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solvers.cc
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/**
* @file solvers.cc
*
* @author Till Junge <till.junge@epfl.ch>
*
* @date 20 Dec 2017
*
* @brief implementation of solver functions
*
* Copyright © 2017 Till Junge
*
* µSpectre is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License as
* published by the Free Software Foundation, either version 3, or (at
* your option) any later version.
*
* µSpectre is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with GNU Emacs; see the file COPYING. If not, write to the
* Free Software Foundation, Inc., 59 Temple Place - Suite 330,
* Boston, MA 02111-1307, USA.
*/
#include "solver/solvers.hh"
#include "solver/solver_cg.hh"
#include "common/iterators.hh"
#include <Eigen/IterativeLinearSolvers>
#include <iomanip>
#include <cmath>
namespace muSpectre {
template <Dim_t DimS, Dim_t DimM>
std::vector<OptimizeResult>
de_geus (CellBase<DimS, DimM> & cell, const GradIncrements<DimM> & delFs,
SolverBase<DimS, DimM> & solver, Real newton_tol,
Real equil_tol,
Dim_t verbose) {
using Field_t = typename MaterialBase<DimS, DimM>::StrainField_t;
const Communicator & comm = cell.get_communicator();
auto solver_fields{std::make_unique<GlobalFieldCollection<DimS>>()};
solver_fields->initialise(cell.get_subdomain_resolutions(),
cell.get_subdomain_locations());
// Corresponds to symbol δF or δε
auto & incrF{make_field<Field_t>("δF", *solver_fields)};
// Corresponds to symbol ΔF or Δε
auto & DeltaF{make_field<Field_t>("ΔF", *solver_fields)};
// field to store the rhs for cg calculations
auto & rhs{make_field<Field_t>("rhs", *solver_fields)};
solver.initialise();
if (solver.get_maxiter() == 0) {
solver.set_maxiter(cell.size()*DimM*DimM*10);
}
size_t count_width{};
const auto form{cell.get_formulation()};
std::string strain_symb{};
if (verbose > 0 && comm.rank() == 0) {
//setup of algorithm 5.2 in Nocedal, Numerical Optimization (p. 111)
std::cout << "de Geus-" << solver.name() << " for ";
switch (form) {
case Formulation::small_strain: {
strain_symb = "ε";
std::cout << "small";
break;
}
case Formulation::finite_strain: {
strain_symb = "F";
std::cout << "finite";
break;
}
default:
throw SolverError("unknown formulation");
break;
}
std::cout << " strain with" << std::endl
<< "newton_tol = " << newton_tol << ", cg_tol = "
<< solver.get_tol() << " maxiter = " << solver.get_maxiter() << " and Δ"
<< strain_symb << " =" <<std::endl;
for (auto&& tup: akantu::enumerate(delFs)) {
auto && counter{std::get<0>(tup)};
auto && grad{std::get<1>(tup)};
std::cout << "Step " << counter + 1 << ":" << std::endl
<< grad << std::endl;
}
count_width = size_t(std::log10(solver.get_maxiter()))+1;
}
// initialise F = I or ε = 0
auto & F{cell.get_strain()};
switch (form) {
case Formulation::finite_strain: {
F.get_map() = Matrices::I2<DimM>();
break;
}
case Formulation::small_strain: {
F.get_map() = Matrices::I2<DimM>().Zero();
for (const auto & delF: delFs) {
if (!check_symmetry(delF)) {
throw SolverError("all Δε must be symmetric!");
}
}
break;
}
default:
throw SolverError("Unknown formulation");
break;
}
// initialise return value
std::vector<OptimizeResult> ret_val{};
// initialise materials
constexpr bool need_tangent{true};
cell.initialise_materials(need_tangent);
Grad_t<DimM> previous_grad{Grad_t<DimM>::Zero()};
for (const auto & delF: delFs) { //incremental loop
std::string message{"Has not converged"};
Real incrNorm{2*newton_tol}, gradNorm{1};
Real stressNorm{2*equil_tol};
bool has_converged{false};
auto convergence_test = [&incrNorm, &gradNorm, &newton_tol,
&stressNorm, &equil_tol, &message, &has_converged] () {
bool incr_test = incrNorm/gradNorm <= newton_tol;
bool stress_test = stressNorm < equil_tol;
if (incr_test) {
message = "Residual tolerance reached";
} else if (stress_test) {
message = "Reached stress divergence tolerance";
}
has_converged = incr_test || stress_test;
return has_converged;
};
Uint newt_iter{0};
for (;
(newt_iter < solver.get_maxiter()) && (!has_converged ||
(newt_iter==1));
++newt_iter) {
// obtain material response
auto res_tup{cell.evaluate_stress_tangent(F)};
auto & P{std::get<0>(res_tup)};
auto & K{std::get<1>(res_tup)};
auto tangent_effect = [&cell, &K] (const Field_t & dF, Field_t & dP) {
cell.directional_stiffness(K, dF, dP);
};
if (newt_iter == 0) {
DeltaF.get_map() = -(delF-previous_grad); // neg sign because rhs
tangent_effect(DeltaF, rhs);
stressNorm = std::sqrt(comm.sum(rhs.eigen().matrix().squaredNorm()));
if (convergence_test()) {
break;
}
incrF.eigenvec() = solver.solve(rhs.eigenvec(), incrF.eigenvec());
F.eigen() -= DeltaF.eigen();
} else {
rhs.eigen() = -P.eigen();
cell.project(rhs);
stressNorm = std::sqrt(comm.sum(rhs.eigen().matrix().squaredNorm()));
if (convergence_test()) {
break;
}
incrF.eigen() = 0;
incrF.eigenvec() = solver.solve(rhs.eigenvec(), incrF.eigenvec());
}
F.eigen() += incrF.eigen();
incrNorm = std::sqrt(comm.sum(incrF.eigen().matrix().squaredNorm()));
gradNorm = std::sqrt(comm.sum(F.eigen().matrix().squaredNorm()));
if (verbose > 0 && comm.rank() == 0) {
std::cout << "at Newton step " << std::setw(count_width) << newt_iter
<< ", |δ" << strain_symb << "|/|Δ" << strain_symb
<< "| = " << std::setw(17) << incrNorm/gradNorm
<< ", tol = " << newton_tol << std::endl;
if (verbose-1>1) {
std::cout << "<" << strain_symb << "> =" << std::endl
<< F.get_map().mean() << std::endl;
}
}
convergence_test();
}
// update previous gradient
previous_grad = delF;
ret_val.push_back(OptimizeResult{F.eigen(), cell.get_stress().eigen(),
has_converged, Int(has_converged),
message,
newt_iter, solver.get_counter()});
// store history variables here
cell.save_history_variables();
}
return ret_val;
}
//! instantiation for two-dimensional cells
template std::vector<OptimizeResult>
de_geus (CellBase<twoD, twoD> & cell, const GradIncrements<twoD>& delF0,
SolverBase<twoD, twoD> & solver, Real newton_tol,
Real equil_tol,
Dim_t verbose);
// template typename CellBase<twoD, threeD>::StrainField_t &
// de_geus (CellBase<twoD, threeD> & cell, const GradIncrements<threeD>& delF0,
// const Real cg_tol, const Real newton_tol, Uint maxiter,
// Dim_t verbose);
//! instantiation for three-dimensional cells
template std::vector<OptimizeResult>
de_geus (CellBase<threeD, threeD> & cell, const GradIncrements<threeD>& delF0,
SolverBase<threeD, threeD> & solver, Real newton_tol,
Real equil_tol,
Dim_t verbose);
/* ---------------------------------------------------------------------- */
template <Dim_t DimS, Dim_t DimM>
std::vector<OptimizeResult>
newton_cg (CellBase<DimS, DimM> & cell, const GradIncrements<DimM> & delFs,
SolverBase<DimS, DimM> & solver, Real newton_tol,
Real equil_tol,
Dim_t verbose) {
using Field_t = typename MaterialBase<DimS, DimM>::StrainField_t;
const Communicator & comm = cell.get_communicator();
auto solver_fields{std::make_unique<GlobalFieldCollection<DimS>>()};
solver_fields->initialise(cell.get_subdomain_resolutions(),
cell.get_subdomain_locations());
// Corresponds to symbol δF or δε
auto & incrF{make_field<Field_t>("δF", *solver_fields)};
// field to store the rhs for cg calculations
auto & rhs{make_field<Field_t>("rhs", *solver_fields)};
solver.initialise();
if (solver.get_maxiter() == 0) {
solver.set_maxiter(cell.size()*DimM*DimM*10);
}
size_t count_width{};
const auto form{cell.get_formulation()};
std::string strain_symb{};
if (verbose > 0 && comm.rank() == 0) {
//setup of algorithm 5.2 in Nocedal, Numerical Optimization (p. 111)
std::cout << "Newton-" << solver.name() << " for ";
switch (form) {
case Formulation::small_strain: {
strain_symb = "ε";
std::cout << "small";
break;
}
case Formulation::finite_strain: {
strain_symb = "Fy";
std::cout << "finite";
break;
}
default:
throw SolverError("unknown formulation");
break;
}
std::cout << " strain with" << std::endl
<< "newton_tol = " << newton_tol << ", cg_tol = "
<< solver.get_tol() << " maxiter = " << solver.get_maxiter() << " and Δ"
<< strain_symb << " =" <<std::endl;
for (auto&& tup: akantu::enumerate(delFs)) {
auto && counter{std::get<0>(tup)};
auto && grad{std::get<1>(tup)};
std::cout << "Step " << counter + 1 << ":" << std::endl
<< grad << std::endl;
}
count_width = size_t(std::log10(solver.get_maxiter()))+1;
}
// initialise F = I or ε = 0
auto & F{cell.get_strain()};
switch (cell.get_formulation()) {
case Formulation::finite_strain: {
F.get_map() = Matrices::I2<DimM>();
break;
}
case Formulation::small_strain: {
F.get_map() = Matrices::I2<DimM>().Zero();
for (const auto & delF: delFs) {
if (!check_symmetry(delF)) {
throw SolverError("all Δε must be symmetric!");
}
}
break;
}
default:
throw SolverError("Unknown formulation");
break;
}
// initialise return value
std::vector<OptimizeResult> ret_val{};
// initialise materials
constexpr bool need_tangent{true};
cell.initialise_materials(need_tangent);
Grad_t<DimM> previous_grad{Grad_t<DimM>::Zero()};
for (const auto & delF: delFs) { //incremental loop
// apply macroscopic strain increment
for (auto && grad: F.get_map()) {
grad += delF - previous_grad;
}
std::string message{"Has not converged"};
Real incrNorm{2*newton_tol}, gradNorm{1};
Real stressNorm{2*equil_tol};
bool has_converged{false};
auto convergence_test = [&incrNorm, &gradNorm, &newton_tol,
&stressNorm, &equil_tol, &message, &has_converged] () {
bool incr_test = incrNorm/gradNorm <= newton_tol;
bool stress_test = stressNorm < equil_tol;
if (incr_test) {
message = "Residual tolerance reached";
} else if (stress_test) {
message = "Reached stress divergence tolerance";
}
has_converged = incr_test || stress_test;
return has_converged;
};
Uint newt_iter{0};
for (;
newt_iter < solver.get_maxiter() && !has_converged;
++newt_iter) {
// obtain material response
auto res_tup{cell.evaluate_stress_tangent(F)};
auto & P{std::get<0>(res_tup)};
rhs.eigen() = -P.eigen();
cell.project(rhs);
stressNorm = std::sqrt(comm.sum(rhs.eigen().matrix().squaredNorm()));
if (convergence_test()) {
break;
}
incrF.eigen() = 0;
incrF.eigenvec() = solver.solve(rhs.eigenvec(), incrF.eigenvec());
F.eigen() += incrF.eigen();
incrNorm = std::sqrt(comm.sum(incrF.eigen().matrix().squaredNorm()));
gradNorm = std::sqrt(comm.sum(F.eigen().matrix().squaredNorm()));
if (verbose > 0 && comm.rank() == 0) {
std::cout << "at Newton step " << std::setw(count_width) << newt_iter
<< ", |δ" << strain_symb << "|/|Δ" << strain_symb
<< "| = " << std::setw(17) << incrNorm/gradNorm
<< ", tol = " << newton_tol << std::endl;
if (verbose-1>1) {
std::cout << "<" << strain_symb << "> =" << std::endl
<< F.get_map().mean() << std::endl;
}
}
convergence_test();
}
// update previous gradient
previous_grad = delF;
ret_val.push_back(OptimizeResult{F.eigen(), cell.get_stress().eigen(),
convergence_test(), Int(convergence_test()),
message,
newt_iter, solver.get_counter()});
//store history variables for next load increment
cell.save_history_variables();
}
return ret_val;
}
//! instantiation for two-dimensional cells
template std::vector<OptimizeResult>
newton_cg (CellBase<twoD, twoD> & cell, const GradIncrements<twoD>& delF0,
SolverBase<twoD, twoD> & solver, Real newton_tol,
Real equil_tol,
Dim_t verbose);
// template typename CellBase<twoD, threeD>::StrainField_t &
// newton_cg (CellBase<twoD, threeD> & cell, const GradIncrements<threeD>& delF0,
// const Real cg_tol, const Real newton_tol, Uint maxiter,
// Dim_t verbose);
//! instantiation for three-dimensional cells
template std::vector<OptimizeResult>
newton_cg (CellBase<threeD, threeD> & cell, const GradIncrements<threeD>& delF0,
SolverBase<threeD, threeD> & solver, Real newton_tol,
Real equil_tol,
Dim_t verbose);
/* ---------------------------------------------------------------------- */
bool check_symmetry(const Eigen::Ref<const Eigen::ArrayXXd>& eps,
Real rel_tol){
return (rel_tol >= (eps-eps.transpose()).matrix().norm()/eps.matrix().norm() ||
rel_tol >= eps.matrix().norm());
}
} // muSpectre

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