void
MultiPlasticityLinearSystem::nrStep(const RankTwoTensor & stress, const std::vector<Real> & intnl_old, const std::vector<Real> & intnl, const std::vector<Real> & pm, const RankFourTensor & E_inv, const RankTwoTensor & delta_dp, RankTwoTensor & dstress, std::vector<Real> & dpm, std::vector<Real> & dintnl, const std::vector<bool> & active, std::vector<bool> & deactivated_due_to_ld)
{
// Calculate RHS and Jacobian
std::vector<Real> rhs;
calculateRHS(stress, intnl_old, intnl, pm, delta_dp, rhs, active, true, deactivated_due_to_ld);
std::vector<std::vector<Real> > jac;
calculateJacobian(stress, intnl, pm, E_inv, active, deactivated_due_to_ld, jac);
// prepare for LAPACKgesv_ routine provided by PETSc
int system_size = rhs.size();
std::vector<double> a(system_size*system_size);
// Fill in the a "matrix" by going down columns
unsigned ind = 0;
for (int col = 0 ; col < system_size ; ++col)
for (int row = 0 ; row < system_size ; ++row)
a[ind++] = jac[row][col];
int nrhs = 1;
std::vector<int> ipiv(system_size);
int info;
LAPACKgesv_(&system_size, &nrhs, &a[0], &system_size, &ipiv[0], &rhs[0], &system_size, &info);
if (info != 0)
mooseError("In solving the linear system in a Newton-Raphson process, the PETSC LAPACK gsev routine returned with error code " << info);
// Extract the results back to dstress, dpm and dintnl
std::vector<bool> active_not_deact(_num_surfaces);
for (unsigned surface = 0 ; surface < _num_surfaces ; ++surface)
active_not_deact[surface] = (active[surface] && !deactivated_due_to_ld[surface]);
unsigned int dim = 3;
ind = 0;
for (unsigned i = 0 ; i < dim ; ++i)
for (unsigned j = 0 ; j <= i ; ++j)
dstress(i, j) = dstress(j, i) = rhs[ind++];
dpm.assign(_num_surfaces, 0);
for (unsigned surface = 0 ; surface < _num_surfaces ; ++surface)
if (active_not_deact[surface])
dpm[surface] = rhs[ind++];
dintnl.assign(_num_models, 0);
for (unsigned model = 0 ; model < _num_models ; ++model)
if (anyActiveSurfaces(model, active_not_deact))
dintnl[model] = rhs[ind++];
mooseAssert(static_cast<int>(ind) == system_size, "Incorrect extracting of changes from NR solution in nrStep");
}
bool
MultiPlasticityDebugger::dof_included(unsigned int dof, const std::vector<bool> & deactivated_due_to_ld)
{
if (dof < unsigned(6))
// these are the stress components
return true;
unsigned eff_dof = dof - 6;
if (eff_dof < _num_surfaces)
// these are the plastic multipliers, pm
return !deactivated_due_to_ld[eff_dof];
eff_dof -= _num_surfaces; // now we know the dof is an intnl parameter
std::vector<bool> active_surface(_num_surfaces);
for (unsigned surface = 0; surface < _num_surfaces; ++surface)
active_surface[surface] = !deactivated_due_to_ld[surface];
return anyActiveSurfaces(eff_dof, active_surface);
}
void
MultiPlasticityLinearSystem::calculateJacobian(const RankTwoTensor & stress, const std::vector<Real> & intnl, const std::vector<Real> & pm, const RankFourTensor & E_inv, const std::vector<bool> & active, const std::vector<bool> & deactivated_due_to_ld, std::vector<std::vector<Real> > & jac)
{
// see comments at the start of .h file
mooseAssert(intnl.size() == _num_models, "Size of intnl is " << intnl.size() << " which is incorrect in calculateJacobian");
mooseAssert(pm.size() == _num_surfaces, "Size of pm is " << pm.size() << " which is incorrect in calculateJacobian");
mooseAssert(active.size() == _num_surfaces, "Size of active is " << active.size() << " which is incorrect in calculateJacobian");
mooseAssert(deactivated_due_to_ld.size() == _num_surfaces, "Size of deactivated_due_to_ld is " << deactivated_due_to_ld.size() << " which is incorrect in calculateJacobian");
unsigned ind = 0;
unsigned active_surface_ind = 0;
std::vector<bool> active_surface(_num_surfaces); // active and not deactivated_due_to_ld
for (unsigned surface = 0 ; surface < _num_surfaces ; ++surface)
active_surface[surface] = (active[surface] && !deactivated_due_to_ld[surface]);
unsigned num_active_surface = 0;
for (unsigned surface = 0 ; surface < _num_surfaces ; ++surface)
if (active_surface[surface])
num_active_surface++;
std::vector<bool> active_model(_num_models); // whether a model has surfaces that are active and not deactivated_due_to_ld
for (unsigned model = 0 ; model < _num_models ; ++model)
active_model[model] = anyActiveSurfaces(model, active_surface);
unsigned num_active_model = 0;
for (unsigned model = 0 ; model < _num_models ; ++model)
if (active_model[model])
num_active_model++;
ind = 0;
std::vector<unsigned int> active_model_index(_num_models);
for (unsigned model = 0 ; model < _num_models ; ++model)
if (active_model[model])
active_model_index[model] = ind++;
else
active_model_index[model] = _num_models+1; // just a dummy, that will probably cause a crash if something goes wrong
std::vector<RankTwoTensor> df_dstress;
dyieldFunction_dstress(stress, intnl, active_surface, df_dstress);
std::vector<Real> df_dintnl;
dyieldFunction_dintnl(stress, intnl, active_surface, df_dintnl);
std::vector<RankTwoTensor> r;
flowPotential(stress, intnl, active, r);
std::vector<RankFourTensor> dr_dstress;
dflowPotential_dstress(stress, intnl, active, dr_dstress);
std::vector<RankTwoTensor> dr_dintnl;
dflowPotential_dintnl(stress, intnl, active, dr_dintnl);
std::vector<Real> h;
hardPotential(stress, intnl, active, h);
std::vector<RankTwoTensor> dh_dstress;
dhardPotential_dstress(stress, intnl, active, dh_dstress);
std::vector<Real> dh_dintnl;
dhardPotential_dintnl(stress, intnl, active, dh_dintnl);
// d(epp)/dstress = sum_{active alpha} pm[alpha]*dr_dstress
RankFourTensor depp_dstress;
ind = 0;
for (unsigned surface = 0 ; surface < _num_surfaces ; ++surface)
if (active[surface]) // includes deactivated_due_to_ld
depp_dstress += pm[surface]*dr_dstress[ind++];
depp_dstress += E_inv;
// d(epp)/dpm_{active_surface_index} = r_{active_surface_index}
std::vector<RankTwoTensor> depp_dpm;
depp_dpm.resize(num_active_surface);
ind = 0;
active_surface_ind = 0;
for (unsigned surface = 0 ; surface < _num_surfaces ; ++surface)
{
if (active[surface])
{
if (active_surface[surface]) // do not include the deactived_due_to_ld, since their pm are not dofs in the NR
depp_dpm[active_surface_ind++] = r[ind];
ind++;
}
}
// d(epp)/dintnl_{active_model_index} = sum(pm[asdf]*dr_dintnl[fdsa])
std::vector<RankTwoTensor> depp_dintnl;
depp_dintnl.assign(num_active_model, RankTwoTensor());
ind = 0;
for (unsigned surface = 0 ; surface < _num_surfaces ; ++surface)
{
if (active[surface])
{
unsigned int model_num = modelNumber(surface);
if (active_model[model_num]) // only include models with surfaces which are still active after deactivated_due_to_ld
depp_dintnl[active_model_index[model_num]] += pm[surface]*dr_dintnl[ind];
ind++;
}
}
// df_dstress has been calculated above
// df_dpm is always zero
// df_dintnl has been calculated above, but only the active_surface+active_model stuff needs to be included in Jacobian: see below
std::vector<RankTwoTensor> dic_dstress;
dic_dstress.assign(num_active_model, RankTwoTensor());
ind = 0;
for (unsigned surface = 0 ; surface < _num_surfaces ; ++surface)
{
if (active[surface])
{
unsigned int model_num = modelNumber(surface);
if (active_model[model_num]) // only include ic for models with active_surface (ie, if model only contains deactivated_due_to_ld don't include it)
dic_dstress[active_model_index[model_num]] += pm[surface]*dh_dstress[ind];
ind++;
}
}
std::vector<std::vector<Real> > dic_dpm;
dic_dpm.resize(num_active_model);
ind = 0;
active_surface_ind = 0;
for (unsigned model = 0 ; model < num_active_model ; ++model)
dic_dpm[model].assign(num_active_surface, 0);
for (unsigned surface = 0 ; surface < _num_surfaces ; ++surface)
{
if (active[surface])
{
if (active_surface[surface]) // only take derivs wrt active-but-not-deactivated_due_to_ld pm
{
unsigned int model_num = modelNumber(surface);
// if (active_model[model_num]) // do not need this check as if the surface has active_surface, the model must be deemed active!
dic_dpm[active_model_index[model_num]][active_surface_ind] = h[ind];
active_surface_ind++;
}
ind++;
}
}
std::vector<std::vector<Real> > dic_dintnl;
dic_dintnl.resize(num_active_model);
for (unsigned model = 0 ; model < num_active_model ; ++model)
{
dic_dintnl[model].assign(num_active_model, 0);
dic_dintnl[model][model] = 1; // deriv wrt internal parameter
}
ind = 0;
for (unsigned surface = 0 ; surface < _num_surfaces ; ++surface)
{
if (active[surface])
{
unsigned int model_num = modelNumber(surface);
if (active_model[model_num]) // only the models that contain surfaces that are still active after deactivation_due_to_ld
dic_dintnl[active_model_index[model_num]][active_model_index[model_num]] += pm[surface]*dh_dintnl[ind];
ind++;
}
}
unsigned int dim = 3;
unsigned int system_size = 6 + num_active_surface + num_active_model; // "6" comes from symmeterizing epp
jac.resize(system_size);
for (unsigned i = 0 ; i < system_size ; ++i)
jac[i].assign(system_size, 0);
unsigned int row_num = 0;
unsigned int col_num = 0;
for (unsigned i = 0 ; i < dim ; ++i)
for (unsigned j = 0 ; j <= i ; ++j)
{
for (unsigned k = 0 ; k < dim ; ++k)
for (unsigned l = 0 ; l <= k ; ++l)
jac[col_num][row_num++] = depp_dstress(i, j, k, l) + (k != l ? depp_dstress(i, j, l, k) : 0); // extra part is needed because i assume dstress(i, j) = dstress(j, i)
for (unsigned surface = 0 ; surface < num_active_surface ; ++surface)
jac[col_num][row_num++] = depp_dpm[surface](i, j);
for (unsigned a = 0 ; a < num_active_model ; ++a)
jac[col_num][row_num++] = depp_dintnl[a](i, j);
row_num = 0;
col_num++;
}
ind = 0;
for (unsigned surface = 0 ; surface < _num_surfaces ; ++surface)
if (active_surface[surface])
{
for (unsigned k = 0 ; k < dim ; ++k)
for (unsigned l = 0 ; l <= k ; ++l)
jac[col_num][row_num++] = df_dstress[ind](k, l) + (k != l ? df_dstress[ind](l, k) : 0); // extra part is needed because i assume dstress(i, j) = dstress(j, i)
for (unsigned beta = 0 ; beta < num_active_surface ; ++beta)
jac[col_num][row_num++] = 0; // df_dpm
for (unsigned model = 0 ; model < _num_models ; ++model)
if (active_model[model]) // only use df_dintnl for models in active_model
{
if (modelNumber(surface) == model)
jac[col_num][row_num++] = df_dintnl[ind];
else
jac[col_num][row_num++] = 0;
}
ind++;
row_num = 0;
col_num++;
}
for (unsigned a = 0 ; a < num_active_model ; ++a)
{
for (unsigned k = 0 ; k < dim ; ++k)
for (unsigned l = 0 ; l <= k ; ++l)
jac[col_num][row_num++] = dic_dstress[a](k, l) + (k != l ? dic_dstress[a](l, k) : 0); // extra part is needed because i assume dstress(i, j) = dstress(j, i)
for (unsigned alpha = 0 ; alpha < num_active_surface ; ++alpha)
jac[col_num][row_num++] = dic_dpm[a][alpha];
for (unsigned b = 0 ; b < num_active_model ; ++b)
jac[col_num][row_num++] = dic_dintnl[a][b];
row_num = 0;
col_num++;
}
mooseAssert(col_num == system_size, "Incorrect filling of cols in Jacobian");
}
void
MultiPlasticityLinearSystem::calculateRHS(const RankTwoTensor & stress, const std::vector<Real> & intnl_old, const std::vector<Real> & intnl, const std::vector<Real> & pm, const RankTwoTensor & delta_dp, std::vector<Real> & rhs, const std::vector<bool> & active, bool eliminate_ld, std::vector<bool> & deactivated_due_to_ld)
{
// see comments at the start of .h file
mooseAssert(intnl_old.size() == _num_models, "Size of intnl_old is " << intnl_old.size() << " which is incorrect in calculateRHS");
mooseAssert(intnl.size() == _num_models, "Size of intnl is " << intnl.size() << " which is incorrect in calculateRHS");
mooseAssert(pm.size() == _num_surfaces, "Size of pm is " << pm.size() << " which is incorrect in calculateRHS");
mooseAssert(active.size() == _num_surfaces, "Size of active is " << active.size() << " which is incorrect in calculateRHS");
std::vector<Real> f; // the yield functions
RankTwoTensor epp; // the plastic-strain constraint ("direction constraint")
std::vector<Real> ic; // the "internal constraints"
std::vector<RankTwoTensor> r;
calculateConstraints(stress, intnl_old, intnl, pm, delta_dp, f, r, epp, ic, active);
if (eliminate_ld)
eliminateLinearDependence(stress, intnl, f, r, active, deactivated_due_to_ld);
else
deactivated_due_to_ld.assign(_num_surfaces, false);
std::vector<bool> active_not_deact(_num_surfaces);
for (unsigned surface = 0 ; surface < _num_surfaces ; ++surface)
active_not_deact[surface] = (active[surface] && !deactivated_due_to_ld[surface]);
unsigned num_active_f = 0;
for (unsigned surface = 0 ; surface < _num_surfaces ; ++surface)
if (active_not_deact[surface])
num_active_f++;
unsigned num_active_ic = 0;
for (unsigned model = 0 ; model < _num_models ; ++model)
if (anyActiveSurfaces(model, active_not_deact))
num_active_ic++;
unsigned int dim = 3;
unsigned int system_size = 6 + num_active_f + num_active_ic; // "6" comes from symmeterizing epp, num_active_f comes from "f", num_active_f comes from "ic"
rhs.resize(system_size);
unsigned ind = 0;
for (unsigned i = 0 ; i < dim ; ++i)
for (unsigned j = 0 ; j <= i ; ++j)
rhs[ind++] = -epp(i, j);
unsigned active_surface = 0;
for (unsigned surface = 0 ; surface < _num_surfaces ; ++surface)
if (active[surface])
{
if (!deactivated_due_to_ld[surface])
rhs[ind++] = -f[active_surface];
active_surface++;
}
unsigned active_model = 0;
for (unsigned model = 0 ; model < _num_models ; ++model)
if (anyActiveSurfaces(model, active))
{
if (anyActiveSurfaces(model, active_not_deact))
rhs[ind++] = -ic[active_model];
active_model++;
}
mooseAssert(ind == system_size, "Incorrect filling of the rhs in calculateRHS");
}
void
MultiPlasticityDebugger::checkSolution(const RankFourTensor & E_inv)
{
Moose::err << "\n\n+++++++++++++++++++++\nChecking the Solution\n";
Moose::err << "(Ie, checking Ax = b)\n+++++++++++++++++++++\n";
outputAndCheckDebugParameters();
std::vector<bool> act;
act.assign(_num_surfaces, true);
std::vector<bool> deactivated_due_to_ld;
deactivated_due_to_ld.assign(_num_surfaces, false);
RankTwoTensor delta_dp = -E_inv * _fspb_debug_stress;
std::vector<Real> orig_rhs;
calculateRHS(_fspb_debug_stress,
_fspb_debug_intnl,
_fspb_debug_intnl,
_fspb_debug_pm,
delta_dp,
orig_rhs,
act,
true,
deactivated_due_to_ld);
Moose::err << "\nb = ";
for (unsigned i = 0; i < orig_rhs.size(); ++i)
Moose::err << orig_rhs[i] << " ";
Moose::err << "\n\n";
std::vector<std::vector<Real>> jac_coded;
calculateJacobian(_fspb_debug_stress,
_fspb_debug_intnl,
_fspb_debug_pm,
E_inv,
act,
deactivated_due_to_ld,
jac_coded);
Moose::err
<< "Before checking Ax=b is correct, check that the Jacobians given below are equal.\n";
Moose::err
<< "The hand-coded Jacobian is used in calculating the solution 'x', given 'b' above.\n";
Moose::err << "Note that this only includes degrees of freedom that aren't deactivated due to "
"linear dependence.\n";
Moose::err << "Hand-coded Jacobian:\n";
for (unsigned row = 0; row < jac_coded.size(); ++row)
{
for (unsigned col = 0; col < jac_coded.size(); ++col)
Moose::err << jac_coded[row][col] << " ";
Moose::err << "\n";
}
deactivated_due_to_ld.assign(_num_surfaces,
false); // this potentially gets changed by nrStep, below
RankTwoTensor dstress;
std::vector<Real> dpm;
std::vector<Real> dintnl;
nrStep(_fspb_debug_stress,
_fspb_debug_intnl,
_fspb_debug_intnl,
_fspb_debug_pm,
E_inv,
delta_dp,
dstress,
dpm,
dintnl,
act,
deactivated_due_to_ld);
std::vector<bool> active_not_deact(_num_surfaces);
for (unsigned surface = 0; surface < _num_surfaces; ++surface)
active_not_deact[surface] = !deactivated_due_to_ld[surface];
std::vector<Real> x;
x.assign(orig_rhs.size(), 0);
unsigned ind = 0;
for (unsigned i = 0; i < 3; ++i)
for (unsigned j = 0; j <= i; ++j)
x[ind++] = dstress(i, j);
for (unsigned surface = 0; surface < _num_surfaces; ++surface)
if (active_not_deact[surface])
x[ind++] = dpm[surface];
for (unsigned model = 0; model < _num_models; ++model)
if (anyActiveSurfaces(model, active_not_deact))
x[ind++] = dintnl[model];
mooseAssert(ind == orig_rhs.size(),
"Incorrect extracting of changes from NR solution in the "
"finite-difference checking of nrStep");
Moose::err << "\nThis yields x =";
for (unsigned i = 0; i < orig_rhs.size(); ++i)
Moose::err << x[i] << " ";
Moose::err << "\n";
std::vector<std::vector<Real>> jac_fd;
fdJacobian(_fspb_debug_stress,
_fspb_debug_intnl,
_fspb_debug_intnl,
_fspb_debug_pm,
delta_dp,
E_inv,
true,
jac_fd);
Moose::err << "\nThe finite-difference Jacobian is used to multiply by this 'x',\n";
Moose::err << "in order to check that the solution is correct\n";
Moose::err << "Finite-difference Jacobian:\n";
for (unsigned row = 0; row < jac_fd.size(); ++row)
{
for (unsigned col = 0; col < jac_fd.size(); ++col)
Moose::err << jac_fd[row][col] << " ";
Moose::err << "\n";
}
Real L2_numer = 0;
Real L2_denom = 0;
for (unsigned row = 0; row < jac_coded.size(); ++row)
for (unsigned col = 0; col < jac_coded.size(); ++col)
{
L2_numer += Utility::pow<2>(jac_coded[row][col] - jac_fd[row][col]);
L2_denom += Utility::pow<2>(jac_coded[row][col] + jac_fd[row][col]);
}
Moose::err << "Relative L2norm of the hand-coded and finite-difference Jacobian is "
<< std::sqrt(L2_numer / L2_denom) / 0.5 << "\n";
std::vector<Real> fd_times_x;
fd_times_x.assign(orig_rhs.size(), 0);
for (unsigned row = 0; row < orig_rhs.size(); ++row)
for (unsigned col = 0; col < orig_rhs.size(); ++col)
fd_times_x[row] += jac_fd[row][col] * x[col];
Moose::err << "\n(Finite-difference Jacobian)*x =\n";
for (unsigned i = 0; i < orig_rhs.size(); ++i)
Moose::err << fd_times_x[i] << " ";
Moose::err << "\n";
Moose::err << "Recall that b = \n";
for (unsigned i = 0; i < orig_rhs.size(); ++i)
Moose::err << orig_rhs[i] << " ";
Moose::err << "\n";
L2_numer = 0;
L2_denom = 0;
for (unsigned i = 0; i < orig_rhs.size(); ++i)
{
L2_numer += Utility::pow<2>(orig_rhs[i] - fd_times_x[i]);
L2_denom += Utility::pow<2>(orig_rhs[i] + fd_times_x[i]);
}
Moose::err << "\nRelative L2norm of these is " << std::sqrt(L2_numer / L2_denom) / 0.5 << "\n";
}
