Actual source code: lsc.c
petsc-3.7.1 2016-05-15
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      2: #include <petsc/private/pcimpl.h>   /*I "petscpc.h" I*/

      4: typedef struct {
      5:   PetscBool allocated;
      6:   PetscBool scalediag;
      7:   KSP       kspL;
      8:   Vec       scale;
      9:   Vec       x0,y0,x1;
     10:   Mat       L;             /* keep a copy to reuse when obtained with L = A10*A01 */
     11: } PC_LSC;

     15: static PetscErrorCode PCLSCAllocate_Private(PC pc)
     16: {
     17:   PC_LSC         *lsc = (PC_LSC*)pc->data;
     18:   Mat            A;

     22:   if (lsc->allocated) return(0);
     23:   KSPCreate(PetscObjectComm((PetscObject)pc),&lsc->kspL);
     24:   KSPSetErrorIfNotConverged(lsc->kspL,pc->erroriffailure);
     25:   PetscObjectIncrementTabLevel((PetscObject)lsc->kspL,(PetscObject)pc,1);
     26:   KSPSetType(lsc->kspL,KSPPREONLY);
     27:   KSPSetOptionsPrefix(lsc->kspL,((PetscObject)pc)->prefix);
     28:   KSPAppendOptionsPrefix(lsc->kspL,"lsc_");
     29:   MatSchurComplementGetSubMatrices(pc->mat,&A,NULL,NULL,NULL,NULL);
     30:   MatCreateVecs(A,&lsc->x0,&lsc->y0);
     31:   MatCreateVecs(pc->pmat,&lsc->x1,NULL);
     32:   if (lsc->scalediag) {
     33:     VecDuplicate(lsc->x0,&lsc->scale);
     34:   }
     35:   lsc->allocated = PETSC_TRUE;
     36:   return(0);
     37: }

     41: static PetscErrorCode PCSetUp_LSC(PC pc)
     42: {
     43:   PC_LSC         *lsc = (PC_LSC*)pc->data;
     44:   Mat            L,Lp,B,C;

     48:   PCLSCAllocate_Private(pc);
     49:   PetscObjectQuery((PetscObject)pc->mat,"LSC_L",(PetscObject*)&L);
     50:   if (!L) {PetscObjectQuery((PetscObject)pc->pmat,"LSC_L",(PetscObject*)&L);}
     51:   PetscObjectQuery((PetscObject)pc->pmat,"LSC_Lp",(PetscObject*)&Lp);
     52:   if (!Lp) {PetscObjectQuery((PetscObject)pc->mat,"LSC_Lp",(PetscObject*)&Lp);}
     53:   if (!L) {
     54:     MatSchurComplementGetSubMatrices(pc->mat,NULL,NULL,&B,&C,NULL);
     55:     if (!lsc->L) {
     56:       MatMatMult(C,B,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&lsc->L);
     57:     } else {
     58:       MatMatMult(C,B,MAT_REUSE_MATRIX,PETSC_DEFAULT,&lsc->L);
     59:     }
     60:     Lp = L = lsc->L;
     61:   }
     62:   if (lsc->scale) {
     63:     Mat Ap;
     64:     MatSchurComplementGetSubMatrices(pc->mat,NULL,&Ap,NULL,NULL,NULL);
     65:     MatGetDiagonal(Ap,lsc->scale); /* Should be the mass matrix, but we don't have plumbing for that yet */
     66:     VecReciprocal(lsc->scale);
     67:   }
     68:   KSPSetOperators(lsc->kspL,L,Lp);
     69:   KSPSetFromOptions(lsc->kspL);
     70:   return(0);
     71: }

     75: static PetscErrorCode PCApply_LSC(PC pc,Vec x,Vec y)
     76: {
     77:   PC_LSC         *lsc = (PC_LSC*)pc->data;
     78:   Mat            A,B,C;

     82:   MatSchurComplementGetSubMatrices(pc->mat,&A,NULL,&B,&C,NULL);
     83:   KSPSolve(lsc->kspL,x,lsc->x1);
     84:   MatMult(B,lsc->x1,lsc->x0);
     85:   if (lsc->scale) {
     86:     VecPointwiseMult(lsc->x0,lsc->x0,lsc->scale);
     87:   }
     88:   MatMult(A,lsc->x0,lsc->y0);
     89:   if (lsc->scale) {
     90:     VecPointwiseMult(lsc->y0,lsc->y0,lsc->scale);
     91:   }
     92:   MatMult(C,lsc->y0,lsc->x1);
     93:   KSPSolve(lsc->kspL,lsc->x1,y);
     94:   return(0);
     95: }

     99: static PetscErrorCode PCReset_LSC(PC pc)
    100: {
    101:   PC_LSC         *lsc = (PC_LSC*)pc->data;

    105:   VecDestroy(&lsc->x0);
    106:   VecDestroy(&lsc->y0);
    107:   VecDestroy(&lsc->x1);
    108:   VecDestroy(&lsc->scale);
    109:   KSPDestroy(&lsc->kspL);
    110:   MatDestroy(&lsc->L);
    111:   return(0);
    112: }

    116: static PetscErrorCode PCDestroy_LSC(PC pc)
    117: {

    121:   PCReset_LSC(pc);
    122:   PetscFree(pc->data);
    123:   return(0);
    124: }

    128: static PetscErrorCode PCSetFromOptions_LSC(PetscOptionItems *PetscOptionsObject,PC pc)
    129: {
    130:   PC_LSC         *lsc = (PC_LSC*)pc->data;

    134:   PetscOptionsHead(PetscOptionsObject,"LSC options");
    135:   {
    136:     PetscOptionsBool("-pc_lsc_scale_diag","Use diagonal of velocity block (A) for scaling","None",lsc->scalediag,&lsc->scalediag,NULL);
    137:   }
    138:   PetscOptionsTail();
    139:   return(0);
    140: }

    144: static PetscErrorCode PCView_LSC(PC pc,PetscViewer viewer)
    145: {
    146:   PC_LSC         *jac = (PC_LSC*)pc->data;
    148:   PetscBool      iascii;

    151:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    152:   if (iascii) {
    153:     PetscViewerASCIIPushTab(viewer);
    154:     KSPView(jac->kspL,viewer);
    155:     PetscViewerASCIIPopTab(viewer);
    156:   }
    157:   return(0);
    158: }

    160: /*MC
    161:      PCLSC - Preconditioning for Schur complements, based on Least Squares Commutators

    163:    Options Database Key:
    164: .    -pc_lsc_scale_diag - Use the diagonal of A for scaling

    166:    Level: intermediate

    168:    Notes:
    169:    This preconditioner will normally be used with PCFieldSplit to precondition the Schur complement, but
    170:    it can be used for any Schur complement system.  Consider the Schur complement

    172: .vb
    173:    S = A11 - A10 inv(A00) A01
    174: .ve

    176:    PCLSC currently doesn't do anything with A11, so let's assume it is 0.  The idea is that a good approximation to
    177:    inv(S) is given by

    179: .vb
    180:    inv(A10 A01) A10 A00 A01 inv(A10 A01)
    181: .ve

    183:    The product A10 A01 can be computed for you, but you can provide it (this is
    184:    usually more efficient anyway).  In the case of incompressible flow, A10 A10 is a Laplacian, call it L.  The current
    185:    interface is to hang L and a preconditioning matrix Lp on the preconditioning matrix.

    187:    If you had called KSPSetOperators(ksp,S,Sp), S should have type MATSCHURCOMPLEMENT and Sp can be any type you
    188:    like (PCLSC doesn't use it directly) but should have matrices composed with it, under the names "LSC_L" and "LSC_Lp".
    189:    For example, you might have setup code like this

    191: .vb
    192:    PetscObjectCompose((PetscObject)Sp,"LSC_L",(PetscObject)L);
    193:    PetscObjectCompose((PetscObject)Sp,"LSC_Lp",(PetscObject)Lp);
    194: .ve

    196:    And then your Jacobian assembly would look like

    198: .vb
    199:    PetscObjectQuery((PetscObject)Sp,"LSC_L",(PetscObject*)&L);
    200:    PetscObjectQuery((PetscObject)Sp,"LSC_Lp",(PetscObject*)&Lp);
    201:    if (L) { assembly L }
    202:    if (Lp) { assemble Lp }
    203: .ve

    205:    With this, you should be able to choose LSC preconditioning, using e.g. ML's algebraic multigrid to solve with L

    207: .vb
    208:    -fieldsplit_1_pc_type lsc -fieldsplit_1_lsc_pc_type ml
    209: .ve

    211:    Since we do not use the values in Sp, you can still put an assembled matrix there to use normal preconditioners.

    213:    References:
    214: +  1. - Elman, Howle, Shadid, Shuttleworth, and Tuminaro, Block preconditioners based on approximate commutators, 2006.
    215: -  2. - Silvester, Elman, Kay, Wathen, Efficient preconditioning of the linearized Navier Stokes equations for incompressible flow, 2001.

    217:    Concepts: physics based preconditioners, block preconditioners

    219: .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC, Block_Preconditioners, PCFIELDSPLIT,
    220:            PCFieldSplitGetSubKSP(), PCFieldSplitSetFields(), PCFieldSplitSetType(), PCFieldSplitSetIS(), PCFieldSplitSetSchurPre(),
    221:            MatCreateSchurComplement()
    222: M*/

    226: PETSC_EXTERN PetscErrorCode PCCreate_LSC(PC pc)
    227: {
    228:   PC_LSC         *lsc;

    232:   PetscNewLog(pc,&lsc);
    233:   pc->data = (void*)lsc;

    235:   pc->ops->apply           = PCApply_LSC;
    236:   pc->ops->applytranspose  = 0;
    237:   pc->ops->setup           = PCSetUp_LSC;
    238:   pc->ops->reset           = PCReset_LSC;
    239:   pc->ops->destroy         = PCDestroy_LSC;
    240:   pc->ops->setfromoptions  = PCSetFromOptions_LSC;
    241:   pc->ops->view            = PCView_LSC;
    242:   pc->ops->applyrichardson = 0;
    243:   return(0);
    244: }