void
DruckerPragerModel<EvalT, Traits>::ResidualJacobian(std::vector<ScalarT> & X,
std::vector<ScalarT> & R, std::vector<ScalarT> & dRdX,
const ScalarT ptr, const ScalarT qtr, const ScalarT eqN,
const ScalarT mu, const ScalarT kappa)
{
std::vector<DFadType> Rfad(4);
std::vector<DFadType> Xfad(4);
// initialize DFadType local unknown vector Xfad
// Note that since Xfad is a temporary variable
// that gets changed within local iterations
// when we initialize Xfad, we only pass in the values of X,
// NOT the system sensitivity information
std::vector<ScalarT> Xval(4);
for (std::size_t i = 0; i < 4; ++i) {
Xval[i] = Sacado::ScalarValue<ScalarT>::eval(X[i]);
Xfad[i] = DFadType(4, i, Xval[i]);
}
DFadType pFad = Xfad[0];
DFadType qFad = Xfad[1];
DFadType alphaFad = Xfad[2];
DFadType deqFad = Xfad[3];
DFadType betaFad = alphaFad - b0_;
// check this
DFadType eqFad = eqN + deqFad; // (eqFad + deqFad??)
// have to break down 3.0 * mu * deqFad;
// other wise there wil be compiling error
DFadType dq = deqFad;
dq = mu * dq;
dq = 3.0 * dq;
// local system of equations
Rfad[0] = pFad - ptr + kappa * betaFad * deqFad;
Rfad[1] = qFad - qtr + dq;
Rfad[2] = alphaFad
- (a0_ + a1_ * eqFad * std::exp(a2_ * pFad - a3_ * eqFad));
Rfad[3] = qFad + alphaFad * pFad - Cf_;
// get ScalarT Residual
for (int i = 0; i < 4; i++)
R[i] = Rfad[i].val();
// get local Jacobian
for (int i = 0; i < 4; i++)
for (int j = 0; j < 4; j++)
dRdX[i + 4 * j] = Rfad[i].dx(j);
}// end of ResidualJacobian
void Constraint<Scalar, LocalOrdinal, GlobalOrdinal, Node>::Apply(const Matrix& P, Matrix& Projected) const {
// We check only row maps. Column may be different.
TEUCHOS_TEST_FOR_EXCEPTION(!P.getRowMap()->isSameAs(*Projected.getRowMap()), Exceptions::Incompatible,
"Row maps are incompatible");
const size_t NSDim = X_->getNumVectors();
const size_t numRows = P.getNodeNumRows();
const Map& colMap = *P.getColMap();
const Map& PColMap = *Projected.getColMap();
Projected.resumeFill();
Teuchos::ArrayView<const LO> indices, pindices;
Teuchos::ArrayView<const SC> values, pvalues;
Teuchos::Array<SC> valuesAll(colMap.getNodeNumElements()), newValues;
LO invalid = Teuchos::OrdinalTraits<LO>::invalid();
LO oneLO = Teuchos::OrdinalTraits<LO>::one();
SC zero = Teuchos::ScalarTraits<SC> ::zero();
SC one = Teuchos::ScalarTraits<SC> ::one();
std::vector<const SC*> Xval(NSDim);
for (size_t j = 0; j < NSDim; j++)
Xval[j] = X_->getData(j).get();
for (size_t i = 0; i < numRows; i++) {
P .getLocalRowView(i, indices, values);
Projected.getLocalRowView(i, pindices, pvalues);
size_t nnz = indices.size(); // number of nonzeros in the supplied matrix
size_t pnnz = pindices.size(); // number of nonzeros in the constrained matrix
newValues.resize(pnnz);
// Step 1: fix stencil
// Projected *must* already have the correct stencil
// Step 2: copy correct stencil values
// The algorithm is very similar to the one used in the calculation of
// Frobenius dot product, see src/Transfers/Energy-Minimization/Solvers/MueLu_CGSolver_def.hpp
// NOTE: using extra array allows us to skip the search among indices
for (size_t j = 0; j < nnz; j++)
valuesAll[indices[j]] = values[j];
for (size_t j = 0; j < pnnz; j++) {
LO ind = colMap.getLocalElement(PColMap.getGlobalElement(pindices[j])); // FIXME: we could do that before the full loop just once
if (ind != invalid)
// index indices[j] is part of template, copy corresponding value
newValues[j] = valuesAll[ind];
else
newValues[j] = zero;
}
for (size_t j = 0; j < nnz; j++)
valuesAll[indices[j]] = zero;
// Step 3: project to the space
Teuchos::SerialDenseMatrix<LO,SC>& XXtInv = XXtInv_[i];
Teuchos::SerialDenseMatrix<LO,SC> locX(NSDim, pnnz, false);
for (size_t j = 0; j < pnnz; j++)
for (size_t k = 0; k < NSDim; k++)
locX(k,j) = Xval[k][pindices[j]];
Teuchos::SerialDenseVector<LO,SC> val(pnnz, false), val1(NSDim, false), val2(NSDim, false);
for (size_t j = 0; j < pnnz; j++)
val[j] = newValues[j];
Teuchos::BLAS<LO,SC> blas;
// val1 = locX * val;
blas.GEMV(Teuchos::NO_TRANS, NSDim, pnnz,
one, locX.values(), locX.stride(),
val.values(), oneLO,
zero, val1.values(), oneLO);
// val2 = XXtInv * val1
blas.GEMV(Teuchos::NO_TRANS, NSDim, NSDim,
one, XXtInv.values(), XXtInv.stride(),
val1.values(), oneLO,
zero, val2.values(), oneLO);
// val = X^T * val2
blas.GEMV(Teuchos::CONJ_TRANS, NSDim, pnnz,
one, locX.values(), locX.stride(),
val2.values(), oneLO,
zero, val.values(), oneLO);
for (size_t j = 0; j < pnnz; j++)
newValues[j] -= val[j];
Projected.replaceLocalValues(i, pindices, newValues);
}
Projected.fillComplete(Projected.getDomainMap(), Projected.getRangeMap()); //FIXME: maps needed?
}
void Constraint<Scalar, LocalOrdinal, GlobalOrdinal, Node>::Setup(const MultiVector& B, const MultiVector& Bc, RCP<const CrsGraph> Ppattern) {
const size_t NSDim = Bc.getNumVectors();
Ppattern_ = Ppattern;
size_t numRows = Ppattern_->getNodeNumRows();
XXtInv_.resize(numRows);
RCP<const Import> importer = Ppattern_->getImporter();
X_ = MultiVectorFactory::Build(Ppattern_->getColMap(), NSDim);
if (!importer.is_null())
X_->doImport(Bc, *importer, Xpetra::INSERT);
else
*X_ = Bc;
std::vector<const SC*> Xval(NSDim);
for (size_t j = 0; j < NSDim; j++)
Xval[j] = X_->getData(j).get();
SC zero = Teuchos::ScalarTraits<SC>::zero();
SC one = Teuchos::ScalarTraits<SC>::one();
Teuchos::BLAS <LO,SC> blas;
Teuchos::LAPACK<LO,SC> lapack;
LO lwork = 3*NSDim;
ArrayRCP<LO> IPIV(NSDim);
ArrayRCP<SC> WORK(lwork);
for (size_t i = 0; i < numRows; i++) {
Teuchos::ArrayView<const LO> indices;
Ppattern_->getLocalRowView(i, indices);
size_t nnz = indices.size();
XXtInv_[i] = Teuchos::SerialDenseMatrix<LO,SC>(NSDim, NSDim, false/*zeroOut*/);
Teuchos::SerialDenseMatrix<LO,SC>& XXtInv = XXtInv_[i];
if (NSDim == 1) {
SC d = zero;
for (size_t j = 0; j < nnz; j++)
d += Xval[0][indices[j]] * Xval[0][indices[j]];
XXtInv(0,0) = one/d;
} else {
Teuchos::SerialDenseMatrix<LO,SC> locX(NSDim, nnz, false/*zeroOut*/);
for (size_t j = 0; j < nnz; j++)
for (size_t k = 0; k < NSDim; k++)
locX(k,j) = Xval[k][indices[j]];
// XXtInv_ = (locX*locX^T)^{-1}
blas.GEMM(Teuchos::NO_TRANS, Teuchos::CONJ_TRANS, NSDim, NSDim, nnz,
one, locX.values(), locX.stride(),
locX.values(), locX.stride(),
zero, XXtInv.values(), XXtInv.stride());
LO info;
// Compute LU factorization using partial pivoting with row exchanges
lapack.GETRF(NSDim, NSDim, XXtInv.values(), XXtInv.stride(), IPIV.get(), &info);
// Use the computed factorization to compute the inverse
lapack.GETRI(NSDim, XXtInv.values(), XXtInv.stride(), IPIV.get(), WORK.get(), lwork, &info);
}
}
}
void ElastoViscoplasticModel<EvalT, Traits>::
computeState(typename Traits::EvalData workset,
std::map<std::string, Teuchos::RCP<PHX::MDField<ScalarT> > > dep_fields,
std::map<std::string, Teuchos::RCP<PHX::MDField<ScalarT> > > eval_fields)
{
std::string cauchy_string = (*field_name_map_)["Cauchy_Stress"];
std::string Fp_string = (*field_name_map_)["Fp"];
std::string eqps_string = (*field_name_map_)["eqps"];
std::string eps_ss_string = (*field_name_map_)["eps_ss"];
std::string kappa_string = (*field_name_map_)["isotropic_hardening"];
std::string source_string = (*field_name_map_)["Mechanical_Source"];
std::string F_string = (*field_name_map_)["F"];
std::string J_string = (*field_name_map_)["J"];
// extract dependent MDFields
PHX::MDField<ScalarT> def_grad_field = *dep_fields[F_string];
PHX::MDField<ScalarT> J = *dep_fields[J_string];
PHX::MDField<ScalarT> poissons_ratio = *dep_fields["Poissons Ratio"];
PHX::MDField<ScalarT> elastic_modulus = *dep_fields["Elastic Modulus"];
PHX::MDField<ScalarT> yield_strength = *dep_fields["Yield Strength"];
PHX::MDField<ScalarT> hardening_modulus = *dep_fields["Hardening Modulus"];
PHX::MDField<ScalarT> recovery_modulus = *dep_fields["Recovery Modulus"];
PHX::MDField<ScalarT> flow_exp = *dep_fields["Flow Rule Exponent"];
PHX::MDField<ScalarT> flow_coeff = *dep_fields["Flow Rule Coefficient"];
PHX::MDField<ScalarT> delta_time = *dep_fields["Delta Time"];
// extract evaluated MDFields
PHX::MDField<ScalarT> stress_field = *eval_fields[cauchy_string];
PHX::MDField<ScalarT> Fp_field = *eval_fields[Fp_string];
PHX::MDField<ScalarT> eqps_field = *eval_fields[eqps_string];
PHX::MDField<ScalarT> eps_ss_field = *eval_fields[eps_ss_string];
PHX::MDField<ScalarT> kappa_field = *eval_fields[kappa_string];
PHX::MDField<ScalarT> source_field;
if (have_temperature_) {
source_field = *eval_fields[source_string];
}
// get State Variables
Albany::MDArray Fp_field_old = (*workset.stateArrayPtr)[Fp_string + "_old"];
Albany::MDArray eqps_field_old = (*workset.stateArrayPtr)[eqps_string + "_old"];
Albany::MDArray eps_ss_field_old = (*workset.stateArrayPtr)[eps_ss_string + "_old"];
Albany::MDArray kappa_field_old = (*workset.stateArrayPtr)[kappa_string + "_old"];
// define constants
RealType sq23(std::sqrt(2. / 3.));
RealType sq32(std::sqrt(3. / 2.));
// pre-define some tensors that will be re-used below
Intrepid::Tensor<ScalarT> F(num_dims_), be(num_dims_);
Intrepid::Tensor<ScalarT> s(num_dims_), sigma(num_dims_);
Intrepid::Tensor<ScalarT> N(num_dims_), A(num_dims_);
Intrepid::Tensor<ScalarT> expA(num_dims_), Fpnew(num_dims_);
Intrepid::Tensor<ScalarT> I(Intrepid::eye<ScalarT>(num_dims_));
Intrepid::Tensor<ScalarT> Fpn(num_dims_), Cpinv(num_dims_), Fpinv(num_dims_);
for (std::size_t cell(0); cell < workset.numCells; ++cell) {
for (std::size_t pt(0); pt < num_pts_; ++pt) {
ScalarT bulk = elastic_modulus(cell, pt)
/ (3. * (1. - 2. * poissons_ratio(cell, pt)));
ScalarT mu = elastic_modulus(cell, pt) / (2. * (1. + poissons_ratio(cell, pt)));
ScalarT Y = yield_strength(cell, pt);
ScalarT Jm23 = std::pow(J(cell, pt), -2. / 3.);
// assign local state variables
//
//ScalarT kappa = kappa_field(cell,pt);
ScalarT kappa_old = kappa_field_old(cell,pt);
ScalarT eps_ss = eps_ss_field(cell,pt);
ScalarT eps_ss_old = eps_ss_field_old(cell,pt);
ScalarT eqps_old = eqps_field_old(cell,pt);
// fill local tensors
//
F.fill(&def_grad_field(cell, pt, 0, 0));
for (std::size_t i(0); i < num_dims_; ++i) {
for (std::size_t j(0); j < num_dims_; ++j) {
Fpn(i, j) = ScalarT(Fp_field_old(cell, pt, i, j));
}
}
// compute trial state
// compute the Kirchhoff stress in the current configuration
//
Cpinv = Intrepid::inverse(Fpn) * Intrepid::transpose(Intrepid::inverse(Fpn));
be = Jm23 * F * Cpinv * Intrepid::transpose(F);
s = mu * Intrepid::dev(be);
ScalarT smag = Intrepid::norm(s);
ScalarT mubar = Intrepid::trace(be) * mu / (num_dims_);
// check yield condition
//
ScalarT Phi = sq32 * smag - ( Y + kappa_old );
std::cout << "======== Phi: " << Phi << std::endl;
std::cout << "======== eps: " << std::numeric_limits<RealType>::epsilon() << std::endl;
if (Phi > std::numeric_limits<RealType>::epsilon()) {
// return mapping algorithm
//
bool converged = false;
int iter = 0;
RealType max_norm = std::numeric_limits<RealType>::min();
// hardening and recovery parameters
//
ScalarT H = hardening_modulus(cell, pt);
ScalarT Rd = recovery_modulus(cell, pt);
// flow rule temperature dependent parameters
//
ScalarT f = flow_coeff(cell,pt);
ScalarT n = flow_exp(cell,pt);
// This solver deals with Sacado type info
//
LocalNonlinearSolver<EvalT, Traits> solver;
// create some vectors to store solver data
//
std::vector<ScalarT> R(2);
std::vector<ScalarT> dRdX(4);
std::vector<ScalarT> X(2);
// initial guess
X[0] = 0.0;
X[1] = eps_ss_old;
// create a copy of be as a Fad
Intrepid::Tensor<Fad> beF(num_dims_);
for (std::size_t i = 0; i < num_dims_; ++i) {
for (std::size_t j = 0; j < num_dims_; ++j) {
beF(i, j) = be(i, j);
}
}
Fad two_mubarF = 2.0 * Intrepid::trace(beF) * mu / (num_dims_);
//Fad sq32F = std::sqrt(3.0/2.0);
// FIXME this seems to be necessary to get PhiF to compile below
// need to look into this more, it appears to be a conflict
// between the Intrepid::norm and FadType operations
//
Fad smagF = smag;
while (!converged) {
// set up data types
//
std::vector<Fad> XFad(2);
std::vector<Fad> RFad(2);
std::vector<ScalarT> Xval(2);
for (std::size_t i = 0; i < 2; ++i) {
Xval[i] = Sacado::ScalarValue<ScalarT>::eval(X[i]);
XFad[i] = Fad(2, i, Xval[i]);
}
// get solution vars
//
Fad dgamF = XFad[0];
Fad eps_ssF = XFad[1];
// compute yield function
//
Fad eqps_rateF = 0.0;
if (delta_time(0) > 0) eqps_rateF = sq23 * dgamF / delta_time(0);
Fad rate_termF = 1.0 + std::asinh( std::pow(eqps_rateF / f, n));
Fad kappaF = two_mubarF * eps_ssF;
Fad PhiF = sq32 * (smagF - two_mubarF * dgamF) - ( Y + kappaF ) * rate_termF;
// compute the hardening residual
//
Fad eps_resF = eps_ssF - eps_ss_old - (H - Rd*eps_ssF) * dgamF;
// for convenience put the residuals into a container
//
RFad[0] = PhiF;
RFad[1] = eps_resF;
// extract the values of the residuals
//
for (int i = 0; i < 2; ++i)
R[i] = RFad[i].val();
// extract the sensitivities of the residuals
//
for (int i = 0; i < 2; ++i)
for (int j = 0; j < 2; ++j)
dRdX[i + 2 * j] = RFad[i].dx(j);
// this call invokes the solver and updates the solution in X
//
solver.solve(dRdX, X, R);
// compute the norm of the residual
//
RealType R0 = Sacado::ScalarValue<ScalarT>::eval(R[0]);
RealType R1 = Sacado::ScalarValue<ScalarT>::eval(R[1]);
RealType norm_res = std::sqrt(R0*R0 + R1*R1);
max_norm = std::max(norm_res, max_norm);
// check against too many inerations
//
TEUCHOS_TEST_FOR_EXCEPTION(iter == 30, std::runtime_error,
std::endl <<
"Error in ElastoViscoplastic return mapping\n" <<
"iter count = " << iter << "\n" << std::endl);
// check for a sufficiently small residual
//
std::cout << "======== norm_res : " << norm_res << std::endl;
if ( (norm_res/max_norm < 1.e-12) || (norm_res < 1.e-12) )
converged = true;
// increment the iteratio counter
//
iter++;
}
solver.computeFadInfo(dRdX, X, R);
ScalarT dgam = X[0];
ScalarT eps_ss = X[1];
ScalarT kappa = 2.0 * mubar * eps_ss;
std::cout << "======== dgam : " << dgam << std::endl;
std::cout << "======== e_ss : " << eps_ss << std::endl;
std::cout << "======== kapp : " << kappa << std::endl;
// plastic direction
N = (1 / smag) * s;
// update s
s -= 2 * mubar * dgam * N;
// update state variables
eps_ss_field(cell, pt) = eps_ss;
eqps_field(cell,pt) = eqps_old + sq23 * dgam;
kappa_field(cell,pt) = kappa;
// mechanical source
// FIXME this is not correct, just a placeholder
//
if (have_temperature_ && delta_time(0) > 0) {
source_field(cell, pt) = (sq23 * dgam / delta_time(0))
* (Y + kappa) / (density_ * heat_capacity_);
}
// exponential map to get Fpnew
//
A = dgam * N;
expA = Intrepid::exp(A);
Fpnew = expA * Fpn;
for (std::size_t i(0); i < num_dims_; ++i) {
for (std::size_t j(0); j < num_dims_; ++j) {
Fp_field(cell, pt, i, j) = Fpnew(i, j);
}
}
} else {
// we are not yielding, variables do not evolve
//
eps_ss_field(cell, pt) = eps_ss_old;
eqps_field(cell,pt) = eqps_old;
kappa_field(cell,pt) = kappa_old;
if (have_temperature_) source_field(cell, pt) = 0.0;
for (std::size_t i(0); i < num_dims_; ++i) {
for (std::size_t j(0); j < num_dims_; ++j) {
Fp_field(cell, pt, i, j) = Fpn(i, j);
}
}
}
// compute pressure
ScalarT p = 0.5 * bulk * (J(cell, pt) - 1. / (J(cell, pt)));
// compute stress
sigma = p * I + s / J(cell, pt);
for (std::size_t i(0); i < num_dims_; ++i) {
for (std::size_t j(0); j < num_dims_; ++j) {
stress_field(cell, pt, i, j) = sigma(i, j);
}
}
}
}
if (have_temperature_) {
for (std::size_t cell(0); cell < workset.numCells; ++cell) {
for (std::size_t pt(0); pt < num_pts_; ++pt) {
F.fill(&def_grad_field(cell,pt,0,0));
ScalarT J = Intrepid::det(F);
sigma.fill(&stress_field(cell,pt,0,0));
sigma -= 3.0 * expansion_coeff_ * (1.0 + 1.0 / (J*J))
* (temperature_(cell,pt) - ref_temperature_) * I;
for (std::size_t i = 0; i < num_dims_; ++i) {
for (std::size_t j = 0; j < num_dims_; ++j) {
stress_field(cell, pt, i, j) = sigma(i, j);
}
}
}
}
}
}
