/*@C
KSPMonitorSingularValue - Prints the two norm of the true residual and
estimation of the extreme singular values of the preconditioned problem
at each iteration.
Logically Collective on KSP
Input Parameters:
+ ksp - the iterative context
. n - the iteration
- rnorm - the two norm of the residual
Options Database Key:
. -ksp_monitor_singular_value - Activates KSPMonitorSingularValue()
Notes:
The CG solver uses the Lanczos technique for eigenvalue computation,
while GMRES uses the Arnoldi technique; other iterative methods do
not currently compute singular values.
Level: intermediate
.keywords: KSP, CG, default, monitor, extreme, singular values, Lanczos, Arnoldi
.seealso: KSPComputeExtremeSingularValues()
@*/
PetscErrorCode KSPMonitorSingularValue(KSP ksp,PetscInt n,PetscReal rnorm,PetscViewerAndFormat *dummy)
{
PetscReal emin,emax,c;
PetscErrorCode ierr;
PetscViewer viewer = dummy->viewer;
PetscFunctionBegin;
PetscValidHeaderSpecific(ksp,KSP_CLASSID,1);
PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,4);
ierr = PetscViewerPushFormat(viewer,dummy->format);
CHKERRQ(ierr);
ierr = PetscViewerASCIIAddTab(viewer,((PetscObject)ksp)->tablevel);
CHKERRQ(ierr);
if (!ksp->calc_sings) {
ierr = PetscViewerASCIIPrintf(viewer,"%3D KSP Residual norm %14.12e \n",n,(double)rnorm);
CHKERRQ(ierr);
} else {
ierr = KSPComputeExtremeSingularValues(ksp,&emax,&emin);
CHKERRQ(ierr);
c = emax/emin;
ierr = PetscViewerASCIIPrintf(viewer,"%3D KSP Residual norm %14.12e %% max %14.12e min %14.12e max/min %14.12e\n",n,(double)rnorm,(double)emax,(double)emin,(double)c);
CHKERRQ(ierr);
}
ierr = PetscViewerASCIISubtractTab(viewer,((PetscObject)ksp)->tablevel);
CHKERRQ(ierr);
ierr = PetscViewerPopFormat(viewer);
CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode KSPSolve_SpecEst(KSP ksp)
{
PetscErrorCode ierr;
KSP_SpecEst *spec = (KSP_SpecEst*)ksp->data;
PetscFunctionBegin;
if (spec->current) {
ierr = KSPSolve(spec->kspcheap,ksp->vec_rhs,ksp->vec_sol);CHKERRQ(ierr);
ierr = KSPSpecEstPropagateUp(ksp,spec->kspcheap);CHKERRQ(ierr);
} else {
PetscInt i,its,neig;
PetscReal *real,*imag,rad = 0;
ierr = KSPSolve(spec->kspest,ksp->vec_rhs,ksp->vec_sol);CHKERRQ(ierr);
ierr = KSPSpecEstPropagateUp(ksp,spec->kspest);CHKERRQ(ierr);
ierr = KSPComputeExtremeSingularValues(spec->kspest,&spec->max,&spec->min);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(spec->kspest,&its);CHKERRQ(ierr);
ierr = PetscMalloc2(its,PetscReal,&real,its,PetscReal,&imag);CHKERRQ(ierr);
ierr = KSPComputeEigenvalues(spec->kspest,its,real,imag,&neig);CHKERRQ(ierr);
for (i=0; i<neig; i++) {
/* We would really like to compute w (nominally 1/radius) to minimize |1-wB|. Empirically it
is better to compute rad = |1-B| than rad = |B|. There must be a cheap way to do better. */
rad = PetscMax(rad,PetscRealPart(PetscSqrtScalar((PetscScalar)(PetscSqr(real[i]-1.) + PetscSqr(imag[i])))));
}
ierr = PetscFree2(real,imag);CHKERRQ(ierr);
spec->radius = rad;
ierr = KSPChebyshevSetEigenvalues(spec->kspcheap,spec->max*spec->maxfactor,spec->min*spec->minfactor);CHKERRQ(ierr);
ierr = KSPRichardsonSetScale(spec->kspcheap,spec->richfactor/spec->radius);
ierr = PetscInfo3(ksp,"Estimated singular value min=%G max=%G, spectral radius=%G",spec->min,spec->max,spec->radius);CHKERRQ(ierr);
spec->current = PETSC_TRUE;
}
PetscFunctionReturn(0);
}
/*@C
KSPMonitorSAWs - monitor solution using SAWs
Logically Collective on KSP
Input Parameters:
+ ksp - iterative context
. n - iteration number
. rnorm - 2-norm (preconditioned) residual value (may be estimated).
- ctx - PetscViewer of type SAWs
Level: advanced
.keywords: KSP, CG, monitor, SAWs, singular values
.seealso: KSPMonitorSingularValue(), KSPComputeExtremeSingularValues(), PetscViewerSAWsOpen()
@*/
PetscErrorCode KSPMonitorSAWs(KSP ksp,PetscInt n,PetscReal rnorm,void *ctx)
{
PetscErrorCode ierr;
KSPMonitor_SAWs *mon = (KSPMonitor_SAWs*)ctx;
PetscReal emax,emin;
PetscMPIInt rank;
PetscFunctionBegin;
PetscValidHeaderSpecific(ksp,KSP_CLASSID,1);
ierr = KSPComputeExtremeSingularValues(ksp,&emax,&emin);CHKERRQ(ierr);
ierr = PetscFree2(mon->eigr,mon->eigi);CHKERRQ(ierr);
ierr = PetscMalloc2(n,&mon->eigr,n,&mon->eigi);CHKERRQ(ierr);
if (n) {
ierr = KSPComputeEigenvalues(ksp,n,mon->eigr,mon->eigi,&mon->neigs);CHKERRQ(ierr);
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
if (!rank) {
SAWs_Delete("/PETSc/ksp_monitor_saws/eigr");
SAWs_Delete("/PETSc/ksp_monitor_saws/eigi");
PetscStackCallSAWs(SAWs_Register,("/PETSc/ksp_monitor_saws/rnorm",&ksp->rnorm,1,SAWs_READ,SAWs_DOUBLE));
PetscStackCallSAWs(SAWs_Register,("/PETSc/ksp_monitor_saws/neigs",&mon->neigs,1,SAWs_READ,SAWs_INT));
if (mon->neigs > 0) {
PetscStackCallSAWs(SAWs_Register,("/PETSc/ksp_monitor_saws/eigr",mon->eigr,mon->neigs,SAWs_READ,SAWs_DOUBLE));
PetscStackCallSAWs(SAWs_Register,("/PETSc/ksp_monitor_saws/eigi",mon->eigi,mon->neigs,SAWs_READ,SAWs_DOUBLE));
}
ierr = PetscInfo2(ksp,"KSP extreme singular values min=%g max=%g\n",(double)emin,(double)emax);CHKERRQ(ierr);
ierr = PetscSAWsBlock();CHKERRQ(ierr);
}
}
PetscFunctionReturn(0);
}
/*@C
KSPMonitorAMS - monitor solution using AMS
Logically Collective on KSP
Input Parameters:
+ ksp - iterative context
. n - iteration number
. rnorm - 2-norm (preconditioned) residual value (may be estimated).
- ctx - PetscViewer of type AMS
Level: advanced
.keywords: KSP, CG, monitor, AMS, singular values
.seealso: KSPMonitorSingularValue(), KSPComputeExtremeSingularValues(), PetscViewerAMSOpen()
@*/
PetscErrorCode KSPMonitorAMS(KSP ksp,PetscInt n,PetscReal rnorm,void *ctx)
{
#if defined(PETSC_HAVE_AMS)
PetscErrorCode ierr;
KSPMonitor_AMS *mon = (KSPMonitor_AMS*)ctx;
PetscViewer viewer = mon->viewer;
PetscReal emax,emin;;
AMS_Comm acomm;
PetscFunctionBegin;
PetscValidHeaderSpecific(ksp,KSP_CLASSID,1);
PetscValidHeaderSpecific(viewer,PETSC_VIEWER_CLASSID,4);
ierr = KSPComputeExtremeSingularValues(ksp,&emax,&emin);CHKERRQ(ierr);
/* UnPublish */
if (mon->amem != -1) {ierr = AMS_Memory_destroy(mon->amem);CHKERRQ(ierr);}
mon->amem = -1;
ierr = PetscFree(mon->eigr);CHKERRQ(ierr);
ierr = PetscMalloc(2*n*sizeof(PetscReal),&mon->eigr);CHKERRQ(ierr);
mon->eigi = mon->eigr + n;
if (n) {ierr = KSPComputeEigenvalues(ksp,n,mon->eigr,mon->eigi,&mon->neigs);CHKERRQ(ierr);}
ierr = PetscViewerAMSGetAMSComm(viewer,&acomm);CHKERRQ(ierr);
ierr = AMS_Memory_create(acomm,"ksp_monitor_ams",&mon->amem);CHKERRQ(ierr);
ierr = AMS_Memory_take_access(mon->amem);CHKERRQ(ierr);
ierr = AMS_Memory_add_field(mon->amem,"rnorm",&ksp->rnorm,1,AMS_DOUBLE,AMS_READ,AMS_COMMON,AMS_REDUCT_UNDEF);CHKERRQ(ierr);
ierr = AMS_Memory_add_field(mon->amem,"neigs",&mon->neigs,1,AMS_INT,AMS_READ,AMS_COMMON,AMS_REDUCT_UNDEF);CHKERRQ(ierr);
if (mon->neigs > 0) {
ierr = AMS_Memory_add_field(mon->amem,"eigr",&mon->eigr,mon->neigs,AMS_DOUBLE,AMS_READ,AMS_COMMON,AMS_REDUCT_UNDEF);CHKERRQ(ierr);
ierr = AMS_Memory_add_field(mon->amem,"eigi",&mon->eigr,mon->neigs,AMS_DOUBLE,AMS_READ,AMS_COMMON,AMS_REDUCT_UNDEF);CHKERRQ(ierr);
}
ierr = AMS_Memory_publish(mon->amem);CHKERRQ(ierr);
ierr = AMS_Memory_grant_access(mon->amem);CHKERRQ(ierr);
ierr = PetscInfo2(ksp,"KSP extreme singular values min=%G max=%G\n",emin,emax);CHKERRQ(ierr);
PetscFunctionReturn(0);
#else
PetscFunctionBegin;
SETERRQ(((PetscObject)ksp)->comm,PETSC_ERR_SUP,"Missing package AMS");
PetscFunctionReturn(0);
#endif
}
PetscErrorCode PCBDDCNullSpaceAssembleCorrection(PC pc, PetscBool isdir, IS local_dofs)
{
PC_BDDC *pcbddc = (PC_BDDC*)pc->data;
PC_IS *pcis = (PC_IS*)pc->data;
Mat_IS* matis = (Mat_IS*)pc->pmat->data;
KSP local_ksp;
PC newpc;
NullSpaceCorrection_ctx shell_ctx;
Mat local_mat,local_pmat,small_mat,inv_small_mat;
Vec work1,work2;
const Vec *nullvecs;
VecScatter scatter_ctx;
IS is_aux;
MatFactorInfo matinfo;
PetscScalar *basis_mat,*Kbasis_mat,*array,*array_mat;
PetscScalar one = 1.0,zero = 0.0, m_one = -1.0;
PetscInt basis_dofs,basis_size,nnsp_size,i,k;
PetscBool nnsp_has_cnst;
PetscErrorCode ierr;
PetscFunctionBegin;
/* Infer the local solver */
ierr = ISGetSize(local_dofs,&basis_dofs);CHKERRQ(ierr);
if (isdir) {
/* Dirichlet solver */
local_ksp = pcbddc->ksp_D;
} else {
/* Neumann solver */
local_ksp = pcbddc->ksp_R;
}
ierr = KSPGetOperators(local_ksp,&local_mat,&local_pmat);CHKERRQ(ierr);
/* Get null space vecs */
ierr = MatNullSpaceGetVecs(pcbddc->NullSpace,&nnsp_has_cnst,&nnsp_size,&nullvecs);CHKERRQ(ierr);
basis_size = nnsp_size;
if (nnsp_has_cnst) {
basis_size++;
}
if (basis_dofs) {
/* Create shell ctx */
ierr = PetscNew(&shell_ctx);CHKERRQ(ierr);
/* Create work vectors in shell context */
ierr = VecCreate(PETSC_COMM_SELF,&shell_ctx->work_small_1);CHKERRQ(ierr);
ierr = VecSetSizes(shell_ctx->work_small_1,basis_size,basis_size);CHKERRQ(ierr);
ierr = VecSetType(shell_ctx->work_small_1,VECSEQ);CHKERRQ(ierr);
ierr = VecDuplicate(shell_ctx->work_small_1,&shell_ctx->work_small_2);CHKERRQ(ierr);
ierr = VecCreate(PETSC_COMM_SELF,&shell_ctx->work_full_1);CHKERRQ(ierr);
ierr = VecSetSizes(shell_ctx->work_full_1,basis_dofs,basis_dofs);CHKERRQ(ierr);
ierr = VecSetType(shell_ctx->work_full_1,VECSEQ);CHKERRQ(ierr);
ierr = VecDuplicate(shell_ctx->work_full_1,&shell_ctx->work_full_2);CHKERRQ(ierr);
/* Allocate workspace */
ierr = MatCreateSeqDense(PETSC_COMM_SELF,basis_dofs,basis_size,NULL,&shell_ctx->basis_mat );CHKERRQ(ierr);
ierr = MatCreateSeqDense(PETSC_COMM_SELF,basis_dofs,basis_size,NULL,&shell_ctx->Kbasis_mat);CHKERRQ(ierr);
ierr = MatDenseGetArray(shell_ctx->basis_mat,&basis_mat);CHKERRQ(ierr);
ierr = MatDenseGetArray(shell_ctx->Kbasis_mat,&Kbasis_mat);CHKERRQ(ierr);
/* Restrict local null space on selected dofs (Dirichlet or Neumann)
and compute matrices N and K*N */
ierr = VecDuplicate(shell_ctx->work_full_1,&work1);CHKERRQ(ierr);
ierr = VecDuplicate(shell_ctx->work_full_1,&work2);CHKERRQ(ierr);
ierr = VecScatterCreate(pcis->vec1_N,local_dofs,work1,(IS)0,&scatter_ctx);CHKERRQ(ierr);
}
for (k=0;k<nnsp_size;k++) {
ierr = VecScatterBegin(matis->rctx,nullvecs[k],pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
ierr = VecScatterEnd(matis->rctx,nullvecs[k],pcis->vec1_N,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
if (basis_dofs) {
ierr = VecPlaceArray(work1,(const PetscScalar*)&basis_mat[k*basis_dofs]);CHKERRQ(ierr);
ierr = VecScatterBegin(scatter_ctx,pcis->vec1_N,work1,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
ierr = VecScatterEnd(scatter_ctx,pcis->vec1_N,work1,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
ierr = VecPlaceArray(work2,(const PetscScalar*)&Kbasis_mat[k*basis_dofs]);CHKERRQ(ierr);
ierr = MatMult(local_mat,work1,work2);CHKERRQ(ierr);
ierr = VecResetArray(work1);CHKERRQ(ierr);
ierr = VecResetArray(work2);CHKERRQ(ierr);
}
}
if (basis_dofs) {
if (nnsp_has_cnst) {
ierr = VecPlaceArray(work1,(const PetscScalar*)&basis_mat[k*basis_dofs]);CHKERRQ(ierr);
ierr = VecSet(work1,one);CHKERRQ(ierr);
ierr = VecPlaceArray(work2,(const PetscScalar*)&Kbasis_mat[k*basis_dofs]);CHKERRQ(ierr);
ierr = MatMult(local_mat,work1,work2);CHKERRQ(ierr);
ierr = VecResetArray(work1);CHKERRQ(ierr);
ierr = VecResetArray(work2);CHKERRQ(ierr);
}
ierr = VecDestroy(&work1);CHKERRQ(ierr);
ierr = VecDestroy(&work2);CHKERRQ(ierr);
ierr = VecScatterDestroy(&scatter_ctx);CHKERRQ(ierr);
ierr = MatDenseRestoreArray(shell_ctx->basis_mat,&basis_mat);CHKERRQ(ierr);
ierr = MatDenseRestoreArray(shell_ctx->Kbasis_mat,&Kbasis_mat);CHKERRQ(ierr);
/* Assemble another Mat object in shell context */
ierr = MatTransposeMatMult(shell_ctx->basis_mat,shell_ctx->Kbasis_mat,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&small_mat);CHKERRQ(ierr);
ierr = MatFactorInfoInitialize(&matinfo);CHKERRQ(ierr);
ierr = ISCreateStride(PETSC_COMM_SELF,basis_size,0,1,&is_aux);CHKERRQ(ierr);
ierr = MatLUFactor(small_mat,is_aux,is_aux,&matinfo);CHKERRQ(ierr);
ierr = ISDestroy(&is_aux);CHKERRQ(ierr);
ierr = PetscMalloc1(basis_size*basis_size,&array_mat);CHKERRQ(ierr);
for (k=0;k<basis_size;k++) {
ierr = VecSet(shell_ctx->work_small_1,zero);CHKERRQ(ierr);
ierr = VecSetValue(shell_ctx->work_small_1,k,one,INSERT_VALUES);CHKERRQ(ierr);
ierr = VecAssemblyBegin(shell_ctx->work_small_1);CHKERRQ(ierr);
ierr = VecAssemblyEnd(shell_ctx->work_small_1);CHKERRQ(ierr);
ierr = MatSolve(small_mat,shell_ctx->work_small_1,shell_ctx->work_small_2);CHKERRQ(ierr);
ierr = VecGetArrayRead(shell_ctx->work_small_2,(const PetscScalar**)&array);CHKERRQ(ierr);
for (i=0;i<basis_size;i++) {
array_mat[i*basis_size+k]=array[i];
}
ierr = VecRestoreArrayRead(shell_ctx->work_small_2,(const PetscScalar**)&array);CHKERRQ(ierr);
}
ierr = MatCreateSeqDense(PETSC_COMM_SELF,basis_size,basis_size,array_mat,&inv_small_mat);CHKERRQ(ierr);
ierr = MatMatMult(shell_ctx->basis_mat,inv_small_mat,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&shell_ctx->Lbasis_mat);CHKERRQ(ierr);
ierr = PetscFree(array_mat);CHKERRQ(ierr);
ierr = MatDestroy(&inv_small_mat);CHKERRQ(ierr);
ierr = MatDestroy(&small_mat);CHKERRQ(ierr);
ierr = MatScale(shell_ctx->Kbasis_mat,m_one);CHKERRQ(ierr);
/* Rebuild local PC */
ierr = KSPGetPC(local_ksp,&shell_ctx->local_pc);CHKERRQ(ierr);
ierr = PetscObjectReference((PetscObject)shell_ctx->local_pc);CHKERRQ(ierr);
ierr = PCCreate(PETSC_COMM_SELF,&newpc);CHKERRQ(ierr);
ierr = PCSetOperators(newpc,local_mat,local_mat);CHKERRQ(ierr);
ierr = PCSetType(newpc,PCSHELL);CHKERRQ(ierr);
ierr = PCShellSetContext(newpc,shell_ctx);CHKERRQ(ierr);
ierr = PCShellSetApply(newpc,PCBDDCApplyNullSpaceCorrectionPC);CHKERRQ(ierr);
ierr = PCShellSetDestroy(newpc,PCBDDCDestroyNullSpaceCorrectionPC);CHKERRQ(ierr);
ierr = PCSetUp(newpc);CHKERRQ(ierr);
ierr = KSPSetPC(local_ksp,newpc);CHKERRQ(ierr);
ierr = PCDestroy(&newpc);CHKERRQ(ierr);
ierr = KSPSetUp(local_ksp);CHKERRQ(ierr);
}
/* test */
if (pcbddc->dbg_flag && basis_dofs) {
KSP check_ksp;
PC check_pc;
Mat test_mat;
Vec work3;
PetscReal test_err,lambda_min,lambda_max;
PetscBool setsym,issym=PETSC_FALSE;
PetscInt tabs;
ierr = PetscViewerASCIIGetTab(pcbddc->dbg_viewer,&tabs);CHKERRQ(ierr);
ierr = KSPGetPC(local_ksp,&check_pc);CHKERRQ(ierr);
ierr = VecDuplicate(shell_ctx->work_full_1,&work1);CHKERRQ(ierr);
ierr = VecDuplicate(shell_ctx->work_full_1,&work2);CHKERRQ(ierr);
ierr = VecDuplicate(shell_ctx->work_full_1,&work3);CHKERRQ(ierr);
ierr = VecSetRandom(shell_ctx->work_small_1,NULL);CHKERRQ(ierr);
ierr = MatMult(shell_ctx->basis_mat,shell_ctx->work_small_1,work1);CHKERRQ(ierr);
ierr = VecCopy(work1,work2);CHKERRQ(ierr);
ierr = MatMult(local_mat,work1,work3);CHKERRQ(ierr);
ierr = PCApply(check_pc,work3,work1);CHKERRQ(ierr);
ierr = VecAXPY(work1,m_one,work2);CHKERRQ(ierr);
ierr = VecNorm(work1,NORM_INFINITY,&test_err);CHKERRQ(ierr);
ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d error for nullspace correction for ",PetscGlobalRank);CHKERRQ(ierr);
ierr = PetscViewerASCIIUseTabs(pcbddc->dbg_viewer,PETSC_FALSE);CHKERRQ(ierr);
if (isdir) {
ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Dirichlet ");CHKERRQ(ierr);
} else {
ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Neumann ");CHKERRQ(ierr);
}
ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"solver is :%1.14e\n",test_err);CHKERRQ(ierr);
ierr = PetscViewerASCIISetTab(pcbddc->dbg_viewer,tabs);CHKERRQ(ierr);
ierr = PetscViewerASCIIUseTabs(pcbddc->dbg_viewer,PETSC_TRUE);CHKERRQ(ierr);
ierr = MatTransposeMatMult(shell_ctx->Lbasis_mat,shell_ctx->Kbasis_mat,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&test_mat);CHKERRQ(ierr);
ierr = MatShift(test_mat,one);CHKERRQ(ierr);
ierr = MatNorm(test_mat,NORM_INFINITY,&test_err);CHKERRQ(ierr);
ierr = MatDestroy(&test_mat);CHKERRQ(ierr);
ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d error for nullspace matrices is :%1.14e\n",PetscGlobalRank,test_err);CHKERRQ(ierr);
/* Create ksp object suitable for extreme eigenvalues' estimation */
ierr = KSPCreate(PETSC_COMM_SELF,&check_ksp);CHKERRQ(ierr);
ierr = KSPSetErrorIfNotConverged(check_ksp,pc->erroriffailure);CHKERRQ(ierr);
ierr = KSPSetOperators(check_ksp,local_mat,local_mat);CHKERRQ(ierr);
ierr = KSPSetTolerances(check_ksp,1.e-8,1.e-8,PETSC_DEFAULT,basis_dofs);CHKERRQ(ierr);
ierr = KSPSetComputeSingularValues(check_ksp,PETSC_TRUE);CHKERRQ(ierr);
ierr = MatIsSymmetricKnown(pc->pmat,&setsym,&issym);CHKERRQ(ierr);
if (issym) {
ierr = KSPSetType(check_ksp,KSPCG);CHKERRQ(ierr);
}
ierr = KSPSetPC(check_ksp,check_pc);CHKERRQ(ierr);
ierr = KSPSetUp(check_ksp);CHKERRQ(ierr);
ierr = VecSetRandom(work1,NULL);CHKERRQ(ierr);
ierr = MatMult(local_mat,work1,work2);CHKERRQ(ierr);
ierr = KSPSolve(check_ksp,work2,work2);CHKERRQ(ierr);
ierr = VecAXPY(work2,m_one,work1);CHKERRQ(ierr);
ierr = VecNorm(work2,NORM_INFINITY,&test_err);CHKERRQ(ierr);
ierr = KSPComputeExtremeSingularValues(check_ksp,&lambda_max,&lambda_min);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(check_ksp,&k);CHKERRQ(ierr);
ierr = PetscViewerASCIISynchronizedPrintf(pcbddc->dbg_viewer,"Subdomain %04d error for adapted KSP %1.14e (it %d, eigs %1.6e %1.6e)\n",PetscGlobalRank,test_err,k,lambda_min,lambda_max);CHKERRQ(ierr);
ierr = KSPDestroy(&check_ksp);CHKERRQ(ierr);
ierr = VecDestroy(&work1);CHKERRQ(ierr);
ierr = VecDestroy(&work2);CHKERRQ(ierr);
ierr = VecDestroy(&work3);CHKERRQ(ierr);
}
/* all processes shoud call this, even the void ones */
if (pcbddc->dbg_flag) {
ierr = PetscViewerFlush(pcbddc->dbg_viewer);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
int main(int argc,char **args)
{
PetscErrorCode ierr;
DomainData dd;
PetscReal norm,maxeig,mineig;
PetscScalar scalar_value;
PetscInt ndofs,its;
Mat A =0,F=0;
KSP KSPwithBDDC =0,KSPwithFETIDP=0;
Vec fetidp_solution_all=0,bddc_solution=0,bddc_rhs=0;
Vec exact_solution =0,fetidp_solution=0,fetidp_rhs=0;
/* Init PETSc */
ierr = PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
/* Initialize DomainData */
ierr = InitializeDomainData(&dd);CHKERRQ(ierr);
/* Decompose domain */
ierr = DomainDecomposition(&dd);CHKERRQ(ierr);
#if DEBUG
printf("Subdomain data\n");
printf("IPS : %d %d %d\n",dd.ipx,dd.ipy,dd.ipz);
printf("NEG : %d %d %d\n",dd.nex,dd.ney,dd.nez);
printf("NEL : %d %d %d\n",dd.nex_l,dd.ney_l,dd.nez_l);
printf("LDO : %d %d %d\n",dd.xm_l,dd.ym_l,dd.zm_l);
printf("SIZES : %d %d %d\n",dd.xm,dd.ym,dd.zm);
printf("STARTS: %d %d %d\n",dd.startx,dd.starty,dd.startz);
#endif
/* assemble global matrix */
ierr = ComputeMatrix(dd,&A);CHKERRQ(ierr);
/* get work vectors */
ierr = MatCreateVecs(A,&bddc_solution,NULL);CHKERRQ(ierr);
ierr = VecDuplicate(bddc_solution,&bddc_rhs);CHKERRQ(ierr);
ierr = VecDuplicate(bddc_solution,&fetidp_solution_all);CHKERRQ(ierr);
ierr = VecDuplicate(bddc_solution,&exact_solution);CHKERRQ(ierr);
/* create and customize KSP/PC for BDDC */
ierr = ComputeKSPBDDC(dd,A,&KSPwithBDDC);CHKERRQ(ierr);
/* create KSP/PC for FETIDP */
ierr = ComputeKSPFETIDP(dd,KSPwithBDDC,&KSPwithFETIDP);CHKERRQ(ierr);
/* create random exact solution */
ierr = VecSetRandom(exact_solution,NULL);CHKERRQ(ierr);
ierr = VecShift(exact_solution,-0.5);CHKERRQ(ierr);
ierr = VecScale(exact_solution,100.0);CHKERRQ(ierr);
ierr = VecGetSize(exact_solution,&ndofs);CHKERRQ(ierr);
if (dd.pure_neumann) {
ierr = VecSum(exact_solution,&scalar_value);CHKERRQ(ierr);
scalar_value = -scalar_value/(PetscScalar)ndofs;
ierr = VecShift(exact_solution,scalar_value);CHKERRQ(ierr);
}
/* assemble BDDC rhs */
ierr = MatMult(A,exact_solution,bddc_rhs);CHKERRQ(ierr);
/* test ksp with BDDC */
ierr = KSPSolve(KSPwithBDDC,bddc_rhs,bddc_solution);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(KSPwithBDDC,&its);CHKERRQ(ierr);
ierr = KSPComputeExtremeSingularValues(KSPwithBDDC,&maxeig,&mineig);CHKERRQ(ierr);
if (dd.pure_neumann) {
ierr = VecSum(bddc_solution,&scalar_value);CHKERRQ(ierr);
scalar_value = -scalar_value/(PetscScalar)ndofs;
ierr = VecShift(bddc_solution,scalar_value);CHKERRQ(ierr);
}
/* check exact_solution and BDDC solultion */
ierr = VecAXPY(bddc_solution,-1.0,exact_solution);CHKERRQ(ierr);
ierr = VecNorm(bddc_solution,NORM_INFINITY,&norm);CHKERRQ(ierr);
ierr = PetscPrintf(dd.gcomm,"---------------------BDDC stats-------------------------------\n");CHKERRQ(ierr);
ierr = PetscPrintf(dd.gcomm,"Number of degrees of freedom : %8D \n",ndofs);CHKERRQ(ierr);
ierr = PetscPrintf(dd.gcomm,"Number of iterations : %8D \n",its);CHKERRQ(ierr);
ierr = PetscPrintf(dd.gcomm,"Eigenvalues preconditioned operator : %1.2e %1.2e\n",(double)mineig,(double)maxeig);CHKERRQ(ierr);
ierr = PetscPrintf(dd.gcomm,"Error betweeen exact and computed solution : %1.2e\n",(double)norm);CHKERRQ(ierr);
ierr = PetscPrintf(dd.gcomm,"--------------------------------------------------------------\n");CHKERRQ(ierr);
/* assemble fetidp rhs on the space of Lagrange multipliers */
ierr = KSPGetOperators(KSPwithFETIDP,&F,NULL);CHKERRQ(ierr);
ierr = MatCreateVecs(F,&fetidp_solution,&fetidp_rhs);CHKERRQ(ierr);
ierr = PCBDDCMatFETIDPGetRHS(F,bddc_rhs,fetidp_rhs);CHKERRQ(ierr);
ierr = VecSet(fetidp_solution,0.0);CHKERRQ(ierr);
/* test ksp with FETIDP */
ierr = KSPSolve(KSPwithFETIDP,fetidp_rhs,fetidp_solution);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(KSPwithFETIDP,&its);CHKERRQ(ierr);
ierr = KSPComputeExtremeSingularValues(KSPwithFETIDP,&maxeig,&mineig);CHKERRQ(ierr);
/* assemble fetidp solution on physical domain */
ierr = PCBDDCMatFETIDPGetSolution(F,fetidp_solution,fetidp_solution_all);CHKERRQ(ierr);
/* check FETIDP sol */
if (dd.pure_neumann) {
ierr = VecSum(fetidp_solution_all,&scalar_value);CHKERRQ(ierr);
scalar_value = -scalar_value/(PetscScalar)ndofs;
ierr = VecShift(fetidp_solution_all,scalar_value);CHKERRQ(ierr);
}
ierr = VecAXPY(fetidp_solution_all,-1.0,exact_solution);CHKERRQ(ierr);
ierr = VecNorm(fetidp_solution_all,NORM_INFINITY,&norm);CHKERRQ(ierr);
ierr = VecGetSize(fetidp_solution,&ndofs);CHKERRQ(ierr);
ierr = PetscPrintf(dd.gcomm,"------------------FETI-DP stats-------------------------------\n");CHKERRQ(ierr);
ierr = PetscPrintf(dd.gcomm,"Number of degrees of freedom : %8D \n",ndofs);CHKERRQ(ierr);
ierr = PetscPrintf(dd.gcomm,"Number of iterations : %8D \n",its);CHKERRQ(ierr);
ierr = PetscPrintf(dd.gcomm,"Eigenvalues preconditioned operator : %1.2e %1.2e\n",(double)mineig,(double)maxeig);CHKERRQ(ierr);
ierr = PetscPrintf(dd.gcomm,"Error betweeen exact and computed solution : %1.2e\n",(double)norm);CHKERRQ(ierr);
ierr = PetscPrintf(dd.gcomm,"--------------------------------------------------------------\n");CHKERRQ(ierr);
/* Free workspace */
ierr = VecDestroy(&exact_solution);CHKERRQ(ierr);
ierr = VecDestroy(&bddc_solution);CHKERRQ(ierr);
ierr = VecDestroy(&fetidp_solution);CHKERRQ(ierr);
ierr = VecDestroy(&fetidp_solution_all);CHKERRQ(ierr);
ierr = VecDestroy(&bddc_rhs);CHKERRQ(ierr);
ierr = VecDestroy(&fetidp_rhs);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = KSPDestroy(&KSPwithBDDC);CHKERRQ(ierr);
ierr = KSPDestroy(&KSPwithFETIDP);CHKERRQ(ierr);
/* Quit PETSc */
ierr = PetscFinalize();
return ierr;
}
