Date: 2022-03-31T04:48:47+00:00

Actual source code: ex50.c

      2: static char help[] ="Solves one dimensional Burger's equation compares with exact solution\n\n";

      4: /*

      6:     Not yet tested in parallel

      8: */
      9: /*
     10:    Concepts: TS^time-dependent nonlinear problems
     11:    Concepts: TS^Burger's equation
     12:    Processors: n
     13: */

     15: /* ------------------------------------------------------------------------

     17:    This program uses the one-dimensional Burger's equation
     18:        u_t = mu*u_xx - u u_x,
     19:    on the domain 0 <= x <= 1, with periodic boundary conditions

     21:    The operators are discretized with the spectral element method

     23:    See the paper PDE-CONSTRAINED OPTIMIZATION WITH SPECTRAL ELEMENTS USING PETSC AND TAO
     24:    by OANA MARIN, EMIL CONSTANTINESCU, AND BARRY SMITH for details on the exact solution
     25:    used

     27:    See src/tao/unconstrained/tutorials/burgers_spectral.c

     29:   ------------------------------------------------------------------------- */

     31: #include <petscts.h>
     32: #include <petscdt.h>
     33: #include <petscdraw.h>
     34: #include <petscdmda.h>

     36: /*
     37:    User-defined application context - contains data needed by the
     38:    application-provided call-back routines.
     39: */

     41: typedef struct {
     42:   PetscInt  n;                /* number of nodes */
     43:   PetscReal *nodes;           /* GLL nodes */
     44:   PetscReal *weights;         /* GLL weights */
     45: } PetscGLL;

     47: typedef struct {
     48:   PetscInt    N;             /* grid points per elements*/
     49:   PetscInt    E;              /* number of elements */
     50:   PetscReal   tol_L2,tol_max; /* error norms */
     51:   PetscInt    steps;          /* number of timesteps */
     52:   PetscReal   Tend;           /* endtime */
     53:   PetscReal   mu;             /* viscosity */
     54:   PetscReal   L;              /* total length of domain */
     55:   PetscReal   Le;
     56:   PetscReal   Tadj;
     57: } PetscParam;

     59: typedef struct {
     60:   Vec         grid;              /* total grid */
     61:   Vec         curr_sol;
     62: } PetscData;

     64: typedef struct {
     65:   Vec         grid;              /* total grid */
     66:   Vec         mass;              /* mass matrix for total integration */
     67:   Mat         stiff;             /* stifness matrix */
     68:   Mat         keptstiff;
     69:   Mat         grad;
     70:   PetscGLL    gll;
     71: } PetscSEMOperators;

     73: typedef struct {
     74:   DM                da;                /* distributed array data structure */
     75:   PetscSEMOperators SEMop;
     76:   PetscParam        param;
     77:   PetscData         dat;
     78:   TS                ts;
     79:   PetscReal         initial_dt;
     80: } AppCtx;

     82: /*
     83:    User-defined routines
     84: */
     85: extern PetscErrorCode RHSMatrixLaplaciangllDM(TS,PetscReal,Vec,Mat,Mat,void*);
     86: extern PetscErrorCode RHSMatrixAdvectiongllDM(TS,PetscReal,Vec,Mat,Mat,void*);
     87: extern PetscErrorCode TrueSolution(TS,PetscReal,Vec,AppCtx*);
     88: extern PetscErrorCode RHSFunction(TS,PetscReal,Vec,Vec,void*);
     89: extern PetscErrorCode RHSJacobian(TS,PetscReal,Vec,Mat,Mat,void*);

     91: int main(int argc,char **argv)
     92: {
     93:   AppCtx         appctx;                 /* user-defined application context */
     94:   PetscInt       i, xs, xm, ind, j, lenglob;
     95:   PetscReal      x, *wrk_ptr1, *wrk_ptr2;
     96:   MatNullSpace   nsp;
     97:   PetscMPIInt    size;

     99:    /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    100:      Initialize program and set problem parameters
    101:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    103:   PetscInitialize(&argc,&argv,(char*)0,help);

    105:   /*initialize parameters */
    106:   appctx.param.N    = 10;  /* order of the spectral element */
    107:   appctx.param.E    = 10;  /* number of elements */
    108:   appctx.param.L    = 4.0;  /* length of the domain */
    109:   appctx.param.mu   = 0.01; /* diffusion coefficient */
    110:   appctx.initial_dt = 5e-3;
    111:   appctx.param.steps = PETSC_MAX_INT;
    112:   appctx.param.Tend  = 4;

    114:   PetscOptionsGetInt(NULL,NULL,"-N",&appctx.param.N,NULL);
    115:   PetscOptionsGetInt(NULL,NULL,"-E",&appctx.param.E,NULL);
    116:   PetscOptionsGetReal(NULL,NULL,"-Tend",&appctx.param.Tend,NULL);
    117:   PetscOptionsGetReal(NULL,NULL,"-mu",&appctx.param.mu,NULL);
    118:   appctx.param.Le = appctx.param.L/appctx.param.E;

    120:   MPI_Comm_size(PETSC_COMM_WORLD,&size);

    123:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    124:      Create GLL data structures
    125:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    126:   PetscMalloc2(appctx.param.N,&appctx.SEMop.gll.nodes,appctx.param.N,&appctx.SEMop.gll.weights);
    127:   PetscDTGaussLobattoLegendreQuadrature(appctx.param.N,PETSCGAUSSLOBATTOLEGENDRE_VIA_LINEAR_ALGEBRA,appctx.SEMop.gll.nodes,appctx.SEMop.gll.weights);
    128:   appctx.SEMop.gll.n = appctx.param.N;
    129:   lenglob  = appctx.param.E*(appctx.param.N-1);

    131:   /*
    132:      Create distributed array (DMDA) to manage parallel grid and vectors
    133:      and to set up the ghost point communication pattern.  There are E*(Nl-1)+1
    134:      total grid values spread equally among all the processors, except first and last
    135:   */

    137:   DMDACreate1d(PETSC_COMM_WORLD,DM_BOUNDARY_PERIODIC,lenglob,1,1,NULL,&appctx.da);
    138:   DMSetFromOptions(appctx.da);
    139:   DMSetUp(appctx.da);

    141:   /*
    142:      Extract global and local vectors from DMDA; we use these to store the
    143:      approximate solution.  Then duplicate these for remaining vectors that
    144:      have the same types.
    145:   */

    147:   DMCreateGlobalVector(appctx.da,&appctx.dat.curr_sol);
    148:   VecDuplicate(appctx.dat.curr_sol,&appctx.SEMop.grid);
    149:   VecDuplicate(appctx.dat.curr_sol,&appctx.SEMop.mass);

    151:   DMDAGetCorners(appctx.da,&xs,NULL,NULL,&xm,NULL,NULL);
    152:   DMDAVecGetArray(appctx.da,appctx.SEMop.grid,&wrk_ptr1);
    153:   DMDAVecGetArray(appctx.da,appctx.SEMop.mass,&wrk_ptr2);

    155:   /* Compute function over the locally owned part of the grid */

    157:     xs=xs/(appctx.param.N-1);
    158:     xm=xm/(appctx.param.N-1);

    160:   /*
    161:      Build total grid and mass over entire mesh (multi-elemental)
    162:   */

    164:   for (i=xs; i<xs+xm; i++) {
    165:     for (j=0; j<appctx.param.N-1; j++) {
    166:       x = (appctx.param.Le/2.0)*(appctx.SEMop.gll.nodes[j]+1.0)+appctx.param.Le*i;
    167:       ind=i*(appctx.param.N-1)+j;
    168:       wrk_ptr1[ind]=x;
    169:       wrk_ptr2[ind]=.5*appctx.param.Le*appctx.SEMop.gll.weights[j];
    170:       if (j==0) wrk_ptr2[ind]+=.5*appctx.param.Le*appctx.SEMop.gll.weights[j];
    171:     }
    172:   }
    173:   DMDAVecRestoreArray(appctx.da,appctx.SEMop.grid,&wrk_ptr1);
    174:   DMDAVecRestoreArray(appctx.da,appctx.SEMop.mass,&wrk_ptr2);

    176:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    177:    Create matrix data structure; set matrix evaluation routine.
    178:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
    179:   DMSetMatrixPreallocateOnly(appctx.da, PETSC_TRUE);
    180:   DMCreateMatrix(appctx.da,&appctx.SEMop.stiff);
    181:   DMCreateMatrix(appctx.da,&appctx.SEMop.grad);
    182:   /*
    183:    For linear problems with a time-dependent f(u,t) in the equation
    184:    u_t = f(u,t), the user provides the discretized right-hand-side
    185:    as a time-dependent matrix.
    186:    */
    187:   RHSMatrixLaplaciangllDM(appctx.ts,0.0,appctx.dat.curr_sol,appctx.SEMop.stiff,appctx.SEMop.stiff,&appctx);
    188:   RHSMatrixAdvectiongllDM(appctx.ts,0.0,appctx.dat.curr_sol,appctx.SEMop.grad,appctx.SEMop.grad,&appctx);
    189:    /*
    190:        For linear problems with a time-dependent f(u,t) in the equation
    191:        u_t = f(u,t), the user provides the discretized right-hand-side
    192:        as a time-dependent matrix.
    193:     */

    195:   MatDuplicate(appctx.SEMop.stiff,MAT_COPY_VALUES,&appctx.SEMop.keptstiff);

    197:   /* attach the null space to the matrix, this probably is not needed but does no harm */
    198:   MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,NULL,&nsp);
    199:   MatSetNullSpace(appctx.SEMop.stiff,nsp);
    200:   MatSetNullSpace(appctx.SEMop.keptstiff,nsp);
    201:   MatNullSpaceTest(nsp,appctx.SEMop.stiff,NULL);
    202:   MatNullSpaceDestroy(&nsp);
    203:   /* attach the null space to the matrix, this probably is not needed but does no harm */
    204:   MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,NULL,&nsp);
    205:   MatSetNullSpace(appctx.SEMop.grad,nsp);
    206:   MatNullSpaceTest(nsp,appctx.SEMop.grad,NULL);
    207:   MatNullSpaceDestroy(&nsp);

    209:   /* Create the TS solver that solves the ODE and its adjoint; set its options */
    210:   TSCreate(PETSC_COMM_WORLD,&appctx.ts);
    211:   TSSetProblemType(appctx.ts,TS_NONLINEAR);
    212:   TSSetType(appctx.ts,TSRK);
    213:   TSSetDM(appctx.ts,appctx.da);
    214:   TSSetTime(appctx.ts,0.0);
    215:   TSSetTimeStep(appctx.ts,appctx.initial_dt);
    216:   TSSetMaxSteps(appctx.ts,appctx.param.steps);
    217:   TSSetMaxTime(appctx.ts,appctx.param.Tend);
    218:   TSSetExactFinalTime(appctx.ts,TS_EXACTFINALTIME_MATCHSTEP);
    219:   TSSetTolerances(appctx.ts,1e-7,NULL,1e-7,NULL);
    220:   TSSetSaveTrajectory(appctx.ts);
    221:   TSSetFromOptions(appctx.ts);
    222:   TSSetRHSFunction(appctx.ts,NULL,RHSFunction,&appctx);
    223:   TSSetRHSJacobian(appctx.ts,appctx.SEMop.stiff,appctx.SEMop.stiff,RHSJacobian,&appctx);

    225:   /* Set Initial conditions for the problem  */
    226:   TrueSolution(appctx.ts,0,appctx.dat.curr_sol,&appctx);

    228:   TSSetSolutionFunction(appctx.ts,(PetscErrorCode (*)(TS,PetscReal,Vec,void *))TrueSolution,&appctx);
    229:   TSSetTime(appctx.ts,0.0);
    230:   TSSetStepNumber(appctx.ts,0);

    232:   TSSolve(appctx.ts,appctx.dat.curr_sol);

    234:   MatDestroy(&appctx.SEMop.stiff);
    235:   MatDestroy(&appctx.SEMop.keptstiff);
    236:   MatDestroy(&appctx.SEMop.grad);
    237:   VecDestroy(&appctx.SEMop.grid);
    238:   VecDestroy(&appctx.SEMop.mass);
    239:   VecDestroy(&appctx.dat.curr_sol);
    240:   PetscFree2(appctx.SEMop.gll.nodes,appctx.SEMop.gll.weights);
    241:   DMDestroy(&appctx.da);
    242:   TSDestroy(&appctx.ts);

    244:   /*
    245:      Always call PetscFinalize() before exiting a program.  This routine
    246:        - finalizes the PETSc libraries as well as MPI
    247:        - provides summary and diagnostic information if certain runtime
    248:          options are chosen (e.g., -log_summary).
    249:   */
    250:     PetscFinalize();
    251:     return 0;
    252: }

    254: /*
    255:    TrueSolution() computes the true solution for the PDE

    257:    Input Parameter:
    258:    u - uninitialized solution vector (global)
    259:    appctx - user-defined application context

    261:    Output Parameter:
    262:    u - vector with solution at initial time (global)
    263: */
    264: PetscErrorCode TrueSolution(TS ts, PetscReal t, Vec u,AppCtx *appctx)
    265: {
    266:   PetscScalar       *s;
    267:   const PetscScalar *xg;
    268:   PetscInt          i,xs,xn;

    270:   DMDAVecGetArray(appctx->da,u,&s);
    271:   DMDAVecGetArrayRead(appctx->da,appctx->SEMop.grid,(void*)&xg);
    272:   DMDAGetCorners(appctx->da,&xs,NULL,NULL,&xn,NULL,NULL);
    273:   for (i=xs; i<xs+xn; i++) {
    274:     s[i]=2.0*appctx->param.mu*PETSC_PI*PetscSinScalar(PETSC_PI*xg[i])*PetscExpReal(-appctx->param.mu*PETSC_PI*PETSC_PI*t)/(2.0+PetscCosScalar(PETSC_PI*xg[i])*PetscExpReal(-appctx->param.mu*PETSC_PI*PETSC_PI*t));
    275:   }
    276:   DMDAVecRestoreArray(appctx->da,u,&s);
    277:   DMDAVecRestoreArrayRead(appctx->da,appctx->SEMop.grid,(void*)&xg);
    278:   return 0;
    279: }

    281: PetscErrorCode RHSFunction(TS ts,PetscReal t,Vec globalin,Vec globalout,void *ctx)
    282: {
    283:   AppCtx          *appctx = (AppCtx*)ctx;

    285:   MatMult(appctx->SEMop.grad,globalin,globalout); /* grad u */
    286:   VecPointwiseMult(globalout,globalin,globalout); /* u grad u */
    287:   VecScale(globalout, -1.0);
    288:   MatMultAdd(appctx->SEMop.keptstiff,globalin,globalout,globalout);
    289:   return 0;
    290: }

    292: /*

    294:       K is the discretiziation of the Laplacian
    295:       G is the discretization of the gradient

    297:       Computes Jacobian of      K u + diag(u) G u   which is given by
    298:               K   + diag(u)G + diag(Gu)
    299: */
    300: PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec globalin,Mat A, Mat B,void *ctx)
    301: {
    302:   AppCtx         *appctx = (AppCtx*)ctx;
    303:   Vec            Gglobalin;

    305:   /*    A = diag(u) G */

    307:   MatCopy(appctx->SEMop.grad,A,SAME_NONZERO_PATTERN);
    308:   MatDiagonalScale(A,globalin,NULL);

    310:   /*    A  = A + diag(Gu) */
    311:   VecDuplicate(globalin,&Gglobalin);
    312:   MatMult(appctx->SEMop.grad,globalin,Gglobalin);
    313:   MatDiagonalSet(A,Gglobalin,ADD_VALUES);
    314:   VecDestroy(&Gglobalin);

    316:   /*   A  = K - A    */
    317:   MatScale(A,-1.0);
    318:   MatAXPY(A,0.0,appctx->SEMop.keptstiff,SAME_NONZERO_PATTERN);
    319:   return 0;
    320: }

    322: /* --------------------------------------------------------------------- */

    324: #include "petscblaslapack.h"
    325: /*
    326:      Matrix free operation of 1d Laplacian and Grad for GLL spectral elements
    327: */
    328: PetscErrorCode MatMult_Laplacian(Mat A,Vec x,Vec y)
    329: {
    330:   AppCtx            *appctx;
    331:   PetscReal         **temp,vv;
    332:   PetscInt          i,j,xs,xn;
    333:   Vec               xlocal,ylocal;
    334:   const PetscScalar *xl;
    335:   PetscScalar       *yl;
    336:   PetscBLASInt      _One = 1,n;
    337:   PetscScalar       _DOne = 1;

    339:   MatShellGetContext(A,&appctx);
    340:   DMGetLocalVector(appctx->da,&xlocal);
    341:   DMGlobalToLocalBegin(appctx->da,x,INSERT_VALUES,xlocal);
    342:   DMGlobalToLocalEnd(appctx->da,x,INSERT_VALUES,xlocal);
    343:   DMGetLocalVector(appctx->da,&ylocal);
    344:   VecSet(ylocal,0.0);
    345:   PetscGaussLobattoLegendreElementLaplacianCreate(appctx->SEMop.gll.n,appctx->SEMop.gll.nodes,appctx->SEMop.gll.weights,&temp);
    346:   for (i=0; i<appctx->param.N; i++) {
    347:     vv =-appctx->param.mu*2.0/appctx->param.Le;
    348:     for (j=0; j<appctx->param.N; j++) temp[i][j]=temp[i][j]*vv;
    349:   }
    350:   DMDAVecGetArrayRead(appctx->da,xlocal,(void*)&xl);
    351:   DMDAVecGetArray(appctx->da,ylocal,&yl);
    352:   DMDAGetCorners(appctx->da,&xs,NULL,NULL,&xn,NULL,NULL);
    353:   PetscBLASIntCast(appctx->param.N,&n);
    354:   for (j=xs; j<xs+xn; j += appctx->param.N-1) {
    355:     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&_DOne,&temp[0][0],&n,&xl[j],&_One,&_DOne,&yl[j],&_One));
    356:   }
    357:   DMDAVecRestoreArrayRead(appctx->da,xlocal,(void*)&xl);
    358:   DMDAVecRestoreArray(appctx->da,ylocal,&yl);
    359:   PetscGaussLobattoLegendreElementLaplacianDestroy(appctx->SEMop.gll.n,appctx->SEMop.gll.nodes,appctx->SEMop.gll.weights,&temp);
    360:   VecSet(y,0.0);
    361:   DMLocalToGlobalBegin(appctx->da,ylocal,ADD_VALUES,y);
    362:   DMLocalToGlobalEnd(appctx->da,ylocal,ADD_VALUES,y);
    363:   DMRestoreLocalVector(appctx->da,&xlocal);
    364:   DMRestoreLocalVector(appctx->da,&ylocal);
    365:   VecPointwiseDivide(y,y,appctx->SEMop.mass);
    366:   return 0;
    367: }

    369: PetscErrorCode MatMult_Advection(Mat A,Vec x,Vec y)
    370: {
    371:   AppCtx            *appctx;
    372:   PetscReal         **temp;
    373:   PetscInt          j,xs,xn;
    374:   Vec               xlocal,ylocal;
    375:   const PetscScalar *xl;
    376:   PetscScalar       *yl;
    377:   PetscBLASInt      _One = 1,n;
    378:   PetscScalar       _DOne = 1;

    380:   MatShellGetContext(A,&appctx);
    381:   DMGetLocalVector(appctx->da,&xlocal);
    382:   DMGlobalToLocalBegin(appctx->da,x,INSERT_VALUES,xlocal);
    383:   DMGlobalToLocalEnd(appctx->da,x,INSERT_VALUES,xlocal);
    384:   DMGetLocalVector(appctx->da,&ylocal);
    385:   VecSet(ylocal,0.0);
    386:   PetscGaussLobattoLegendreElementAdvectionCreate(appctx->SEMop.gll.n,appctx->SEMop.gll.nodes,appctx->SEMop.gll.weights,&temp);
    387:   DMDAVecGetArrayRead(appctx->da,xlocal,(void*)&xl);
    388:   DMDAVecGetArray(appctx->da,ylocal,&yl);
    389:   DMDAGetCorners(appctx->da,&xs,NULL,NULL,&xn,NULL,NULL);
    390:   PetscBLASIntCast(appctx->param.N,&n);
    391:   for (j=xs; j<xs+xn; j += appctx->param.N-1) {
    392:     PetscStackCallBLAS("BLASgemv",BLASgemv_("N",&n,&n,&_DOne,&temp[0][0],&n,&xl[j],&_One,&_DOne,&yl[j],&_One));
    393:   }
    394:   DMDAVecRestoreArrayRead(appctx->da,xlocal,(void*)&xl);
    395:   DMDAVecRestoreArray(appctx->da,ylocal,&yl);
    396:   PetscGaussLobattoLegendreElementAdvectionDestroy(appctx->SEMop.gll.n,appctx->SEMop.gll.nodes,appctx->SEMop.gll.weights,&temp);
    397:   VecSet(y,0.0);
    398:   DMLocalToGlobalBegin(appctx->da,ylocal,ADD_VALUES,y);
    399:   DMLocalToGlobalEnd(appctx->da,ylocal,ADD_VALUES,y);
    400:   DMRestoreLocalVector(appctx->da,&xlocal);
    401:   DMRestoreLocalVector(appctx->da,&ylocal);
    402:   VecPointwiseDivide(y,y,appctx->SEMop.mass);
    403:   VecScale(y,-1.0);
    404:   return 0;
    405: }

    407: /*
    408:    RHSMatrixLaplacian - User-provided routine to compute the right-hand-side
    409:    matrix for the Laplacian operator

    411:    Input Parameters:
    412:    ts - the TS context
    413:    t - current time  (ignored)
    414:    X - current solution (ignored)
    415:    dummy - optional user-defined context, as set by TSetRHSJacobian()

    417:    Output Parameters:
    418:    AA - Jacobian matrix
    419:    BB - optionally different matrix from which the preconditioner is built
    420:    str - flag indicating matrix structure

    422: */
    423: PetscErrorCode RHSMatrixLaplaciangllDM(TS ts,PetscReal t,Vec X,Mat A,Mat BB,void *ctx)
    424: {
    425:   PetscReal      **temp;
    426:   PetscReal      vv;
    427:   AppCtx         *appctx = (AppCtx*)ctx;     /* user-defined application context */
    428:   PetscInt       i,xs,xn,l,j;
    429:   PetscInt       *rowsDM;
    430:   PetscBool      flg = PETSC_FALSE;

    432:   PetscOptionsGetBool(NULL,NULL,"-gll_mf",&flg,NULL);

    434:   if (!flg) {
    435:     /*
    436:      Creates the element stiffness matrix for the given gll
    437:      */
    438:     PetscGaussLobattoLegendreElementLaplacianCreate(appctx->SEMop.gll.n,appctx->SEMop.gll.nodes,appctx->SEMop.gll.weights,&temp);
    439:     /* workaround for clang analyzer warning: Division by zero */

    442:     /* scale by the size of the element */
    443:     for (i=0; i<appctx->param.N; i++) {
    444:       vv=-appctx->param.mu*2.0/appctx->param.Le;
    445:       for (j=0; j<appctx->param.N; j++) temp[i][j]=temp[i][j]*vv;
    446:     }

    448:     MatSetOption(A,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);
    449:     DMDAGetCorners(appctx->da,&xs,NULL,NULL,&xn,NULL,NULL);

    451:     xs   = xs/(appctx->param.N-1);
    452:     xn   = xn/(appctx->param.N-1);

    454:     PetscMalloc1(appctx->param.N,&rowsDM);
    455:     /*
    456:      loop over local elements
    457:      */
    458:     for (j=xs; j<xs+xn; j++) {
    459:       for (l=0; l<appctx->param.N; l++) {
    460:         rowsDM[l] = 1+(j-xs)*(appctx->param.N-1)+l;
    461:       }
    462:       MatSetValuesLocal(A,appctx->param.N,rowsDM,appctx->param.N,rowsDM,&temp[0][0],ADD_VALUES);
    463:     }
    464:     PetscFree(rowsDM);
    465:     MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    466:     MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
    467:     VecReciprocal(appctx->SEMop.mass);
    468:     MatDiagonalScale(A,appctx->SEMop.mass,0);
    469:     VecReciprocal(appctx->SEMop.mass);

    471:     PetscGaussLobattoLegendreElementLaplacianDestroy(appctx->SEMop.gll.n,appctx->SEMop.gll.nodes,appctx->SEMop.gll.weights,&temp);
    472:   } else {
    473:     MatSetType(A,MATSHELL);
    474:     MatSetUp(A);
    475:     MatShellSetContext(A,appctx);
    476:     MatShellSetOperation(A,MATOP_MULT,(void (*)(void))MatMult_Laplacian);
    477:   }
    478:   return 0;
    479: }

    481: /*
    482:    RHSMatrixAdvection - User-provided routine to compute the right-hand-side
    483:    matrix for the Advection (gradient) operator.

    485:    Input Parameters:
    486:    ts - the TS context
    487:    t - current time
    488:    global_in - global input vector
    489:    dummy - optional user-defined context, as set by TSetRHSJacobian()

    491:    Output Parameters:
    492:    AA - Jacobian matrix
    493:    BB - optionally different preconditioning matrix
    494:    str - flag indicating matrix structure

    496: */
    497: PetscErrorCode RHSMatrixAdvectiongllDM(TS ts,PetscReal t,Vec X,Mat A,Mat BB,void *ctx)
    498: {
    499:   PetscReal      **temp;
    500:   AppCtx         *appctx = (AppCtx*)ctx;     /* user-defined application context */
    501:   PetscInt       xs,xn,l,j;
    502:   PetscInt       *rowsDM;
    503:   PetscBool      flg = PETSC_FALSE;

    505:   PetscOptionsGetBool(NULL,NULL,"-gll_mf",&flg,NULL);

    507:   if (!flg) {
    508:     /*
    509:      Creates the advection matrix for the given gll
    510:      */
    511:     PetscGaussLobattoLegendreElementAdvectionCreate(appctx->SEMop.gll.n,appctx->SEMop.gll.nodes,appctx->SEMop.gll.weights,&temp);
    512:     MatSetOption(A,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);
    513:     DMDAGetCorners(appctx->da,&xs,NULL,NULL,&xn,NULL,NULL);
    514:     xs   = xs/(appctx->param.N-1);
    515:     xn   = xn/(appctx->param.N-1);

    517:     PetscMalloc1(appctx->param.N,&rowsDM);
    518:     for (j=xs; j<xs+xn; j++) {
    519:       for (l=0; l<appctx->param.N; l++) {
    520:         rowsDM[l] = 1+(j-xs)*(appctx->param.N-1)+l;
    521:       }
    522:       MatSetValuesLocal(A,appctx->param.N,rowsDM,appctx->param.N,rowsDM,&temp[0][0],ADD_VALUES);
    523:     }
    524:     PetscFree(rowsDM);
    525:     MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
    526:     MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);

    528:     VecReciprocal(appctx->SEMop.mass);
    529:     MatDiagonalScale(A,appctx->SEMop.mass,0);
    530:     VecReciprocal(appctx->SEMop.mass);

    532:     PetscGaussLobattoLegendreElementAdvectionDestroy(appctx->SEMop.gll.n,appctx->SEMop.gll.nodes,appctx->SEMop.gll.weights,&temp);
    533:   } else {
    534:     MatSetType(A,MATSHELL);
    535:     MatSetUp(A);
    536:     MatShellSetContext(A,appctx);
    537:     MatShellSetOperation(A,MATOP_MULT,(void (*)(void))MatMult_Advection);
    538:   }
    539:   return 0;
    540: }

    542: /*TEST

    544:     build:
    545:       requires: !complex

    547:     test:
    548:       suffix: 1
    549:       requires: !single

    551:     test:
    552:       suffix: 2
    553:       nsize: 5
    554:       requires: !single

    556:     test:
    557:       suffix: 3
    558:       requires: !single
    559:       args: -ts_view  -ts_type beuler -gll_mf -pc_type none -ts_max_steps 5 -ts_monitor_error

    561:     test:
    562:       suffix: 4
    563:       requires: !single
    564:       args: -ts_view  -ts_type beuler  -pc_type none -ts_max_steps 5 -ts_monitor_error

    566: TEST*/