void SchmidCostaExponentialLaw2d::ComputeStressAndStressDerivative(c_matrix<double,2,2>& rC,
c_matrix<double,2,2>& rInvC,
double pressure,
c_matrix<double,2,2>& rT,
FourthOrderTensor<2,2,2,2>& rDTdE,
bool computeDTdE)
{
static c_matrix<double,2,2> C_transformed;
static c_matrix<double,2,2> invC_transformed;
// The material law parameters are set up assuming the fibre direction is (1,0,0)
// and sheet direction is (0,1,0), so we have to transform C,inv(C),and T.
// Let P be the change-of-basis matrix P = (\mathbf{m}_f, \mathbf{m}_s, \mathbf{m}_n).
// The transformed C for the fibre/sheet basis is C* = P^T C P.
// We then compute T* = T*(C*), and then compute T = P T* P^T.
ComputeTransformedDeformationTensor(rC, rInvC, C_transformed, invC_transformed);
// Compute T*
c_matrix<double,2,2> E = 0.5*(C_transformed - mIdentity);
double QQ = 0;
for (unsigned M=0; M<2; M++)
{
for (unsigned N=0; N<2; N++)
{
QQ += mB[M][N]*E(M,N)*E(M,N);
}
}
double multiplier = mA*exp(QQ)/2;
rDTdE.Zero();
for (unsigned M=0; M<2; M++)
{
for (unsigned N=0; N<2; N++)
{
rT(M,N) = multiplier*mB[M][N]*E(M,N) - pressure*invC_transformed(M,N);
if (computeDTdE)
{
for (unsigned P=0; P<2; P++)
{
for (unsigned Q=0; Q<2; Q++)
{
rDTdE(M,N,P,Q) = multiplier * mB[M][N] * (M==P)*(N==Q)
+ 2*multiplier*mB[M][N]*mB[P][Q]*E(M,N)*E(P,Q)
+ 2*pressure*invC_transformed(M,P)*invC_transformed(Q,N);
}
}
}
}
}
// Now do: T = P T* P^T and dTdE_{MNPQ} = P_{Mm}P_{Nn}P_{Pp}P_{Qq} dT*dE*_{mnpq}
this->TransformStressAndStressDerivative(rT, rDTdE, computeDTdE);
}
Foam::SolverPerformance<Type>
Foam::PBiCICG<Type, DType, LUType>::solve(Field<Type>& psi) const
{
word preconditionerName(this->controlDict_.lookup("preconditioner"));
// --- Setup class containing solver performance data
SolverPerformance<Type> solverPerf
(
preconditionerName + typeName,
this->fieldName_
);
register label nCells = psi.size();
Type* __restrict__ psiPtr = psi.begin();
Field<Type> pA(nCells);
Type* __restrict__ pAPtr = pA.begin();
Field<Type> pT(nCells, pTraits<Type>::zero);
Type* __restrict__ pTPtr = pT.begin();
Field<Type> wA(nCells);
Type* __restrict__ wAPtr = wA.begin();
Field<Type> wT(nCells);
Type* __restrict__ wTPtr = wT.begin();
Type wArT = solverPerf.great_*pTraits<Type>::one;
Type wArTold = wArT;
// --- Calculate A.psi and T.psi
this->matrix_.Amul(wA, psi);
this->matrix_.Tmul(wT, psi);
// --- Calculate initial residual and transpose residual fields
Field<Type> rA(this->matrix_.source() - wA);
Field<Type> rT(this->matrix_.source() - wT);
Type* __restrict__ rAPtr = rA.begin();
Type* __restrict__ rTPtr = rT.begin();
// --- Calculate normalisation factor
Type normFactor = this->normFactor(psi, wA, pA);
if (LduMatrix<Type, DType, LUType>::debug >= 2)
{
Info<< " Normalisation factor = " << normFactor << endl;
}
// --- Calculate normalised residual norm
solverPerf.initialResidual() = cmptDivide(gSumCmptMag(rA), normFactor);
solverPerf.finalResidual() = solverPerf.initialResidual();
// --- Check convergence, solve if not converged
if (!solverPerf.checkConvergence(this->tolerance_, this->relTol_))
{
// --- Select and construct the preconditioner
autoPtr<typename LduMatrix<Type, DType, LUType>::preconditioner>
preconPtr = LduMatrix<Type, DType, LUType>::preconditioner::New
(
*this,
this->controlDict_
);
// --- Solver iteration
do
{
// --- Store previous wArT
wArTold = wArT;
// --- Precondition residuals
preconPtr->precondition(wA, rA);
preconPtr->preconditionT(wT, rT);
// --- Update search directions:
wArT = gSumCmptProd(wA, rT);
if (solverPerf.nIterations() == 0)
{
for (register label cell=0; cell<nCells; cell++)
{
pAPtr[cell] = wAPtr[cell];
pTPtr[cell] = wTPtr[cell];
}
}
else
{
Type beta = cmptDivide
(
wArT,
stabilise(wArTold, solverPerf.vsmall_)
);
for (register label cell=0; cell<nCells; cell++)
{
pAPtr[cell] = wAPtr[cell] + cmptMultiply(beta, pAPtr[cell]);
pTPtr[cell] = wTPtr[cell] + cmptMultiply(beta, pTPtr[cell]);
}
}
// --- Update preconditioned residuals
this->matrix_.Amul(wA, pA);
this->matrix_.Tmul(wT, pT);
Type wApT = gSumCmptProd(wA, pT);
// --- Test for singularity
if
(
solverPerf.checkSingularity
(
cmptDivide(cmptMag(wApT), normFactor)
)
)
{
break;
}
// --- Update solution and residual:
Type alpha = cmptDivide
(
wArT,
stabilise(wApT, solverPerf.vsmall_)
);
for (register label cell=0; cell<nCells; cell++)
{
psiPtr[cell] += cmptMultiply(alpha, pAPtr[cell]);
rAPtr[cell] -= cmptMultiply(alpha, wAPtr[cell]);
rTPtr[cell] -= cmptMultiply(alpha, wTPtr[cell]);
}
solverPerf.finalResidual() =
cmptDivide(gSumCmptMag(rA), normFactor);
} while
(
solverPerf.nIterations()++ < this->maxIter_
&& !(solverPerf.checkConvergence(this->tolerance_, this->relTol_))
);
}
return solverPerf;
}
Foam::lduSolverPerformance Foam::PBiCG::solve
(
scalarField& x,
const scalarField& b,
const direction cmpt
) const
{
// --- Setup class containing solver performance data
lduSolverPerformance solverPerf
(
lduMatrix::preconditioner::getName(dict()) + typeName,
fieldName()
);
register label nCells = x.size();
scalar* __restrict__ xPtr = x.begin();
scalarField pA(nCells);
scalar* __restrict__ pAPtr = pA.begin();
scalarField pT(nCells, 0.0);
scalar* __restrict__ pTPtr = pT.begin();
scalarField wA(nCells);
scalar* __restrict__ wAPtr = wA.begin();
scalarField wT(nCells);
scalar* __restrict__ wTPtr = wT.begin();
scalar wArT = matrix_.great_;
scalar wArTold = wArT;
// Calculate A.x and T.x
matrix_.Amul(wA, x, coupleBouCoeffs_, interfaces_, cmpt);
matrix_.Tmul(wT, x, coupleIntCoeffs_, interfaces_, cmpt);
// Calculate initial residual and transpose residual fields
scalarField rA(b - wA);
scalarField rT(b - wT);
scalar* __restrict__ rAPtr = rA.begin();
scalar* __restrict__ rTPtr = rT.begin();
// Calculate normalisation factor
scalar normFactor = this->normFactor(x, b, wA, pA, cmpt);
if (lduMatrix::debug >= 2)
{
Info<< " Normalisation factor = " << normFactor << endl;
}
// Calculate normalised residual norm
solverPerf.initialResidual() = gSumMag(rA)/normFactor;
solverPerf.finalResidual() = solverPerf.initialResidual();
// Check convergence, solve if not converged
if (!stop(solverPerf))
{
// Select and construct the preconditioner
autoPtr<lduPreconditioner> preconPtr;
preconPtr =
lduPreconditioner::New
(
matrix_,
coupleBouCoeffs_,
coupleIntCoeffs_,
interfaces_,
dict()
);
// Solver iteration
do
{
// Store previous wArT
wArTold = wArT;
// Precondition residuals
preconPtr->precondition(wA, rA, cmpt);
preconPtr->preconditionT(wT, rT, cmpt);
// Update search directions:
wArT = gSumProd(wA, rT);
if (solverPerf.nIterations() == 0)
{
for (register label cell=0; cell<nCells; cell++)
{
pAPtr[cell] = wAPtr[cell];
pTPtr[cell] = wTPtr[cell];
}
}
else
{
scalar beta = wArT/wArTold;
for (register label cell=0; cell<nCells; cell++)
{
pAPtr[cell] = wAPtr[cell] + beta*pAPtr[cell];
pTPtr[cell] = wTPtr[cell] + beta*pTPtr[cell];
}
}
// Update preconditioned residuals
matrix_.Amul(wA, pA, coupleBouCoeffs_, interfaces_, cmpt);
matrix_.Tmul(wT, pT, coupleIntCoeffs_, interfaces_, cmpt);
scalar wApT = gSumProd(wA, pT);
// Test for singularity
if (solverPerf.checkSingularity(mag(wApT)/normFactor)) break;
// Update solution and residual:
scalar alpha = wArT/wApT;
for (register label cell=0; cell<nCells; cell++)
{
xPtr[cell] += alpha*pAPtr[cell];
rAPtr[cell] -= alpha*wAPtr[cell];
rTPtr[cell] -= alpha*wTPtr[cell];
}
solverPerf.finalResidual() = gSumMag(rA)/normFactor;
solverPerf.nIterations()++;
} while (!stop(solverPerf));
}
return solverPerf;
}
Foam::solverPerformance Foam::PBiCG::solve
(
scalarField& psi,
const scalarField& source,
const direction cmpt
) const
{
// --- Setup class containing solver performance data
solverPerformance solverPerf
(
lduMatrix::preconditioner::getName(controlDict_) + typeName,
fieldName_
);
label nCells = psi.size();
scalar* __restrict__ psiPtr = psi.begin();
scalarField pA(nCells);
scalar* __restrict__ pAPtr = pA.begin();
scalarField pT(nCells, 0.0);
scalar* __restrict__ pTPtr = pT.begin();
scalarField wA(nCells);
scalar* __restrict__ wAPtr = wA.begin();
scalarField wT(nCells);
scalar* __restrict__ wTPtr = wT.begin();
scalar wArT = solverPerf.great_;
scalar wArTold = wArT;
// --- Calculate A.psi and T.psi
matrix_.Amul(wA, psi, interfaceBouCoeffs_, interfaces_, cmpt);
matrix_.Tmul(wT, psi, interfaceIntCoeffs_, interfaces_, cmpt);
// --- Calculate initial residual and transpose residual fields
scalarField rA(source - wA);
scalarField rT(source - wT);
scalar* __restrict__ rAPtr = rA.begin();
scalar* __restrict__ rTPtr = rT.begin();
// --- Calculate normalisation factor
scalar normFactor = this->normFactor(psi, source, wA, pA);
if (lduMatrix::debug >= 2)
{
Info<< " Normalisation factor = " << normFactor << endl;
}
// --- Calculate normalised residual norm
solverPerf.initialResidual() =
gSumMag(rA, matrix().mesh().comm())
/normFactor;
solverPerf.finalResidual() = solverPerf.initialResidual();
// --- Check convergence, solve if not converged
if
(
minIter_ > 0
|| !solverPerf.checkConvergence(tolerance_, relTol_)
)
{
// --- Select and construct the preconditioner
autoPtr<lduMatrix::preconditioner> preconPtr =
lduMatrix::preconditioner::New
(
*this,
controlDict_
);
// --- Solver iteration
do
{
// --- Store previous wArT
wArTold = wArT;
// --- Precondition residuals
preconPtr->precondition(wA, rA, cmpt);
preconPtr->preconditionT(wT, rT, cmpt);
// --- Update search directions:
wArT = gSumProd(wA, rT, matrix().mesh().comm());
if (solverPerf.nIterations() == 0)
{
for (label cell=0; cell<nCells; cell++)
{
pAPtr[cell] = wAPtr[cell];
pTPtr[cell] = wTPtr[cell];
}
}
else
{
scalar beta = wArT/wArTold;
for (label cell=0; cell<nCells; cell++)
{
pAPtr[cell] = wAPtr[cell] + beta*pAPtr[cell];
pTPtr[cell] = wTPtr[cell] + beta*pTPtr[cell];
}
}
// --- Update preconditioned residuals
matrix_.Amul(wA, pA, interfaceBouCoeffs_, interfaces_, cmpt);
matrix_.Tmul(wT, pT, interfaceIntCoeffs_, interfaces_, cmpt);
scalar wApT = gSumProd(wA, pT, matrix().mesh().comm());
// --- Test for singularity
if (solverPerf.checkSingularity(mag(wApT)/normFactor))
{
break;
}
// --- Update solution and residual:
scalar alpha = wArT/wApT;
for (label cell=0; cell<nCells; cell++)
{
psiPtr[cell] += alpha*pAPtr[cell];
rAPtr[cell] -= alpha*wAPtr[cell];
rTPtr[cell] -= alpha*wTPtr[cell];
}
solverPerf.finalResidual() =
gSumMag(rA, matrix().mesh().comm())
/normFactor;
} while
(
(
solverPerf.nIterations()++ < maxIter_
&& !solverPerf.checkConvergence(tolerance_, relTol_)
)
|| solverPerf.nIterations() < minIter_
);
}
return solverPerf;
}
Foam::SolverPerformance<Type>
Foam::PBiCCCG<Type, DType, LUType>::solve
(
gpuField<Type>& psi
) const
{
word preconditionerName(this->controlDict_.lookup("preconditioner"));
// --- Setup class containing solver performance data
SolverPerformance<Type> solverPerf
(
preconditionerName + typeName,
this->fieldName_
);
register label nCells = psi.size();
gpuField<Type> pA(nCells);
gpuField<Type> pT(nCells, pTraits<Type>::zero);
gpuField<Type> wA(nCells);
gpuField<Type> wT(nCells);
scalar wArT = 1e15; //this->matrix_.great_;
scalar wArTold = wArT;
// --- Calculate A.psi and T.psi
this->matrix_.Amul(wA, psi);
this->matrix_.Tmul(wT, psi);
// --- Calculate initial residual and transpose residual fields
gpuField<Type> rA(this->matrix_.source() - wA);
gpuField<Type> rT(this->matrix_.source() - wT);
// --- Calculate normalisation factor
Type normFactor = this->normFactor(psi, wA, pA);
if (LduMatrix<Type, DType, LUType>::debug >= 2)
{
Info<< " Normalisation factor = " << normFactor << endl;
}
// --- Calculate normalised residual norm
solverPerf.initialResidual() = cmptDivide(gSumCmptMag(rA), normFactor);
solverPerf.finalResidual() = solverPerf.initialResidual();
// --- Check convergence, solve if not converged
if
(
this->minIter_ > 0
|| !solverPerf.checkConvergence(this->tolerance_, this->relTol_)
)
{
// --- Select and construct the preconditioner
autoPtr<typename LduMatrix<Type, DType, LUType>::preconditioner>
preconPtr = LduMatrix<Type, DType, LUType>::preconditioner::New
(
*this,
this->controlDict_
);
// --- Solver iteration
do
{
// --- Store previous wArT
wArTold = wArT;
// --- Precondition residuals
preconPtr->precondition(wA, rA);
preconPtr->preconditionT(wT, rT);
// --- Update search directions:
wArT = gSumProd(wA, rT);
if (solverPerf.nIterations() == 0)
{
thrust::copy(wA.begin(),wA.end(),pA.begin());
thrust::copy(wT.begin(),wT.end(),pT.begin());
}
else
{
scalar beta = wArT/wArTold;
thrust::transform
(
wA.begin(),
wA.end(),
thrust::make_transform_iterator
(
pA.begin(),
multiplyOperatorSFFunctor<scalar,Type,Type>(beta)
),
pA.begin(),
addOperatorFunctor<Type,Type,Type>()
);
thrust::transform
(
wT.begin(),
wT.end(),
thrust::make_transform_iterator
(
pT.begin(),
multiplyOperatorSFFunctor<scalar,Type,Type>(beta)
),
pT.begin(),
addOperatorFunctor<Type,Type,Type>()
);
}
// --- Update preconditioned residuals
this->matrix_.Amul(wA, pA);
this->matrix_.Tmul(wT, pT);
scalar wApT = gSumProd(wA, pT);
// --- Test for singularity
if
(
solverPerf.checkSingularity
(
cmptDivide(pTraits<Type>::one*mag(wApT), normFactor)
)
)
{
break;
}
// --- Update solution and residual:
scalar alpha = wArT/wApT;
thrust::transform
(
psi.begin(),
psi.end(),
thrust::make_transform_iterator
(
pA.begin(),
multiplyOperatorSFFunctor<scalar,Type,Type>(alpha)
),
psi.begin(),
addOperatorFunctor<Type,Type,Type>()
);
thrust::transform
(
rA.begin(),
rA.end(),
thrust::make_transform_iterator
(
wA.begin(),
multiplyOperatorSFFunctor<scalar,Type,Type>(alpha)
),
rA.begin(),
subtractOperatorFunctor<Type,Type,Type>()
);
thrust::transform
(
rT.begin(),
rT.end(),
thrust::make_transform_iterator
(
wT.begin(),
multiplyOperatorSFFunctor<scalar,Type,Type>(alpha)
),
rT.begin(),
subtractOperatorFunctor<Type,Type,Type>()
);
solverPerf.finalResidual() =
cmptDivide(gSumCmptMag(rA), normFactor);
} while
(
(
solverPerf.nIterations()++ < this->maxIter_
&& !solverPerf.checkConvergence(this->tolerance_, this->relTol_)
)
|| solverPerf.nIterations() < this->minIter_
);
}
return solverPerf;
}
