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Reducing the two nested GMRES solvers to just one. Also implemented a complex version of AMS.

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This commit is contained in:
Dylan Copeland
2021-02-19 14:49:23 -08:00
parent 1e367f7970
commit 83bf172ebc
6 changed files with 873 additions and 431 deletions
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examples/ex3p_complex.cpp
+35 -200
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@@ -24,200 +24,6 @@ int dim;
const double omega = 1.4;
/// General product operator: x -> A(x)+B(x)
class SumOperator : public Operator
{
const Operator *A, *B;
bool ownA, ownB;
mutable Vector z, w;
double cA, cB;
public:
SumOperator(const Operator *A_, const Operator *B_,
bool ownA_, bool ownB_, double cA_, double cB_)
: Operator(A_->Height(), B_->Width()),
A(A_), B(B_), ownA(ownA_), ownB(ownB_), z(A_->Height()), w(A_->Width()),
cA(cA_), cB(cB_)
{
MFEM_VERIFY(A->Width() == B->Width() && A->Height() == B->Height(),
"incompatible Operators: A->Width() = " << A->Width()
<< ", B->Height() = " << B->Height());
z.UseDevice(true);
w.UseDevice(true);
}
~SumOperator()
{
if (ownA) { delete A; }
if (ownB) { delete B; }
}
virtual void Mult(const Vector &x, Vector &y) const
{ B->Mult(x, z); A->Mult(x, y); y *= cA; z *= cB; y += z;}
virtual void MultTranspose(const Vector &x, Vector &y) const
{ B->MultTranspose(x, w); A->MultTranspose(x, y); y *= cA; w *= cB; y += w;}
};
class Complex_PMHSS : public Solver
{
public:
Complex_PMHSS(Operator *Re, Operator *Im, Solver *prec_Re, Solver *prec_Im,
double a_)
: Solver(2*Re->Height()), a(a_), A(Re, Im, false, false),
A_Re(Re, NULL, false, false),
A_Im(Im, NULL, false, false), u(2*Re->Height()), rhs(2*Re->Height()),
n(Re->Height())
{
MFEM_VERIFY(Re->Height() == Im->Height() && Re->Height() == Re->Width() &&
Im->Height() == Im->Width(), "");
MFEM_VERIFY(this->Height() == A.Height(), "");
// Create CG solver for real operator aV + A_Re in complex space.
V = useIdentityV ? (Operator*) new IdentityOperator(this->Height()) :
(Operator*) &A_Re;
// In the case V = A_Re, it is faster to use a scaled operator than a SumOperator
Operator *sumOpRe = useIdentityV ? (Operator*) new SumOperator(V, &A_Re, false,
false, a, 1.0)
: (Operator*) new ScaledOperator(&A_Re, a + 1.0);
SumOperator *sumOpIm = new SumOperator(V, &A_Im, false, false, a, 1.0);
CGSolver *cg = new CGSolver(MPI_COMM_WORLD);
cg->SetRelTol(1e-6);
cg->SetMaxIter(1000);
cg->SetPrintLevel(0);
cg->SetOperator(*sumOpRe);
cg->SetPreconditioner(*prec_Re);
cg->iterative_mode = false;
SRe = cg;
CGSolver *cgi = new CGSolver(MPI_COMM_WORLD);
cgi->SetRelTol(1e-6);
cgi->SetMaxIter(1000);
cgi->SetPrintLevel(0);
cgi->SetOperator(*sumOpIm);
if (prec_Im && useIdentityV) { cgi->SetPreconditioner(*prec_Im); }
if (!useIdentityV) { cgi->SetPreconditioner(*prec_Re); }
cgi->iterative_mode = false;
/*
// For negative definite imaginary part, but then PMHSS does not work?
MINRESSolver *cgi = new MINRESSolver(MPI_COMM_WORLD);
cgi->SetRelTol(1e-12);
cgi->SetMaxIter(1000);
cgi->SetPrintLevel(0);
cgi->SetOperator(*sumOpIm);
if (prec_Im) cgi->SetPreconditioner(*prec_Im);
*/
SIm = cgi;
}
void SetOperator(const Operator &op)
{
MFEM_VERIFY(false, "Don't call SetOperator");
}
void ComputeResidual(const Vector &b, const Vector &sol, Vector &res) const
{
A.Mult(sol, res);
res -= b;
}
void Mult(const Vector &x, Vector &y) const
{
MFEM_VERIFY(x.Size() == Height() && y.Size() == Height(), "");
const double initNorm = x.Norml2();
mfem::out << "MHSS RHS norm " << initNorm << '\n';
// With V = I, use modified HSS (MHSS) from Bai, Benzi, Chen 2010.
y = 0.0;
for (int it=0; it<maxiter; ++it)
{
// Solve (aI + Re) u = (aI - i Im) y + x
if (it == 0)
{
// Optimize the first iteration, when the initial guess is y=0.
SRe->Mult(x, u);
}
else
{
A_Im.Mult(y, u); // u = Im y
// Set rhs = -i Im y = -i u
for (int j=0; j<n; ++j)
{
rhs[j] = u[n+j];
rhs[n+j] = -u[j];
}
rhs += x;
V->Mult(y, u);
rhs.Add(a, u);
SRe->Mult(rhs, u);
}
// Solve (aI + Im) y = (aI + i Re) u - i x
A_Re.Mult(u, y); // y = Re u
// Set rhs = i (Re u - x) = i (y - x)
for (int j=0; j<n; ++j)
{
rhs[j] = -(y[n+j] - x[n+j]);
rhs[n+j] = y[j] - x[j];
}
if (useIdentityV)
{
//V->Mult(u, y);
//rhs.Add(a, y);
rhs.Add(a, u);
}
else
{
// Using V = A_Re
rhs.Add(a, y);
}
SIm->Mult(rhs, y);
ComputeResidual(x, y, rhs);
const double resNorm = rhs.Norml2();
mfem::out << "MHSS iter " << it << " residual norm " << resNorm << '\n';
if (resNorm / initNorm < tol)
{
mfem::out << "MHSS converged\n";
break;
}
}
}
private:
const double a;
const int maxiter = 1;
ComplexOperator A, A_Re, A_Im;
mutable Vector u, rhs;
const int n;
const double tol = 1.0e-8;
const bool useIdentityV = false;
Operator *V = NULL;
Solver *SRe = NULL;
Solver *SIm = NULL;
};
int main(int argc, char *argv[])
{
@@ -338,13 +144,13 @@ int main(int argc, char *argv[])
//const double imscale = 0.0;
const double imscale = omega;
Coefficient *im = new ConstantCoefficient(-imscale); // im part
Coefficient *im = new ConstantCoefficient(imscale); // im part
//Coefficient *im = new ConstantCoefficient(0.0); // im part
VectorFunctionCoefficient E_Re(sdim, E_exact);
VectorFunctionCoefficient curlE_Re(sdim, curlE_exact);
ScalarVectorProductCoefficient omegaE(-imscale, E_Re); // im part
ScalarVectorProductCoefficient omegaE(imscale, E_Re); // im part
//ScalarVectorProductCoefficient omegaE(0.0, E_Re); // im part
// 9. Set up the parallel linear form b(.) which corresponds to the
@@ -497,17 +303,39 @@ int main(int argc, char *argv[])
//HypreAMS ams(*A_Re.As<HypreParMatrix>(), fespace);
// One option is to use the standard real-valued MatrixFreeAMS to precondition
// the real part of the complex system in the PMHSS preconditioner (BlockDiagonalPreconditioner).
// Another option is to use complex MatrixFreeAMS to precondition the
// complex system without PMHSS and without a BlockDiagonalPreconditioner.
//#define COMPLEX_AMS
#ifdef MFEM_USE_AMGX
bool useAmgX = false;
cout << "Built with AMGX, using AMGX " << useAmgX << endl;
MatrixFreeAMS ams(a_Re, *A_Re, *fespace, muinv, abssigma, NULL, ess_bdr,
MatrixFreeAMS ams(a_Re, *A_Re, *fespace, muinv, abssigma, im, imabs, NULL,
ess_bdr, useAmgX);
MatrixFreeAMS ams(a_Re, *A_Re, *fespace, muinv, abssigma, NULL, NULL, ess_bdr,
useAmgX);
#ifdef COMPLEX_AMS
MFEM_VERIFY(false, "TODO");
#endif
#else
cout << "Not built with AMGX" << endl;
MatrixFreeAMS ams(a_Re, *A_Re, *fespace, muinv, abssigma, NULL, ess_bdr);
#ifdef COMPLEX_AMS
MatrixFreeAMS ams(a_Re, *A_Re, A.Ptr(), *fespace, muinv, abssigma, im, imabs,
NULL, ess_bdr);
#else
MatrixFreeAMS ams(a_Re, *A_Re, NULL, *fespace, muinv, abssigma, NULL, NULL,
NULL, ess_bdr);
#endif
#endif
#ifdef COMPLEX_VERSION
#ifdef COMPLEX_AMS
//MFEM_VERIFY(false, "TODO");
#else
BlockDiagonalPreconditioner BlockDP(offsets);
BlockDP.SetDiagonalBlock(0, &ams);
BlockDP.SetDiagonalBlock(1, &ams);
@@ -533,6 +361,7 @@ int main(int argc, char *argv[])
PMHSSgmres.SetAbsTol(0.0);
PMHSSgmres.SetOperator(AspdComplex);
PMHSSgmres.SetPreconditioner(PMHSS);
#endif
GMRESSolver gmres(MPI_COMM_WORLD);
gmres.SetPrintLevel(1);
@@ -542,8 +371,14 @@ int main(int argc, char *argv[])
gmres.SetAbsTol(0.0);
gmres.SetOperator(*A);
//gmres.SetPreconditioner(BlockDP);
//gmres.SetPreconditioner(PMHSS);
gmres.SetPreconditioner(PMHSSgmres);
#ifdef COMPLEX_AMS
//MFEM_VERIFY(false, "TODO");
gmres.SetPreconditioner(ams);
#else
gmres.SetPreconditioner(PMHSS);
//gmres.SetPreconditioner(PMHSSgmres);
#endif
#else
GMRESSolver gmres(MPI_COMM_WORLD);
gmres.SetPrintLevel(1);