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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
*
* @section LICENCE
*
* Copyright (C) 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 <iomanip>
#include <cmath>
#include "solvers.hh"
#include "solver/solver_cg.hh"
#include "common/iterators.hh"
namespace muSpectre {
template <Dim_t DimS, Dim_t DimM>
typename SystemBase<DimS, DimM>::StrainField_t &
de_geus (SystemBase<DimS, DimM> & sys, const GradIncrements<DimM> & delFs,
const Real cg_tol, const Real newton_tol, Uint maxiter,
Dim_t verbose) {
using Field_t = typename MaterialBase<DimS, DimM>::StrainField_t;
auto solver_fields{std::make_unique<GlobalFieldCollection<DimS, DimM>>()};
solver_fields->initialise(sys.get_resolutions());
// 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)};
SolverCG<DimS, DimM> cg(sys.get_resolutions(),
cg_tol, maxiter, verbose-1>0);
cg.initialise();
if (maxiter == 0) {
maxiter = sys.size()*DimM*DimM*10;
}
size_t count_width{};
if (verbose > 0) {
//setup of algorithm 5.2 in Nocedal, Numerical Optimization (p. 111)
std::cout << "Algo 5.2 with newton_tol = " << newton_tol << ", cg_tol = "
<< cg_tol << " maxiter = " << maxiter << " and ΔF =" <<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(maxiter))+1;
}
// initialise F = I
auto & F{sys.get_strain()};
F.get_map() = Matrices::I2<DimM>();
// initialise materials
constexpr bool need_tangent{true};
sys.initialise_materials(need_tangent);
Grad_t<DimM> previous_grad{Grad_t<DimM>::Zero()};
for (const auto & delF: delFs) { //incremental loop
Real incrNorm{2*newton_tol}, gradNorm{1};
for (Uint newt_iter{0};
(newt_iter < maxiter) && ((incrNorm/gradNorm > newton_tol) ||
(newt_iter==1));
++newt_iter) {
// obtain material response
auto res_tup{sys.evaluate_stress_tangent(F)};
auto & P{std::get<0>(res_tup)};
auto & K{std::get<1>(res_tup)};
auto tangent_effect = [&sys, &K] (const Field_t & delF, Field_t & delP) {
sys.directional_stiffness(K, delF, delP);
};
if (newt_iter == 0) {
DeltaF.get_map() = -(delF-previous_grad); // neg sign because rhs
tangent_effect(DeltaF, rhs);
cg.solve(tangent_effect, rhs, incrF);
F.eigen() -= DeltaF.eigen();
} else {
rhs.eigen() = -P.eigen();
sys.project(rhs);
cg.solve(tangent_effect, rhs, incrF);
}
F.eigen() += incrF.eigen();
incrNorm = incrF.eigen().matrix().norm();
gradNorm = F.eigen().matrix().norm();
if (verbose>0) {
std::cout << "at Newton step " << std::setw(count_width) << newt_iter
<< ", |δF|/|ΔF| = " << std::setw(17) << incrNorm/gradNorm
<< ", tol = " << newton_tol << std::endl;
std::cout << "<F> =" << std::endl << F.get_map().mean() << std::endl;
}
}
// update previous gradient
previous_grad = delF;
//store history variables here
}
return F;
}
template typename SystemBase<twoD, twoD>::StrainField_t &
de_geus (SystemBase<twoD, twoD> & sys, const GradIncrements<twoD>& delF0,
const Real cg_tol, const Real newton_tol, Uint maxiter,
Dim_t verbose);
// template typename SystemBase<twoD, threeD>::StrainField_t &
// de_geus (SystemBase<twoD, threeD> & sys, const GradIncrements<threeD>& delF0,
// const Real cg_tol, const Real newton_tol, Uint maxiter,
// Dim_t verbose);
template typename SystemBase<threeD, threeD>::StrainField_t &
de_geus (SystemBase<threeD, threeD> & sys, const GradIncrements<threeD>& delF0,
const Real cg_tol, const Real newton_tol, Uint maxiter,
Dim_t verbose);
/* ---------------------------------------------------------------------- */
template <Dim_t DimS, Dim_t DimM>
typename SystemBase<DimS, DimM>::StrainField_t &
newton_cg (SystemBase<DimS, DimM> & sys, const GradIncrements<DimM> & delFs,
const Real cg_tol, const Real newton_tol, Uint maxiter,
Dim_t verbose) {
using Field_t = typename MaterialBase<DimS, DimM>::StrainField_t;
auto solver_fields{std::make_unique<GlobalFieldCollection<DimS, DimM>>()};
solver_fields->initialise(sys.get_resolutions());
// 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)};
SolverCG<DimS, DimM> cg(sys.get_resolutions(),
cg_tol, maxiter, verbose-1>0);
cg.initialise();
if (maxiter == 0) {
maxiter = sys.size()*DimM*DimM*10;
}
size_t count_width{};
if (verbose > 0) {
//setup of algorithm 5.2 in Nocedal, Numerical Optimization (p. 111)
std::cout << "Algo 5.2 with newton_tol = " << newton_tol << ", cg_tol = "
<< cg_tol << " maxiter = " << maxiter << " and ΔF =" <<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(maxiter))+1;
}
// initialise F = I
auto & F{sys.get_strain()};
F.get_map() = Matrices::I2<DimM>();
// initialise materials
constexpr bool need_tangent{true};
sys.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;
}
Real incrNorm{2*newton_tol}, gradNorm{1};
for (Uint newt_iter{0};
newt_iter < maxiter && incrNorm/gradNorm> newton_tol;
++newt_iter) {
// obtain material response
auto res_tup{sys.evaluate_stress_tangent(F)};
auto & P{std::get<0>(res_tup)};
auto & K{std::get<1>(res_tup)};
auto fun = [&sys, &K] (const Field_t & delF, Field_t & delP) {
sys.directional_stiffness(K, delF, delP);
};
rhs.eigen() = -P.eigen();
sys.project(rhs);
cg.solve(fun, rhs, incrF);
F.eigen() += incrF.eigen();
incrNorm = incrF.eigen().matrix().norm();
gradNorm = F.eigen().matrix().norm();
if (verbose > 0) {
std::cout << "at Newton step " << std::setw(count_width) << newt_iter
<< ", |δF|/|ΔF| = " << std::setw(17) << incrNorm/gradNorm
<< ", tol = " << newton_tol << std::endl;
std::cout << "<F> =" << std::endl << F.get_map().mean() << std::endl;
}
}
// update previous gradient
previous_grad = delF;
//store history variables here
}
return F;
}
template typename SystemBase<twoD, twoD>::StrainField_t &
newton_cg (SystemBase<twoD, twoD> & sys, const GradIncrements<twoD>& delF0,
const Real cg_tol, const Real newton_tol, Uint maxiter,
Dim_t verbose);
// template typename SystemBase<twoD, threeD>::StrainField_t &
// newton_cg (SystemBase<twoD, threeD> & sys, const GradIncrements<threeD>& delF0,
// const Real cg_tol, const Real newton_tol, Uint maxiter,
// Dim_t verbose);
template typename SystemBase<threeD, threeD>::StrainField_t &
newton_cg (SystemBase<threeD, threeD> & sys, const GradIncrements<threeD>& delF0,
const Real cg_tol, const Real newton_tol, Uint maxiter,
Dim_t verbose);
} // muSpectre

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