Date: 2023-09-05T10:18:05+00:00

Actual source code: ex34.c
slepc-3.19.2 2023-09-05
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      1: /*
      2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
      4:    Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain

      6:    This file is part of SLEPc.
      7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
      8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
      9: */
     10: /*
     11:    This is a nonlinear eigenvalue problem. When p=2, it is reduced to a linear Laplace eigenvalue
     12:    problem.

     14:    -\nabla\cdot(|\nabla u|^{p-2} \nabla u) = k |u|^{p-2} u in (0,1)x(0,1),

     16:    u = 0 on the entire boundary.

     18:    The code is implemented based on DMPlex using Q1 FEM on a quadrilateral mesh. In this code, we consider p=3.

     20:    Contributed  by Fande Kong fdkong.jd@gmail.com
     21: */

     23: static char help[] = "Nonlinear inverse iteration for A(x)*x=lambda*B(x)*x.\n\n";

     25: #include <slepceps.h>
     26: #include <petscdmplex.h>
     27: #include <petscds.h>

     29: PetscErrorCode CreateSquareMesh(MPI_Comm,DM*);
     30: PetscErrorCode SetupDiscretization(DM);
     31: PetscErrorCode FormJacobianA(SNES,Vec,Mat,Mat,void*);
     32: PetscErrorCode FormFunctionA(SNES,Vec,Vec,void*);
     33: PetscErrorCode MatMult_A(Mat A,Vec x,Vec y);
     34: PetscErrorCode FormJacobianB(SNES,Vec,Mat,Mat,void*);
     35: PetscErrorCode FormFunctionB(SNES,Vec,Vec,void*);
     36: PetscErrorCode MatMult_B(Mat A,Vec x,Vec y);
     37: PetscErrorCode FormFunctionAB(SNES,Vec,Vec,Vec,void*);
     38: PetscErrorCode BoundaryGlobalIndex(DM,const char*,IS*);

     40: typedef struct {
     41:   IS    bdis; /* global indices for boundary DoFs */
     42:   SNES  snes;
     43: } AppCtx;

     45: int main(int argc,char **argv)
     46: {
     47:   DM             dm;
     48:   MPI_Comm       comm;
     49:   AppCtx         user;
     50:   EPS            eps;  /* eigenproblem solver context */
     51:   ST             st;
     52:   EPSType        type;
     53:   Mat            A,B,P;
     54:   Vec            v0;
     55:   PetscContainer container;
     56:   PetscInt       nev,nconv,m,n,M,N;
     57:   PetscBool      nonlin,flg=PETSC_FALSE,update;
     58:   SNES           snes;
     59:   PetscReal      tol,relerr;
     60:   PetscBool      use_shell_matrix=PETSC_FALSE,test_init_sol=PETSC_FALSE;

     62:   PetscFunctionBeginUser;
     63:   PetscCall(SlepcInitialize(&argc,&argv,(char*)0,help));
     64:   comm = PETSC_COMM_WORLD;
     65:   /* Create a quadrilateral mesh on domain (0,1)x(0,1) */
     66:   PetscCall(CreateSquareMesh(comm,&dm));
     67:   /* Setup basis function */
     68:   PetscCall(SetupDiscretization(dm));
     69:   PetscCall(BoundaryGlobalIndex(dm,"marker",&user.bdis));
     70:   /* Check if we are going to use shell matrices */
     71:   PetscCall(PetscOptionsGetBool(NULL,NULL,"-use_shell_matrix",&use_shell_matrix,NULL));
     72:   if (use_shell_matrix) {
     73:     PetscCall(DMCreateMatrix(dm,&P));
     74:     PetscCall(MatGetLocalSize(P,&m,&n));
     75:     PetscCall(MatGetSize(P,&M,&N));
     76:     PetscCall(MatCreateShell(comm,m,n,M,N,&user,&A));
     77:     PetscCall(MatShellSetOperation(A,MATOP_MULT,(void(*)(void))MatMult_A));
     78:     PetscCall(MatCreateShell(comm,m,n,M,N,&user,&B));
     79:     PetscCall(MatShellSetOperation(B,MATOP_MULT,(void(*)(void))MatMult_B));
     80:   } else {
     81:     PetscCall(DMCreateMatrix(dm,&A));
     82:     PetscCall(MatDuplicate(A,MAT_COPY_VALUES,&B));
     83:   }

     85:   /*
     86:      Compose callback functions and context that will be needed by the solver
     87:   */
     88:   PetscCall(PetscObjectComposeFunction((PetscObject)A,"formFunction",FormFunctionA));
     89:   PetscCall(PetscOptionsGetBool(NULL,NULL,"-form_function_ab",&flg,NULL));
     90:   if (flg) PetscCall(PetscObjectComposeFunction((PetscObject)A,"formFunctionAB",FormFunctionAB));
     91:   PetscCall(PetscObjectComposeFunction((PetscObject)A,"formJacobian",FormJacobianA));
     92:   PetscCall(PetscObjectComposeFunction((PetscObject)B,"formFunction",FormFunctionB));
     93:   PetscCall(PetscContainerCreate(comm,&container));
     94:   PetscCall(PetscContainerSetPointer(container,&user));
     95:   PetscCall(PetscObjectCompose((PetscObject)A,"formFunctionCtx",(PetscObject)container));
     96:   PetscCall(PetscObjectCompose((PetscObject)A,"formJacobianCtx",(PetscObject)container));
     97:   PetscCall(PetscObjectCompose((PetscObject)B,"formFunctionCtx",(PetscObject)container));
     98:   PetscCall(PetscContainerDestroy(&container));

    100:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    101:                 Create the eigensolver and set various options
    102:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    104:   PetscCall(EPSCreate(comm,&eps));
    105:   PetscCall(EPSSetOperators(eps,A,B));
    106:   PetscCall(EPSSetProblemType(eps,EPS_GNHEP));
    107:   /*
    108:      Use nonlinear inverse iteration
    109:   */
    110:   PetscCall(EPSSetType(eps,EPSPOWER));
    111:   PetscCall(EPSPowerSetNonlinear(eps,PETSC_TRUE));
    112:   /*
    113:     Attach DM to SNES
    114:   */
    115:   PetscCall(EPSPowerGetSNES(eps,&snes));
    116:   user.snes = snes;
    117:   PetscCall(SNESSetDM(snes,dm));
    118:   PetscCall(EPSSetFromOptions(eps));

    120:   /* Set a preconditioning matrix to ST */
    121:   if (use_shell_matrix) {
    122:     PetscCall(EPSGetST(eps,&st));
    123:     PetscCall(STSetPreconditionerMat(st,P));
    124:   }

    126:   /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
    127:                       Solve the eigensystem
    128:      - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

    130:   PetscCall(EPSSolve(eps));

    132:   PetscCall(EPSGetConverged(eps,&nconv));
    133:   PetscCall(PetscOptionsGetBool(NULL,NULL,"-test_init_sol",&test_init_sol,NULL));
    134:   if (nconv && test_init_sol) {
    135:     PetscScalar   k;
    136:     PetscReal     norm0;
    137:     PetscInt      nits;

    139:     PetscCall(MatCreateVecs(A,&v0,NULL));
    140:     PetscCall(EPSGetEigenpair(eps,0,&k,NULL,v0,NULL));
    141:     PetscCall(EPSSetInitialSpace(eps,1,&v0));
    142:     PetscCall(VecDestroy(&v0));
    143:     /* Norm of the previous residual */
    144:     PetscCall(SNESGetFunctionNorm(snes,&norm0));
    145:     /* Make the tolerance smaller than the last residual
    146:        SNES will converge right away if the initial is setup correctly */
    147:     PetscCall(SNESSetTolerances(snes,norm0*1.2,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT,PETSC_DEFAULT));
    148:     PetscCall(EPSSolve(eps));
    149:     /* Number of Newton iterations supposes to be zero */
    150:     PetscCall(SNESGetIterationNumber(snes,&nits));
    151:     if (nits) PetscCall(PetscPrintf(comm," Number of Newton iterations %" PetscInt_FMT " should be zero \n",nits));
    152:   }

    154:   /*
    155:      Optional: Get some information from the solver and display it
    156:   */
    157:   PetscCall(EPSGetType(eps,&type));
    158:   PetscCall(EPSGetTolerances(eps,&tol,NULL));
    159:   PetscCall(EPSPowerGetNonlinear(eps,&nonlin));
    160:   PetscCall(EPSPowerGetUpdate(eps,&update));
    161:   PetscCall(PetscPrintf(comm," Solution method: %s%s\n\n",type,nonlin?(update?" (nonlinear with monolithic update)":" (nonlinear)"):""));
    162:   PetscCall(EPSGetDimensions(eps,&nev,NULL,NULL));
    163:   PetscCall(PetscPrintf(comm," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev));

    165:   /* print eigenvalue and error */
    166:   PetscCall(EPSGetConverged(eps,&nconv));
    167:   if (nconv>0) {
    168:     PetscScalar   k;
    169:     PetscReal     na,nb;
    170:     Vec           a,b,eigen;
    171:     PetscCall(DMCreateGlobalVector(dm,&a));
    172:     PetscCall(VecDuplicate(a,&b));
    173:     PetscCall(VecDuplicate(a,&eigen));
    174:     PetscCall(EPSGetEigenpair(eps,0,&k,NULL,eigen,NULL));
    175:     PetscCall(FormFunctionA(snes,eigen,a,&user));
    176:     PetscCall(FormFunctionB(snes,eigen,b,&user));
    177:     PetscCall(VecAXPY(a,-k,b));
    178:     PetscCall(VecNorm(a,NORM_2,&na));
    179:     PetscCall(VecNorm(b,NORM_2,&nb));
    180:     relerr = na/(nb*PetscAbsScalar(k));
    181:     if (relerr<10*tol) PetscCall(PetscPrintf(comm,"k: %g, relative error below tol\n",(double)PetscRealPart(k)));
    182:     else PetscCall(PetscPrintf(comm,"k: %g, relative error: %g\n",(double)PetscRealPart(k),(double)relerr));
    183:     PetscCall(VecDestroy(&a));
    184:     PetscCall(VecDestroy(&b));
    185:     PetscCall(VecDestroy(&eigen));
    186:   } else PetscCall(PetscPrintf(comm,"Solver did not converge\n"));

    188:   PetscCall(MatDestroy(&A));
    189:   PetscCall(MatDestroy(&B));
    190:   if (use_shell_matrix) PetscCall(MatDestroy(&P));
    191:   PetscCall(DMDestroy(&dm));
    192:   PetscCall(EPSDestroy(&eps));
    193:   PetscCall(ISDestroy(&user.bdis));
    194:   PetscCall(SlepcFinalize());
    195:   return 0;
    196: }

    198: /* <|u|u, v> */
    199: static void f0_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    200:                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    201:                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    202:                  PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
    203: {
    204:   PetscScalar cof = PetscAbsScalar(u[0]);

    206:   f0[0] = cof*u[0];
    207: }

    209: /* <|\nabla u| \nabla u, \nabla v> */
    210: static void f1_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    211:                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    212:                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    213:                  PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
    214: {
    215:   PetscInt    d;
    216:   PetscScalar cof = 0;
    217:   for (d = 0; d < dim; ++d)  cof += u_x[d]*u_x[d];

    219:   cof = PetscSqrtScalar(cof);

    221:   for (d = 0; d < dim; ++d) f1[d] = u_x[d]*cof;
    222: }

    224: /* approximate  Jacobian for   <|u|u, v> */
    225: static void g0_uu(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    226:                   const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    227:                   const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    228:                   PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
    229: {
    230:   g0[0] = 1.0*PetscAbsScalar(u[0]);
    231: }

    233: /* approximate  Jacobian for   <|\nabla u| \nabla u, \nabla v> */
    234: static void g3_uu(PetscInt dim, PetscInt Nf, PetscInt NfAux,
    235:                   const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
    236:                   const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
    237:                   PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
    238: {
    239:   PetscInt d;

    241:   for (d = 0; d < dim; ++d) g3[d*dim+d] = 1.0;
    242: }

    244: PetscErrorCode SetupDiscretization(DM dm)
    245: {
    246:   PetscFE        fe;
    247:   MPI_Comm       comm;

    249:   PetscFunctionBeginUser;
    250:   /* Create finite element */
    251:   PetscCall(PetscObjectGetComm((PetscObject)dm,&comm));
    252:   PetscCall(PetscFECreateDefault(comm,2,1,PETSC_FALSE,NULL,-1,&fe));
    253:   PetscCall(PetscObjectSetName((PetscObject)fe,"u"));
    254:   PetscCall(DMSetField(dm,0,NULL,(PetscObject)fe));
    255:   PetscCall(DMCreateDS(dm));
    256:   PetscCall(PetscFEDestroy(&fe));
    257:   PetscFunctionReturn(PETSC_SUCCESS);
    258: }

    260: PetscErrorCode CreateSquareMesh(MPI_Comm comm,DM *dm)
    261: {
    262:   PetscInt       cells[] = {8,8};
    263:   PetscInt       dim = 2;
    264:   DM             pdm;
    265:   PetscMPIInt    size;

    267:   PetscFunctionBegin;
    268:   PetscCall(DMPlexCreateBoxMesh(comm,dim,PETSC_FALSE,cells,NULL,NULL,NULL,PETSC_TRUE,dm));
    269:   PetscCall(DMSetFromOptions(*dm));
    270:   PetscCall(DMSetUp(*dm));
    271:   PetscCallMPI(MPI_Comm_size(comm,&size));
    272:   if (size > 1) {
    273:     PetscCall(DMPlexDistribute(*dm,0,NULL,&pdm));
    274:     PetscCall(DMDestroy(dm));
    275:     *dm = pdm;
    276:   }
    277:   PetscFunctionReturn(PETSC_SUCCESS);
    278: }

    280: PetscErrorCode BoundaryGlobalIndex(DM dm,const char labelname[],IS *bdis)
    281: {
    282:   IS             bdpoints;
    283:   PetscInt       nindices,*indices,numDof,offset,npoints,i,j;
    284:   const PetscInt *bdpoints_indices;
    285:   DMLabel        bdmarker;
    286:   PetscSection   gsection;

    288:   PetscFunctionBegin;
    289:   PetscCall(DMGetGlobalSection(dm,&gsection));
    290:   PetscCall(DMGetLabel(dm,labelname,&bdmarker));
    291:   PetscCall(DMLabelGetStratumIS(bdmarker,1,&bdpoints));
    292:   PetscCall(ISGetLocalSize(bdpoints,&npoints));
    293:   PetscCall(ISGetIndices(bdpoints,&bdpoints_indices));
    294:   nindices = 0;
    295:   for (i=0;i<npoints;i++) {
    296:     PetscCall(PetscSectionGetDof(gsection,bdpoints_indices[i],&numDof));
    297:     if (numDof<=0) continue;
    298:     nindices += numDof;
    299:   }
    300:   PetscCall(PetscCalloc1(nindices,&indices));
    301:   nindices = 0;
    302:   for (i=0;i<npoints;i++) {
    303:     PetscCall(PetscSectionGetDof(gsection,bdpoints_indices[i],&numDof));
    304:     if (numDof<=0) continue;
    305:     PetscCall(PetscSectionGetOffset(gsection,bdpoints_indices[i],&offset));
    306:     for (j=0;j<numDof;j++) indices[nindices++] = offset+j;
    307:   }
    308:   PetscCall(ISRestoreIndices(bdpoints,&bdpoints_indices));
    309:   PetscCall(ISDestroy(&bdpoints));
    310:   PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)dm),nindices,indices,PETSC_OWN_POINTER,bdis));
    311:   PetscFunctionReturn(PETSC_SUCCESS);
    312: }

    314: static PetscErrorCode FormJacobian(SNES snes,Vec X,Mat A,Mat B,void *ctx)
    315: {
    316:   DM             dm;
    317:   Vec            Xloc;

    319:   PetscFunctionBegin;
    320:   PetscCall(SNESGetDM(snes,&dm));
    321:   PetscCall(DMGetLocalVector(dm,&Xloc));
    322:   PetscCall(VecZeroEntries(Xloc));
    323:   PetscCall(DMGlobalToLocalBegin(dm,X,INSERT_VALUES,Xloc));
    324:   PetscCall(DMGlobalToLocalEnd(dm,X,INSERT_VALUES,Xloc));
    325:   CHKMEMQ;
    326:   PetscCall(DMPlexSNESComputeJacobianFEM(dm,Xloc,A,B,ctx));
    327:   if (A!=B) {
    328:     PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY));
    329:     PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY));
    330:   }
    331:   CHKMEMQ;
    332:   PetscCall(DMRestoreLocalVector(dm,&Xloc));
    333:   PetscFunctionReturn(PETSC_SUCCESS);
    334: }

    336: PetscErrorCode FormJacobianA(SNES snes,Vec X,Mat A,Mat B,void *ctx)
    337: {
    338:   DM             dm;
    339:   PetscDS        prob;
    340:   PetscWeakForm  wf;
    341:   AppCtx         *userctx = (AppCtx *)ctx;

    343:   PetscFunctionBegin;
    344:   PetscCall(MatSetOption(B,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE));
    345:   PetscCall(SNESGetDM(snes,&dm));
    346:   PetscCall(DMGetDS(dm,&prob));
    347:   PetscCall(PetscDSGetWeakForm(prob, &wf));
    348:   PetscCall(PetscWeakFormClearIndex(wf, NULL, 0, 0, 0, PETSC_WF_G3, 0));
    349:   PetscCall(PetscWeakFormSetIndexJacobian(wf, NULL, 0, 0, 0, 0, 0, NULL, 0, NULL, 0, NULL, 0, g3_uu));
    350:   PetscCall(FormJacobian(snes,X,A,B,ctx));
    351:   PetscCall(MatZeroRowsIS(B,userctx->bdis,1.0,NULL,NULL));
    352:   PetscFunctionReturn(PETSC_SUCCESS);
    353: }

    355: PetscErrorCode FormJacobianB(SNES snes,Vec X,Mat A,Mat B,void *ctx)
    356: {
    357:   DM             dm;
    358:   PetscDS        prob;
    359:   PetscWeakForm  wf;
    360:   AppCtx         *userctx = (AppCtx *)ctx;

    362:   PetscFunctionBegin;
    363:   PetscCall(MatSetOption(B,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE));
    364:   PetscCall(SNESGetDM(snes,&dm));
    365:   PetscCall(DMGetDS(dm,&prob));
    366:   PetscCall(PetscDSGetWeakForm(prob, &wf));
    367:   PetscCall(PetscWeakFormClearIndex(wf, NULL, 0, 0, 0, PETSC_WF_G3, 0));
    368:   PetscCall(PetscWeakFormSetIndexJacobian(wf, NULL, 0, 0, 0, 0, 0, g0_uu, 0, NULL, 0, NULL, 0, NULL));
    369:   PetscCall(FormJacobian(snes,X,A,B,ctx));
    370:   PetscCall(MatZeroRowsIS(B,userctx->bdis,0.0,NULL,NULL));
    371:   PetscFunctionReturn(PETSC_SUCCESS);
    372: }

    374: PetscErrorCode FormFunctionAB(SNES snes,Vec x,Vec Ax,Vec Bx,void *ctx)
    375: {
    376:   PetscFunctionBegin;
    377:   /*
    378:    * In real applications, users should have a generic formFunctionAB which
    379:    * forms Ax and Bx simultaneously for an more efficient calculation.
    380:    * In this example, we just call FormFunctionA+FormFunctionB to mimic how
    381:    * to use FormFunctionAB
    382:    */
    383:   PetscCall(FormFunctionA(snes,x,Ax,ctx));
    384:   PetscCall(FormFunctionB(snes,x,Bx,ctx));
    385:   PetscFunctionReturn(PETSC_SUCCESS);
    386: }

    388: static PetscErrorCode FormFunction(SNES snes,Vec X,Vec F,void *ctx)
    389: {
    390:   DM             dm;
    391:   Vec            Xloc,Floc;

    393:   PetscFunctionBegin;
    394:   PetscCall(SNESGetDM(snes,&dm));
    395:   PetscCall(DMGetLocalVector(dm,&Xloc));
    396:   PetscCall(DMGetLocalVector(dm,&Floc));
    397:   PetscCall(VecZeroEntries(Xloc));
    398:   PetscCall(VecZeroEntries(Floc));
    399:   PetscCall(DMGlobalToLocalBegin(dm,X,INSERT_VALUES,Xloc));
    400:   PetscCall(DMGlobalToLocalEnd(dm,X,INSERT_VALUES,Xloc));
    401:   CHKMEMQ;
    402:   PetscCall(DMPlexSNESComputeResidualFEM(dm,Xloc,Floc,ctx));
    403:   CHKMEMQ;
    404:   PetscCall(VecZeroEntries(F));
    405:   PetscCall(DMLocalToGlobalBegin(dm,Floc,ADD_VALUES,F));
    406:   PetscCall(DMLocalToGlobalEnd(dm,Floc,ADD_VALUES,F));
    407:   PetscCall(DMRestoreLocalVector(dm,&Xloc));
    408:   PetscCall(DMRestoreLocalVector(dm,&Floc));
    409:   PetscFunctionReturn(PETSC_SUCCESS);
    410: }

    412: PetscErrorCode FormFunctionA(SNES snes,Vec X,Vec F,void *ctx)
    413: {
    414:   DM             dm;
    415:   PetscDS        prob;
    416:   PetscWeakForm  wf;
    417:   PetscInt       nindices,iStart,iEnd,i;
    418:   AppCtx         *userctx = (AppCtx *)ctx;
    419:   PetscScalar    *array,value;
    420:   const PetscInt *indices;
    421:   PetscInt       vecstate;

    423:   PetscFunctionBegin;
    424:   PetscCall(SNESGetDM(snes,&dm));
    425:   PetscCall(DMGetDS(dm,&prob));
    426:   /* hook functions */
    427:   PetscCall(PetscDSGetWeakForm(prob, &wf));
    428:   PetscCall(PetscWeakFormClearIndex(wf, NULL, 0, 0, 0, PETSC_WF_F0, 0));
    429:   PetscCall(PetscWeakFormSetIndexResidual(wf, NULL, 0, 0, 0, 0, NULL, 0, f1_u));
    430:   PetscCall(FormFunction(snes,X,F,ctx));
    431:   /* Boundary condition */
    432:   PetscCall(VecLockGet(X,&vecstate));
    433:   if (vecstate>0) PetscCall(VecLockReadPop(X));
    434:   PetscCall(VecGetOwnershipRange(X,&iStart,&iEnd));
    435:   PetscCall(VecGetArray(X,&array));
    436:   PetscCall(ISGetLocalSize(userctx->bdis,&nindices));
    437:   PetscCall(ISGetIndices(userctx->bdis,&indices));
    438:   for (i=0;i<nindices;i++) {
    439:     value = array[indices[i]-iStart] - 0.0;
    440:     PetscCall(VecSetValue(F,indices[i],value,INSERT_VALUES));
    441:   }
    442:   PetscCall(ISRestoreIndices(userctx->bdis,&indices));
    443:   PetscCall(VecRestoreArray(X,&array));
    444:   if (vecstate>0) PetscCall(VecLockReadPush(X));
    445:   PetscCall(VecAssemblyBegin(F));
    446:   PetscCall(VecAssemblyEnd(F));
    447:   PetscFunctionReturn(PETSC_SUCCESS);
    448: }

    450: PetscErrorCode MatMult_A(Mat A,Vec x,Vec y)
    451: {
    452:   AppCtx         *userctx;

    454:   PetscFunctionBegin;
    455:   PetscCall(MatShellGetContext(A,&userctx));
    456:   PetscCall(FormFunctionA(userctx->snes,x,y,userctx));
    457:   PetscFunctionReturn(PETSC_SUCCESS);
    458: }

    460: PetscErrorCode FormFunctionB(SNES snes,Vec X,Vec F,void *ctx)
    461: {
    462:   DM             dm;
    463:   PetscDS        prob;
    464:   PetscWeakForm  wf;
    465:   PetscInt       nindices,iStart,iEnd,i;
    466:   AppCtx         *userctx = (AppCtx *)ctx;
    467:   PetscScalar    value;
    468:   const PetscInt *indices;

    470:   PetscFunctionBegin;
    471:   PetscCall(SNESGetDM(snes,&dm));
    472:   PetscCall(DMGetDS(dm,&prob));
    473:   /* hook functions */
    474:   PetscCall(PetscDSGetWeakForm(prob, &wf));
    475:   PetscCall(PetscWeakFormClearIndex(wf, NULL, 0, 0, 0, PETSC_WF_F1, 0));
    476:   PetscCall(PetscWeakFormSetIndexResidual(wf, NULL, 0, 0, 0, 0, f0_u, 0, NULL));
    477:   PetscCall(FormFunction(snes,X,F,ctx));
    478:   /* Boundary condition */
    479:   PetscCall(VecGetOwnershipRange(F,&iStart,&iEnd));
    480:   PetscCall(ISGetLocalSize(userctx->bdis,&nindices));
    481:   PetscCall(ISGetIndices(userctx->bdis,&indices));
    482:   for (i=0;i<nindices;i++) {
    483:     value = 0.0;
    484:     PetscCall(VecSetValue(F,indices[i],value,INSERT_VALUES));
    485:   }
    486:   PetscCall(ISRestoreIndices(userctx->bdis,&indices));
    487:   PetscCall(VecAssemblyBegin(F));
    488:   PetscCall(VecAssemblyEnd(F));
    489:   PetscFunctionReturn(PETSC_SUCCESS);
    490: }

    492: PetscErrorCode MatMult_B(Mat B,Vec x,Vec y)
    493: {
    494:   AppCtx         *userctx;

    496:   PetscFunctionBegin;
    497:   PetscCall(MatShellGetContext(B,&userctx));
    498:   PetscCall(FormFunctionB(userctx->snes,x,y,userctx));
    499:   PetscFunctionReturn(PETSC_SUCCESS);
    500: }

    502: /*TEST

    504:    testset:
    505:       requires: double
    506:       args: -petscspace_degree 1 -petscspace_poly_tensor -checkfunctionlist 0
    507:       output_file: output/ex34_1.out
    508:       test:
    509:          suffix: 1
    510:       test:
    511:          suffix: 2
    512:          args: -eps_power_update -form_function_ab {{0 1}}
    513:          filter: sed -e "s/ with monolithic update//"
    514:       test:
    515:          suffix: 3
    516:          args: -use_shell_matrix -eps_power_snes_mf_operator 1
    517:       test:
    518:          suffix: 4
    519:          args: -use_shell_matrix -eps_power_update -init_eps_power_snes_mf_operator 1 -eps_power_snes_mf_operator 1 -form_function_ab {{0 1}}
    520:          filter: sed -e "s/ with monolithic update//"
    521:       test:
    522:          suffix: 5
    523:          args: -use_shell_matrix -eps_power_update -init_eps_power_snes_mf_operator 1 -eps_power_snes_mf_operator 1 -form_function_ab {{0 1}} -test_init_sol 1
    524:          filter: sed -e "s/ with monolithic update//"

    526:       test:
    527:          suffix: 6
    528:          args: -use_shell_matrix -eps_power_update -init_eps_power_snes_mf_operator 1 -eps_power_snes_mf_operator 1 -form_function_ab {{0 1}} -eps_monitor_all
    529:          output_file: output/ex34_6.out
    530:          filter: sed -e "s/\([+-].*i\)//g" -e "1,3s/[0-9]//g" -e "/[45] EPS/d"
    531: TEST*/