Actual source code: lsc.c
petsc-3.10.5 2019-03-28
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      2:  #include <petsc/private/pcimpl.h>

      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;

     13: static PetscErrorCode PCLSCAllocate_Private(PC pc)
     14: {
     15:   PC_LSC         *lsc = (PC_LSC*)pc->data;
     16:   Mat            A;

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

     37: static PetscErrorCode PCSetUp_LSC(PC pc)
     38: {
     39:   PC_LSC         *lsc = (PC_LSC*)pc->data;
     40:   Mat            L,Lp,B,C;

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

     69: static PetscErrorCode PCApply_LSC(PC pc,Vec x,Vec y)
     70: {
     71:   PC_LSC         *lsc = (PC_LSC*)pc->data;
     72:   Mat            A,B,C;

     76:   MatSchurComplementGetSubMatrices(pc->mat,&A,NULL,&B,&C,NULL);
     77:   KSPSolve(lsc->kspL,x,lsc->x1);
     78:   MatMult(B,lsc->x1,lsc->x0);
     79:   if (lsc->scale) {
     80:     VecPointwiseMult(lsc->x0,lsc->x0,lsc->scale);
     81:   }
     82:   MatMult(A,lsc->x0,lsc->y0);
     83:   if (lsc->scale) {
     84:     VecPointwiseMult(lsc->y0,lsc->y0,lsc->scale);
     85:   }
     86:   MatMult(C,lsc->y0,lsc->x1);
     87:   KSPSolve(lsc->kspL,lsc->x1,y);
     88:   return(0);
     89: }

     91: static PetscErrorCode PCReset_LSC(PC pc)
     92: {
     93:   PC_LSC         *lsc = (PC_LSC*)pc->data;

     97:   VecDestroy(&lsc->x0);
     98:   VecDestroy(&lsc->y0);
     99:   VecDestroy(&lsc->x1);
    100:   VecDestroy(&lsc->scale);
    101:   KSPDestroy(&lsc->kspL);
    102:   MatDestroy(&lsc->L);
    103:   return(0);
    104: }

    106: static PetscErrorCode PCDestroy_LSC(PC pc)
    107: {

    111:   PCReset_LSC(pc);
    112:   PetscFree(pc->data);
    113:   return(0);
    114: }

    116: static PetscErrorCode PCSetFromOptions_LSC(PetscOptionItems *PetscOptionsObject,PC pc)
    117: {
    118:   PC_LSC         *lsc = (PC_LSC*)pc->data;

    122:   PetscOptionsHead(PetscOptionsObject,"LSC options");
    123:   {
    124:     PetscOptionsBool("-pc_lsc_scale_diag","Use diagonal of velocity block (A) for scaling","None",lsc->scalediag,&lsc->scalediag,NULL);
    125:   }
    126:   PetscOptionsTail();
    127:   return(0);
    128: }

    130: static PetscErrorCode PCView_LSC(PC pc,PetscViewer viewer)
    131: {
    132:   PC_LSC         *jac = (PC_LSC*)pc->data;
    134:   PetscBool      iascii;

    137:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    138:   if (iascii) {
    139:     PetscViewerASCIIPushTab(viewer);
    140:     KSPView(jac->kspL,viewer);
    141:     PetscViewerASCIIPopTab(viewer);
    142:   }
    143:   return(0);
    144: }

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

    149:    Options Database Key:
    150: .    -pc_lsc_scale_diag - Use the diagonal of A for scaling

    152:    Level: intermediate

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

    158: .vb
    159:    S = A11 - A10 inv(A00) A01
    160: .ve

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

    165: .vb
    166:    inv(A10 A01) A10 A00 A01 inv(A10 A01)
    167: .ve

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

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

    177: .vb
    178:    PetscObjectCompose((PetscObject)Sp,"LSC_L",(PetscObject)L);
    179:    PetscObjectCompose((PetscObject)Sp,"LSC_Lp",(PetscObject)Lp);
    180: .ve

    182:    And then your Jacobian assembly would look like

    184: .vb
    185:    PetscObjectQuery((PetscObject)Sp,"LSC_L",(PetscObject*)&L);
    186:    PetscObjectQuery((PetscObject)Sp,"LSC_Lp",(PetscObject*)&Lp);
    187:    if (L) { assembly L }
    188:    if (Lp) { assemble Lp }
    189: .ve

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

    193: .vb
    194:    -fieldsplit_1_pc_type lsc -fieldsplit_1_lsc_pc_type ml
    195: .ve

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

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

    203:    Concepts: physics based preconditioners, block preconditioners

    205: .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC, Block_Preconditioners, PCFIELDSPLIT,
    206:            PCFieldSplitGetSubKSP(), PCFieldSplitSetFields(), PCFieldSplitSetType(), PCFieldSplitSetIS(), PCFieldSplitSetSchurPre(),
    207:            MatCreateSchurComplement()
    208: M*/

    210: PETSC_EXTERN PetscErrorCode PCCreate_LSC(PC pc)
    211: {
    212:   PC_LSC         *lsc;

    216:   PetscNewLog(pc,&lsc);
    217:   pc->data = (void*)lsc;

    219:   pc->ops->apply           = PCApply_LSC;
    220:   pc->ops->applytranspose  = 0;
    221:   pc->ops->setup           = PCSetUp_LSC;
    222:   pc->ops->reset           = PCReset_LSC;
    223:   pc->ops->destroy         = PCDestroy_LSC;
    224:   pc->ops->setfromoptions  = PCSetFromOptions_LSC;
    225:   pc->ops->view            = PCView_LSC;
    226:   pc->ops->applyrichardson = 0;
    227:   return(0);
    228: }