ierr);

  ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr);
  ierr = SNESSetJacobian(snes,A,A,SNESComputeJacobianDefault,NULL);CHKERRQ(ierr);
  /*  ierr = TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,&user);CHKERRQ(ierr); */
  ierr = TSSetApplicationContext(ts,&user);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set initial conditions
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = TSSetSolution(ts,U);CHKERRQ(ierr);

  /* Save initial solution */
  idx=3*user.stepnum;

  ierr = MatDenseGetArray(user.Sol,&mat);CHKERRQ(ierr);
  ierr = VecGetArrayRead(U,&x);CHKERRQ(ierr);

  mat[idx] = 0.0;

  ierr = PetscMemcpy(mat+idx+1,x,2*sizeof(PetscScalar));CHKERRQ(ierr);
  ierr = MatDenseRestoreArray(user.Sol,&mat);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(U,&x);CHKERRQ(ierr);
  user.stepnum++;


  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set solver options
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = TSSetDuration(ts,2000,20.0);CHKERRQ(ierr);
  ierr = TSSetInitialTimeStep(ts,0.0,.01);CHKERRQ(ierr);
  ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
  ierr = TSSetPostStep(ts,SaveSolution);CHKERRQ(ierr);
  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Solve nonlinear system
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = TSSolve(ts,U);CHKERRQ(ierr);

  ierr = MatCreateSeqDense(PETSC_COMM_SELF,3,user.stepnum,NULL,&B);CHKERRQ(ierr);
  ierr = MatDenseGetArray(user.Sol,&mat);CHKERRQ(ierr);
  ierr = MatDenseGetArray(B,&amat);CHKERRQ(ierr);
  ierr = PetscMemcpy(amat,mat,user.stepnum*3*sizeof(PetscScalar));CHKERRQ(ierr);
//.........这里部分代码省略.........

int main(int argc,char **argv)
{
  PetscErrorCode ierr;
  KSP            ksp;
  PC             pc;
  Vec            x,b;
  DM             da;
  Mat            A,Atrans;
  PetscInt       dof=1,M=-8;
  PetscBool      flg,trans=PETSC_FALSE;

  PetscInitialize(&argc,&argv,(char *)0,help);
  ierr = PetscOptionsGetInt(PETSC_NULL,"-dof",&dof,PETSC_NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetInt(PETSC_NULL,"-M",&M,PETSC_NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetBool(PETSC_NULL,"-trans",&trans,PETSC_NULL);CHKERRQ(ierr);

  ierr = DMDACreate(PETSC_COMM_WORLD,&da);CHKERRQ(ierr);
  ierr = DMDASetDim(da,3);CHKERRQ(ierr);
  ierr = DMDASetBoundaryType(da,DMDA_BOUNDARY_NONE,DMDA_BOUNDARY_NONE,DMDA_BOUNDARY_NONE);CHKERRQ(ierr);
  ierr = DMDASetStencilType(da,DMDA_STENCIL_STAR);CHKERRQ(ierr);
  ierr = DMDASetSizes(da,M,M,M);CHKERRQ(ierr);
  ierr = DMDASetNumProcs(da,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE);CHKERRQ(ierr);
  ierr = DMDASetDof(da,dof);CHKERRQ(ierr);
  ierr = DMDASetStencilWidth(da,1);CHKERRQ(ierr);
  ierr = DMDASetOwnershipRanges(da,PETSC_NULL,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
  ierr = DMSetFromOptions(da);CHKERRQ(ierr);
  ierr = DMSetUp(da);CHKERRQ(ierr);

  ierr = DMCreateGlobalVector(da,&x);CHKERRQ(ierr);
  ierr = DMCreateGlobalVector(da,&b);CHKERRQ(ierr);
  ierr = ComputeRHS(da,b);CHKERRQ(ierr);
  ierr = DMCreateMatrix(da,MATBAIJ,&A);CHKERRQ(ierr);
  ierr = ComputeMatrix(da,A);CHKERRQ(ierr);


  /* A is non-symmetric. Make A = 0.5*(A + Atrans) symmetric for testing icc and cholesky */
  ierr = MatTranspose(A,MAT_INITIAL_MATRIX,&Atrans);CHKERRQ(ierr);
  ierr = MatAXPY(A,1.0,Atrans,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
  ierr = MatScale(A,0.5);CHKERRQ(ierr);
  ierr = MatDestroy(&Atrans);CHKERRQ(ierr);

  /* Test sbaij matrix */
  flg  = PETSC_FALSE;
  ierr = PetscOptionsGetBool(PETSC_NULL, "-test_sbaij1", &flg,PETSC_NULL);CHKERRQ(ierr);
  if (flg){
    Mat sA;
    PetscBool issymm;
    ierr = MatIsTranspose(A,A,0.0,&issymm);CHKERRQ(ierr);
    if (issymm) {
      ierr = MatSetOption(A,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
    } else {
      printf("Warning: A is non-symmetric\n");
    }
    ierr = MatConvert(A,MATSBAIJ,MAT_INITIAL_MATRIX,&sA);CHKERRQ(ierr);
    ierr = MatDestroy(&A);CHKERRQ(ierr);
    A = sA;
  }

  ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
  ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
  ierr = KSPSetOperators(ksp,A,A,SAME_NONZERO_PATTERN);CHKERRQ(ierr);
  ierr = KSPGetPC(ksp,&pc);CHKERRQ(ierr);
  ierr = PCSetDM(pc,(DM)da);CHKERRQ(ierr);
 
  if (trans) {
    ierr = KSPSolveTranspose(ksp,b,x);CHKERRQ(ierr);
  } else {
    ierr = KSPSolve(ksp,b,x);CHKERRQ(ierr);
  }

  /* check final residual */
  flg  = PETSC_FALSE;
  ierr = PetscOptionsGetBool(PETSC_NULL, "-check_final_residual", &flg,PETSC_NULL);CHKERRQ(ierr);
  if (flg){
    Vec            b1;
    PetscReal      norm;
    ierr = KSPGetSolution(ksp,&x);CHKERRQ(ierr);
    ierr = VecDuplicate(b,&b1);CHKERRQ(ierr);
    ierr = MatMult(A,x,b1);CHKERRQ(ierr);
    ierr = VecAXPY(b1,-1.0,b);CHKERRQ(ierr);
    ierr = VecNorm(b1,NORM_2,&norm);CHKERRQ(ierr);
    ierr = PetscPrintf(PETSC_COMM_WORLD,"Final residual %g\n",norm);CHKERRQ(ierr);
    ierr = VecDestroy(&b1);CHKERRQ(ierr);
  }
   
  ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
  ierr = VecDestroy(&x);CHKERRQ(ierr);
  ierr = VecDestroy(&b);CHKERRQ(ierr);
  ierr = MatDestroy(&A);CHKERRQ(ierr);
  ierr = DMDestroy(&da);CHKERRQ(ierr);
  ierr = PetscFinalize();
  return 0;
}

int main(int argc,char **args)
{
  Mat          C;
  int          i,m = 5,rank,size,N,start,end,M;
  int          ierr,idx[4];
  PetscScalar  Ke[16];
  PetscReal    h;
  Vec          u,b;
  KSP          ksp;
  MatNullSpace nullsp;

  ierr = PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
  ierr = PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);CHKERRQ(ierr);
  N    = (m+1)*(m+1); /* dimension of matrix */
  M    = m*m; /* number of elements */
  h    = 1.0/m;    /* mesh width */
  ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
  ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);

  /* Create stiffness matrix */
  ierr  = MatCreate(PETSC_COMM_WORLD,&C);CHKERRQ(ierr);
  ierr  = MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,N,N);CHKERRQ(ierr);
  ierr  = MatSetFromOptions(C);CHKERRQ(ierr);
  ierr  = MatSetUp(C);CHKERRQ(ierr);
  start = rank*(M/size) + ((M%size) < rank ? (M%size) : rank);
  end   = start + M/size + ((M%size) > rank);

  /* Assemble matrix */
  ierr = FormElementStiffness(h*h,Ke);   /* element stiffness for Laplacian */
  for (i=start; i<end; i++) {
    /* location of lower left corner of element */
    /* node numbers for the four corners of element */
    idx[0] = (m+1)*(i/m) + (i % m);
    idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
    ierr   = MatSetValues(C,4,idx,4,idx,Ke,ADD_VALUES);CHKERRQ(ierr);
  }
  ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

  /* Create right-hand-side and solution vectors */
  ierr = VecCreate(PETSC_COMM_WORLD,&u);CHKERRQ(ierr);
  ierr = VecSetSizes(u,PETSC_DECIDE,N);CHKERRQ(ierr);
  ierr = VecSetFromOptions(u);CHKERRQ(ierr);
  ierr = PetscObjectSetName((PetscObject)u,"Approx. Solution");CHKERRQ(ierr);
  ierr = VecDuplicate(u,&b);CHKERRQ(ierr);
  ierr = PetscObjectSetName((PetscObject)b,"Right hand side");CHKERRQ(ierr);

  ierr = VecSet(b,1.0);CHKERRQ(ierr);
  ierr = VecSetValue(b,0,1.2,ADD_VALUES);CHKERRQ(ierr);
  ierr = VecSet(u,0.0);CHKERRQ(ierr);

  /* Solve linear system */
  ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
  ierr = KSPSetOperators(ksp,C,C);CHKERRQ(ierr);
  ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
  ierr = KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);CHKERRQ(ierr);

  ierr = MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,NULL,&nullsp);CHKERRQ(ierr);
  /*
     The KSP solver will remove this nullspace from the solution at each iteration
  */
  ierr = MatSetNullSpace(C,nullsp);CHKERRQ(ierr);
  /*
     The KSP solver will remove from the right hand side any portion in this nullspace, thus making the linear system consistent.
  */
  ierr = MatSetTransposeNullSpace(C,nullsp);CHKERRQ(ierr);
  ierr = MatNullSpaceDestroy(&nullsp);CHKERRQ(ierr);

  ierr = KSPSolve(ksp,b,u);CHKERRQ(ierr);


  /* Free work space */
  ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
  ierr = VecDestroy(&u);CHKERRQ(ierr);
  ierr = VecDestroy(&b);CHKERRQ(ierr);
  ierr = MatDestroy(&C);CHKERRQ(ierr);
  ierr = PetscFinalize();
  return ierr;
}

  -m # : the size of the vectors\n					\
  -n # : the numer of indices (with n<=m)\n				\
  -toFirst # : the starting index of the output vector for strided scatters\n \
  -toStep # : the step size into the output vector for strided scatters\n \
  -fromFirst # : the starting index of the input vector for strided scatters\n\
  -fromStep # : the step size into the input vector for strided scatters\n\n";

int main(int argc, char * argv[]) {

  Vec            X,Y;
  PetscInt       m,n,i,n1,n2;
  PetscInt       toFirst,toStep,fromFirst,fromStep;
  PetscInt       *idx,*idy;
  PetscBool      flg;
  IS             toISStrided,fromISStrided,toISGeneral,fromISGeneral;
  VecScatter     vscatSStoSS,vscatSStoSG,vscatSGtoSS,vscatSGtoSG;
  ScatterMode    mode;
  InsertMode     addv;
  PetscErrorCode ierr;

  ierr = PetscInitialize(&argc,&argv,0,help);if (ierr) return ierr;
  ierr = PetscOptionsGetInt(NULL,NULL,"-m",&m,&flg);CHKERRQ(ierr);
  if (!flg) m = 100;

  ierr = PetscOptionsGetInt(NULL,NULL,"-n",&n,&flg);CHKERRQ(ierr);
  if (!flg) n = 30;

  ierr = PetscOptionsGetInt(NULL,NULL,"-toFirst",&toFirst,&flg);CHKERRQ(ierr);
  if (!flg) toFirst = 3;

  ierr = PetscOptionsGetInt(NULL,NULL,"-toStep",&toStep,&flg);CHKERRQ(ierr);
  if (!flg) toStep = 3;

  ierr = PetscOptionsGetInt(NULL,NULL,"-fromFirst",&fromFirst,&flg);CHKERRQ(ierr);
  if (!flg) fromFirst = 2;

  ierr = PetscOptionsGetInt(NULL,NULL,"-fromStep",&fromStep,&flg);CHKERRQ(ierr);
  if (!flg) fromStep = 2;

  if (n>m) {
    ierr = PetscPrintf(PETSC_COMM_WORLD,"The vector sizes are %D. The number of elements being scattered is %D\n",m,n);CHKERRQ(ierr);
    ierr = PetscPrintf(PETSC_COMM_WORLD,"Adjust the parameters such that m>=n\n");CHKERRQ(ierr);
  } else if (toFirst+(n-1)*toStep >=m) {
    ierr = PetscPrintf(PETSC_COMM_WORLD,"The vector sizes are %D. The number of elements being scattered is %D\n",m,n);CHKERRQ(ierr);
    ierr = PetscPrintf(PETSC_COMM_WORLD,"For the Strided Scatter, toFirst=%D and toStep=%D.\n",toFirst,toStep);CHKERRQ(ierr);
    ierr = PetscPrintf(PETSC_COMM_WORLD,"This produces an index (toFirst+(n-1)*toStep)>=m\n");CHKERRQ(ierr);
    ierr = PetscPrintf(PETSC_COMM_WORLD,"Adjust the parameterrs accordingly with -m, -n, -toFirst, or -toStep\n");CHKERRQ(ierr);
  } else if (fromFirst+(n-1)*fromStep>=m) {
    ierr = PetscPrintf(PETSC_COMM_WORLD,"The vector sizes are %D. The number of elements being scattered is %D\n",m,n);CHKERRQ(ierr);
    ierr = PetscPrintf(PETSC_COMM_WORLD,"For the Strided Scatter, fromFirst=%D and fromStep=%D.\n",fromFirst,toStep);CHKERRQ(ierr);
    ierr = PetscPrintf(PETSC_COMM_WORLD,"This produces an index (fromFirst+(n-1)*fromStep)>=m\n");CHKERRQ(ierr);
    ierr = PetscPrintf(PETSC_COMM_WORLD,"Adjust the parameterrs accordingly with -m, -n, -fromFirst, or -fromStep\n");CHKERRQ(ierr);
  } else {
    ierr = PetscPrintf(PETSC_COMM_WORLD,"m=%D\tn=%D\tfromFirst=%D\tfromStep=%D\ttoFirst=%D\ttoStep=%D\n",m,n,fromFirst,fromStep,toFirst,toStep);CHKERRQ(ierr);
    ierr = PetscPrintf(PETSC_COMM_WORLD,"fromFirst+(n-1)*fromStep=%D\ttoFirst+(n-1)*toStep=%D\n",fromFirst+(n-1)*fromStep,toFirst+(n-1)*toStep);CHKERRQ(ierr);

    /* Build the vectors */
    ierr = VecCreate(PETSC_COMM_WORLD,&Y);CHKERRQ(ierr);
    ierr = VecSetSizes(Y,m,PETSC_DECIDE);CHKERRQ(ierr);
    ierr = VecCreate(PETSC_COMM_WORLD,&X);CHKERRQ(ierr);
    ierr = VecSetSizes(X,m,PETSC_DECIDE);CHKERRQ(ierr);

    ierr = VecSetFromOptions(Y);CHKERRQ(ierr);
    ierr = VecSetFromOptions(X);CHKERRQ(ierr);
    ierr = VecSet(X,2.0);CHKERRQ(ierr);
    ierr = VecSet(Y,1.0);CHKERRQ(ierr);

    /* Build the strided index sets */
    ierr = ISCreate(PETSC_COMM_WORLD,&toISStrided);CHKERRQ(ierr);
    ierr = ISCreate(PETSC_COMM_WORLD,&fromISStrided);CHKERRQ(ierr);
    ierr = ISSetType(toISStrided, ISSTRIDE);CHKERRQ(ierr);
    ierr = ISSetType(fromISStrided, ISSTRIDE);CHKERRQ(ierr);
    ierr = ISStrideSetStride(fromISStrided,n,fromFirst,fromStep);CHKERRQ(ierr);
    ierr = ISStrideSetStride(toISStrided,n,toFirst,toStep);CHKERRQ(ierr);

    /* Build the general index sets */
    ierr = PetscMalloc1(n,&idx);CHKERRQ(ierr);
    ierr = PetscMalloc1(n,&idy);CHKERRQ(ierr);
    for (i=0; i<n; i++) {
      idx[i] = i % m;
      idy[i] = (i+m) % m;
    }
    n1 = n;
    n2 = n;
    ierr = PetscSortRemoveDupsInt(&n1,idx);CHKERRQ(ierr);
    ierr = PetscSortRemoveDupsInt(&n2,idy);CHKERRQ(ierr);

    ierr = ISCreateGeneral(PETSC_COMM_WORLD,n1,idx,PETSC_COPY_VALUES,&toISGeneral);CHKERRQ(ierr);
    ierr = ISCreateGeneral(PETSC_COMM_WORLD,n2,idy,PETSC_COPY_VALUES,&fromISGeneral);CHKERRQ(ierr);

    /* set the mode and the insert/add parameter */
    mode = SCATTER_FORWARD;
    addv = ADD_VALUES;

    /* VecScatter : Seq Strided to Seq Strided */
    ierr = VecScatterCreate(X,fromISStrided,Y,toISStrided,&vscatSStoSS);CHKERRQ(ierr);
    ierr = VecScatterBegin(vscatSStoSS,X,Y,addv,mode);CHKERRQ(ierr);
    ierr = VecScatterEnd(vscatSStoSS,X,Y,addv,mode);CHKERRQ(ierr);
    ierr = VecScatterDestroy(&vscatSStoSS);CHKERRQ(ierr);

//.........这里部分代码省略.........

int main(int argc,char **args)
{
  Mat             A;
  PetscErrorCode  ierr;
  PetscMPIInt     rank,size;
  PetscInt        *ia,*ja;
  MatPartitioning part;
  IS              is,isn;

  PetscInitialize(&argc,&args,(char*)0,help);
  ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
  if (size != 4) SETERRQ(PETSC_COMM_WORLD,1,"Must run with 4 processors");
  ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);

  ierr = PetscMalloc(5*sizeof(PetscInt),&ia);CHKERRQ(ierr);
  ierr = PetscMalloc(16*sizeof(PetscInt),&ja);CHKERRQ(ierr);
  if (!rank) {
    ja[0] = 1; ja[1] = 4; ja[2] = 0; ja[3] = 2; ja[4] = 5; ja[5] = 1; ja[6] = 3; ja[7] = 6;
    ja[8] = 2; ja[9] = 7;
    ia[0] = 0; ia[1] = 2; ia[2] = 5; ia[3] = 8; ia[4] = 10;
  } else if (rank == 1) {
    ja[0] = 0; ja[1] = 5; ja[2] = 8; ja[3] = 1; ja[4] = 4; ja[5] = 6; ja[6] = 9; ja[7] = 2;
    ja[8] = 5; ja[9] = 7; ja[10] = 10; ja[11] = 3; ja[12] = 6; ja[13] = 11;
    ia[0] = 0; ia[1] = 3; ia[2] = 7; ia[3] = 11; ia[4] = 14;
  } else if (rank == 2) {
    ja[0] = 4; ja[1] = 9; ja[2] = 12; ja[3] = 5; ja[4] = 8; ja[5] = 10; ja[6] = 13; ja[7] = 6;
    ja[8] = 9; ja[9] = 11; ja[10] = 14; ja[11] = 7; ja[12] = 10; ja[13] = 15;
    ia[0] = 0; ia[1] = 3; ia[2] = 7; ia[3] = 11; ia[4] = 14;
  } else {
    ja[0] = 8; ja[1] = 13; ja[2] = 9; ja[3] = 12; ja[4] = 14; ja[5] = 10; ja[6] = 13; ja[7] = 15;
    ja[8] = 11; ja[9] = 14;
    ia[0] = 0; ia[1] = 2; ia[2] = 5; ia[3] = 8; ia[4] = 10;
  }

  ierr = MatCreateMPIAdj(PETSC_COMM_WORLD,4,16,ia,ja,NULL,&A);CHKERRQ(ierr);
  ierr = MatView(A,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);

  /*
       Partition the graph of the matrix
  */
  ierr = MatPartitioningCreate(PETSC_COMM_WORLD,&part);CHKERRQ(ierr);
  ierr = MatPartitioningSetAdjacency(part,A);CHKERRQ(ierr);
  ierr = MatPartitioningSetFromOptions(part);CHKERRQ(ierr);
  /* get new processor owner number of each vertex */
  ierr = MatPartitioningApply(part,&is);CHKERRQ(ierr);
  /* get new global number of each old global number */
  ierr = ISPartitioningToNumbering(is,&isn);CHKERRQ(ierr);
  ierr = ISView(isn,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
  ierr = ISDestroy(&is);CHKERRQ(ierr);

  ierr = ISDestroy(&isn);CHKERRQ(ierr);
  ierr = MatPartitioningDestroy(&part);CHKERRQ(ierr);

  /*
       Free work space.  All PETSc objects should be destroyed when they
       are no longer needed.
  */
  ierr = MatDestroy(&A);CHKERRQ(ierr);


  ierr = PetscFinalize();
  return 0;
}

Example: mpiexec -n <np> ./ex130 -f <matrix binary file> -mat_solver_type 1 -mat_superlu_equil \n\n";

#include <petscmat.h>

int main(int argc,char **args)
{
  Mat            A,F;
  Vec            u,x,b;
  PetscErrorCode ierr;
  PetscMPIInt    rank,size;
  PetscInt       m,n,nfact,ipack=0;
  PetscReal      norm,tol=1.e-12,Anorm;
  IS             perm,iperm;
  MatFactorInfo  info;
  PetscBool      flg,testMatSolve=PETSC_TRUE;
  PetscViewer    fd;              /* viewer */
  char           file[PETSC_MAX_PATH_LEN]; /* input file name */

  ierr = PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
  ierr = MPI_Comm_rank(PETSC_COMM_WORLD, &rank);CHKERRQ(ierr);
  ierr = MPI_Comm_size(PETSC_COMM_WORLD, &size);CHKERRQ(ierr);

  /* Determine file from which we read the matrix A */
  ierr = PetscOptionsGetString(NULL,NULL,"-f",file,PETSC_MAX_PATH_LEN,&flg);CHKERRQ(ierr);
  if (!flg) SETERRQ(PETSC_COMM_WORLD,1,"Must indicate binary file with the -f option");

  /* Load matrix A */
  ierr = PetscViewerBinaryOpen(PETSC_COMM_WORLD,file,FILE_MODE_READ,&fd);CHKERRQ(ierr);
  ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
  ierr = MatLoad(A,fd);CHKERRQ(ierr);
  ierr = VecCreate(PETSC_COMM_WORLD,&b);CHKERRQ(ierr);
  ierr = VecLoad(b,fd);CHKERRQ(ierr);
  ierr = PetscViewerDestroy(&fd);CHKERRQ(ierr);
  ierr = MatGetLocalSize(A,&m,&n);CHKERRQ(ierr);
  if (m != n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ, "This example is not intended for rectangular matrices (%d, %d)", m, n);
  ierr = MatNorm(A,NORM_INFINITY,&Anorm);CHKERRQ(ierr);

  /* Create vectors */
  ierr = VecDuplicate(b,&x);CHKERRQ(ierr);
  ierr = VecDuplicate(x,&u);CHKERRQ(ierr); /* save the true solution */

  /* Test LU Factorization */
  ierr = MatGetOrdering(A,MATORDERINGNATURAL,&perm,&iperm);CHKERRQ(ierr);

  ierr = PetscOptionsGetInt(NULL,NULL,"-mat_solver_type",&ipack,NULL);CHKERRQ(ierr);
  switch (ipack) {
  case 1:
#if defined(PETSC_HAVE_SUPERLU)
    if (!rank) printf(" SUPERLU LU:\n");
    ierr = MatGetFactor(A,MATSOLVERSUPERLU,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
    break;
#endif
  case 2:
#if defined(PETSC_HAVE_MUMPS)
    if (!rank) printf(" MUMPS LU:\n");
    ierr = MatGetFactor(A,MATSOLVERMUMPS,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
    {
      /* test mumps options */
      PetscInt icntl_7 = 5;
      ierr = MatMumpsSetIcntl(F,7,icntl_7);CHKERRQ(ierr);
    }
    break;
#endif
  default:
    if (!rank) printf(" PETSC LU:\n");
    ierr = MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_LU,&F);CHKERRQ(ierr);
  }

  info.fill = 5.0;
  ierr      = MatLUFactorSymbolic(F,A,perm,iperm,&info);CHKERRQ(ierr);

  for (nfact = 0; nfact < 1; nfact++) {
    if (!rank) printf(" %d-the LU numfactorization \n",nfact);
    ierr = MatLUFactorNumeric(F,A,&info);CHKERRQ(ierr);

    /* Test MatSolve() */
    if (testMatSolve) {
      ierr = MatSolve(F,b,x);CHKERRQ(ierr);

      /* Check the residual */
      ierr = MatMult(A,x,u);CHKERRQ(ierr);
      ierr = VecAXPY(u,-1.0,b);CHKERRQ(ierr);
      ierr = VecNorm(u,NORM_INFINITY,&norm);CHKERRQ(ierr);
      if (norm > tol) {
        if (!rank) {
          ierr = PetscPrintf(PETSC_COMM_SELF,"MatSolve: rel residual %g/%g = %g, LU numfact %d\n",norm,Anorm,norm/Anorm,nfact);CHKERRQ(ierr);
        }
      }
    }
  }

  /* Free data structures */
  ierr = MatDestroy(&A);CHKERRQ(ierr);
  ierr = MatDestroy(&F);CHKERRQ(ierr);
  ierr = ISDestroy(&perm);CHKERRQ(ierr);
  ierr = ISDestroy(&iperm);CHKERRQ(ierr);
  ierr = VecDestroy(&x);CHKERRQ(ierr);
  ierr = VecDestroy(&b);CHKERRQ(ierr);
  ierr = VecDestroy(&u);CHKERRQ(ierr);
  ierr = PetscFinalize();
//.........这里部分代码省略.........

int main(int argc,char **argv)
{
  TS             ts;            /* nonlinear solver */
  PetscBool      monitor = PETSC_FALSE;
  PetscScalar    *x_ptr,*y_ptr;
  PetscMPIInt    size;
  struct _n_User user;
  PetscErrorCode ierr;

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Initialize program
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = PetscInitialize(&argc,&argv,NULL,help);if (ierr) return ierr;
  ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
  if (size != 1) SETERRQ(PETSC_COMM_SELF,1,"This is a uniprocessor example only!");

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    Set runtime options
    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  user.next_output = 0.0;
  user.mu          = 1.0e6;
  user.steps       = 0;
  user.ftime       = 0.5;
  ierr = PetscOptionsGetBool(NULL,NULL,"-monitor",&monitor,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetReal(NULL,NULL,"-mu",&user.mu,NULL);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    Create necessary matrix and vectors, solve same ODE on every process
    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = MatCreate(PETSC_COMM_WORLD,&user.A);CHKERRQ(ierr);
  ierr = MatSetSizes(user.A,PETSC_DECIDE,PETSC_DECIDE,2,2);CHKERRQ(ierr);
  ierr = MatSetFromOptions(user.A);CHKERRQ(ierr);
  ierr = MatSetUp(user.A);CHKERRQ(ierr);
  ierr = MatCreateVecs(user.A,&user.x,NULL);CHKERRQ(ierr);

  ierr = MatCreate(PETSC_COMM_WORLD,&user.Jacp);CHKERRQ(ierr);
  ierr = MatSetSizes(user.Jacp,PETSC_DECIDE,PETSC_DECIDE,2,1);CHKERRQ(ierr);
  ierr = MatSetFromOptions(user.Jacp);CHKERRQ(ierr);
  ierr = MatSetUp(user.Jacp);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Create timestepping solver context
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
  ierr = TSSetType(ts,TSCN);CHKERRQ(ierr);
  ierr = TSSetIFunction(ts,NULL,IFunction,&user);CHKERRQ(ierr);
  ierr = TSSetIJacobian(ts,user.A,user.A,IJacobian,&user);CHKERRQ(ierr);
  ierr = TSSetMaxTime(ts,user.ftime);CHKERRQ(ierr);
  ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);CHKERRQ(ierr);
  if (monitor) {
    ierr = TSMonitorSet(ts,Monitor,&user,NULL);CHKERRQ(ierr);
  }

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set initial conditions
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = VecGetArray(user.x,&x_ptr);CHKERRQ(ierr);
  x_ptr[0] = 2.0;   x_ptr[1] = -0.66666654321;
  ierr = VecRestoreArray(user.x,&x_ptr);CHKERRQ(ierr);
  ierr = TSSetTimeStep(ts,.0001);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    Save trajectory of solution so that TSAdjointSolve() may be used
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = TSSetSaveTrajectory(ts);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set runtime options
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = TSSetFromOptions(ts);CHKERRQ(ierr);

  ierr = TSSolve(ts,user.x);CHKERRQ(ierr);
  ierr = TSGetSolveTime(ts,&user.ftime);CHKERRQ(ierr);
  ierr = TSGetStepNumber(ts,&user.steps);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Adjoint model starts here
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = MatCreateVecs(user.A,&user.lambda[0],NULL);CHKERRQ(ierr);
  /*   Set initial conditions for the adjoint integration */
  ierr = VecGetArray(user.lambda[0],&y_ptr);CHKERRQ(ierr);
  y_ptr[0] = 1.0; y_ptr[1] = 0.0;
  ierr = VecRestoreArray(user.lambda[0],&y_ptr);CHKERRQ(ierr);
  ierr = MatCreateVecs(user.A,&user.lambda[1],NULL);CHKERRQ(ierr);
  ierr = VecGetArray(user.lambda[1],&y_ptr);CHKERRQ(ierr);
  y_ptr[0] = 0.0; y_ptr[1] = 1.0;
  ierr = VecRestoreArray(user.lambda[1],&y_ptr);CHKERRQ(ierr);

  ierr = MatCreateVecs(user.Jacp,&user.mup[0],NULL);CHKERRQ(ierr);
  ierr = VecGetArray(user.mup[0],&x_ptr);CHKERRQ(ierr);
  x_ptr[0] = 0.0;
  ierr = VecRestoreArray(user.mup[0],&x_ptr);CHKERRQ(ierr);
  ierr = MatCreateVecs(user.Jacp,&user.mup[1],NULL);CHKERRQ(ierr);
  ierr = VecGetArray(user.mup[1],&x_ptr);CHKERRQ(ierr);
  x_ptr[0] = 0.0;
  ierr = VecRestoreArray(user.mup[1],&x_ptr);CHKERRQ(ierr);

  ierr = TSSetCostGradients(ts,2,user.lambda,user.mup);CHKERRQ(ierr);

  /*   Set RHS JacobianP */
//.........这里部分代码省略.........

int main(int argc,char **argv)
{
  TS              ts;                 /* nonlinear solver */
  Vec             C;                  /* solution */
  PetscErrorCode  ierr;
  DM              da;                 /* manages the grid data */
  AppCtx          ctx;                /* holds problem specific paramters */
  PetscInt        He,dof = 3*N+N*N,*ofill;

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Initialize program
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  PetscInitialize(&argc,&argv,(char *)0,help);
  PetscFunctionBeginUser;

  ctx.noreactions     = PETSC_FALSE;
  ctx.nodissociations = PETSC_FALSE;
  ierr = PetscOptionsHasName(PETSC_NULL,"-noreactions",&ctx.noreactions);CHKERRQ(ierr);
  ierr = PetscOptionsHasName(PETSC_NULL,"-nodissociations",&ctx.nodissociations);CHKERRQ(ierr);
  ctx.HeDiffusion[1]    = 1000*2.95e-4; /* From Tibo's notes times 1,000 */
  ctx.HeDiffusion[2]    = 1000*3.24e-4;
  ctx.HeDiffusion[3]    = 1000*2.26e-4;
  ctx.HeDiffusion[4]    = 1000*1.68e-4;
  ctx.HeDiffusion[5]    = 1000*5.20e-5;
  ctx.VDiffusion[1]     = 1000*2.71e-3;
  ctx.IDiffusion[1]     = 1000*2.13e-4;
  ctx.forcingScale      = 100.;         /* made up numbers */
  ctx.reactionScale     = .001;
  ctx.dissociationScale = .0001;
  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Create distributed array (DMDA) to manage parallel grid and vectors
  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = DMDACreate1d(PETSC_COMM_WORLD, DMDA_BOUNDARY_MIRROR,-8,dof,1,PETSC_NULL,&da);CHKERRQ(ierr);

  /* The only spatial coupling in the Jacobian (diffusion) is for the first 5 He, the first V, and the first I.
     The ofill (thought of as a dof by dof 2d (row-oriented) array represents the nonzero coupling between degrees
     of freedom at one point with degrees of freedom on the adjacent point to the left or right. A 1 at i,j in the
     ofill array indicates that the degree of freedom i at a point is coupled to degree of freedom j at the
     adjacent point. In this case ofill has only a few diagonal entries since the only spatial coupling is regular diffusion. */
  ierr = PetscMalloc(dof*dof*sizeof(PetscInt),&ofill);CHKERRQ(ierr);
  ierr = PetscMemzero(ofill,dof*dof*sizeof(PetscInt));CHKERRQ(ierr);
  for (He=0; He<PetscMin(N,5); He++) ofill[He*dof + He] = 1; ofill[N*dof + N] = ofill[2*N*dof + 2*N] = 1;
  ierr = DMDASetBlockFills(da,PETSC_NULL,ofill);CHKERRQ(ierr);
  ierr = PetscFree(ofill);CHKERRQ(ierr);

  /*  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
   Extract global vector from DMDA to hold solution
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = DMCreateGlobalVector(da,&C);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Create timestepping solver context
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr);
  ierr = TSSetType(ts,TSARKIMEX);CHKERRQ(ierr);
  ierr = TSSetDM(ts,da);CHKERRQ(ierr);
  ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr);
  ierr = TSSetIFunction(ts,PETSC_NULL,IFunction,&ctx);CHKERRQ(ierr);
  ierr = TSSetSolution(ts,C);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set solver options
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = TSSetInitialTimeStep(ts,0.0,.001);CHKERRQ(ierr);
  ierr = TSSetDuration(ts,100,50.0);CHKERRQ(ierr);
  ierr = TSSetFromOptions(ts);CHKERRQ(ierr);
  ierr = MyMonitorSetUp(ts);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Set initial conditions
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = InitialConditions(da,C);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Solve the ODE system
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = TSSolve(ts,C);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Free work space.
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  ierr = VecDestroy(&C);CHKERRQ(ierr);
  ierr = TSDestroy(&ts);CHKERRQ(ierr);
  ierr = DMDestroy(&da);CHKERRQ(ierr);
  ierr = PetscFinalize();
  PetscFunctionReturn(0);
}

int main(int argc,char **argv)
{
  PetscMPIInt    rank,size;
  PetscInt       M = 14,time_steps = 20,w=1,s=1,localsize,j,i,mybase,myend;
  PetscErrorCode ierr;
  DM             da;
  Vec            local,global,copy;
  PetscScalar    *localptr,*copyptr;
  PetscReal      h,k;
 
  ierr = PetscInitialize(&argc,&argv,(char*)0,help);CHKERRQ(ierr); 

  ierr = PetscOptionsGetInt(PETSC_NULL,"-M",&M,PETSC_NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetInt(PETSC_NULL,"-time",&time_steps,PETSC_NULL);CHKERRQ(ierr);
    
  /* Set up the array */ 
  ierr = DMDACreate1d(PETSC_COMM_WORLD,DMDA_BOUNDARY_NONE,M,w,s,PETSC_NULL,&da);CHKERRQ(ierr);
  ierr = DMCreateGlobalVector(da,&global);CHKERRQ(ierr);
  ierr = DMCreateLocalVector(da,&local);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
  ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);

  /* Make copy of local array for doing updates */
  ierr = VecDuplicate(local,&copy);CHKERRQ(ierr);
  ierr = VecGetArray (copy,&copyptr);CHKERRQ(ierr);


  /* determine starting point of each processor */
  ierr = VecGetOwnershipRange(global,&mybase,&myend);CHKERRQ(ierr);

  /* Initialize the Array */
  ierr = VecGetLocalSize (local,&localsize);CHKERRQ(ierr);
  ierr = VecGetArray (local,&localptr);CHKERRQ(ierr);
  localptr[0] = copyptr[0] = 0.0;
  localptr[localsize-1] = copyptr[localsize-1] = 1.0;
  for (i=1; i<localsize-1; i++) {
    j=(i-1)+mybase; 
    localptr[i] = sin((PETSC_PI*j*6)/((PetscReal)M) 
                        + 1.2 * sin((PETSC_PI*j*2)/((PetscReal)M))) * 4+4;
  }

  ierr = VecRestoreArray (copy,&copyptr);CHKERRQ(ierr);
  ierr = VecRestoreArray(local,&localptr);CHKERRQ(ierr);
  ierr = DMLocalToGlobalBegin(da,local,INSERT_VALUES,global);CHKERRQ(ierr);
  ierr = DMLocalToGlobalEnd(da,local,INSERT_VALUES,global);CHKERRQ(ierr);

  /* Assign Parameters */
  h= 1.0/M; 
  k= h*h/2.2;

  for (j=0; j<time_steps; j++) {  

    /* Global to Local */
    ierr = DMGlobalToLocalBegin(da,global,INSERT_VALUES,local);CHKERRQ(ierr);
    ierr = DMGlobalToLocalEnd(da,global,INSERT_VALUES,local);CHKERRQ(ierr);

    /*Extract local array */ 
    ierr = VecGetArray(local,&localptr);CHKERRQ(ierr);
    ierr = VecGetArray (copy,&copyptr);CHKERRQ(ierr);

    /* Update Locally - Make array of new values */
    /* Note: I don't do anything for the first and last entry */
    for (i=1; i< localsize-1; i++) {
      copyptr[i] = localptr[i] + (k/(h*h)) *
                           (localptr[i+1]-2.0*localptr[i]+localptr[i-1]);
    }
  
    ierr = VecRestoreArray (copy,&copyptr);CHKERRQ(ierr);
    ierr = VecRestoreArray(local,&localptr);CHKERRQ(ierr);

    /* Local to Global */
    ierr = DMLocalToGlobalBegin(da,copy,INSERT_VALUES,global);CHKERRQ(ierr);
    ierr = DMLocalToGlobalEnd(da,copy,INSERT_VALUES,global);CHKERRQ(ierr);
  
    /* View Wave */ 
  /* Set Up Display to Show Heat Graph */
#if defined(PETSC_USE_SOCKET_VIEWER)
    ierr = VecView(global,PETSC_VIEWER_SOCKET_WORLD);CHKERRQ(ierr);
#endif
  }

  ierr = VecDestroy(&copy);CHKERRQ(ierr);
  ierr = VecDestroy(&local);CHKERRQ(ierr);
  ierr = VecDestroy(&global);CHKERRQ(ierr);
  ierr = DMDestroy(&da);CHKERRQ(ierr);
  ierr = PetscFinalize();
  return 0;
}

int main(int argc,char **argv)
{
  PetscErrorCode ierr;
  PetscMPIInt    rank,nproc;
  PetscInt       rstart,rend,i,k,N,numPoints=1000000;
  PetscScalar    dummy,result=0,h=1.0/numPoints,*xarray;
  Vec            x,xend;

  PetscInitialize(&argc,&argv,(char *)0,help);
  ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
  ierr = MPI_Comm_size(PETSC_COMM_WORLD,&nproc);CHKERRQ(ierr);

  /*
     Create a parallel vector.
       Here we set up our x vector which will be given values below.
       The xend vector is a dummy vector to find the value of the
         elements at the endpoints for use in the trapezoid rule.
  */
  ierr = VecCreate(PETSC_COMM_WORLD,&x);CHKERRQ(ierr);
  ierr = VecSetSizes(x,PETSC_DECIDE,numPoints);CHKERRQ(ierr);
  ierr = VecSetFromOptions(x);CHKERRQ(ierr);
  ierr = VecGetSize(x,&N);CHKERRQ(ierr);
  ierr = VecSet(x,result);CHKERRQ(ierr);
  ierr = VecDuplicate(x,&xend);CHKERRQ(ierr);
  result=0.5;
  if (rank == 0){
    i=0;
    ierr = VecSetValues(xend,1,&i,&result,INSERT_VALUES);CHKERRQ(ierr);
  } else if (rank == nproc){
    i=N-1;
    ierr = VecSetValues(xend,1,&i,&result,INSERT_VALUES);CHKERRQ(ierr);
  }
  /* 
     Assemble vector, using the 2-step process:
       VecAssemblyBegin(), VecAssemblyEnd()
     Computations can be done while messages are in transition
     by placing code between these two statements.
  */
  ierr = VecAssemblyBegin(xend);CHKERRQ(ierr);
  ierr = VecAssemblyEnd(xend);CHKERRQ(ierr);

  /*
     Set the x vector elements.
      i*h will return 0 for i=0 and 1 for i=N-1.
      The function evaluated (2x/(1+x^2)) is defined above.
      Each evaluation is put into the local array of the vector without message passing.
  */
  ierr = VecGetOwnershipRange(x,&rstart,&rend);CHKERRQ(ierr);
  ierr = VecGetArray(x,&xarray);CHKERRQ(ierr);
  k = 0;
  for (i=rstart; i<rend; i++){
    xarray[k] = i*h;
    xarray[k] = func(xarray[k]);
    k++;
  }
  ierr = VecRestoreArray(x,&xarray);CHKERRQ(ierr);

  /*
     Evaluates the integral.  First the sum of all the points is taken.
     That result is multiplied by the step size for the trapezoid rule.
     Then half the value at each endpoint is subtracted,
	this is part of the composite trapezoid rule.
  */
  ierr = VecSum(x,&result);CHKERRQ(ierr);
  result = result*h;
  ierr   = VecDot(x,xend,&dummy);CHKERRQ(ierr);
  result = result-h*dummy;   

  /*
      Return the value of the integral.
  */
  ierr = PetscPrintf(PETSC_COMM_WORLD,"ln(2) is %G\n",result);CHKERRQ(ierr);
  ierr = VecDestroy(&x);CHKERRQ(ierr);
  ierr = VecDestroy(&xend);CHKERRQ(ierr);

  ierr = PetscFinalize();
  return 0;
}