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tamaas/src/solvers/polonsky_keer_rey.cpp
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polonsky_keer_rey.cpp
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/**
* @file
* LICENSE
*
* Copyright (©) 2016-2021 EPFL (École Polytechnique Fédérale de Lausanne),
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU Affero General Public License as published
* by the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program 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 Affero General Public License for more details.
*
* You should have received a copy of the GNU Affero General Public License
* along with this program. If not, see <https://www.gnu.org/licenses/>.
*
*/
/* -------------------------------------------------------------------------- */
#include "polonsky_keer_rey.hh"
#include "elastic_functional.hh"
#include "logger.hh"
#include "loop.hh"
#include "model_type.hh"
#include <boost/preprocessor/seq.hpp>
#include <iomanip>
/* -------------------------------------------------------------------------- */
namespace tamaas {
PolonskyKeerRey::PolonskyKeerRey(Model& model, const GridBase<Real>& surface,
Real tolerance, type variable_type,
type constraint_type)
: ContactSolver(model, surface, tolerance), variable_type(variable_type),
constraint_type(constraint_type) {
#define SET_VIEWS(_, __, type) \
case type: { \
setViews<type>(); \
break; \
}
switch (model.getType()) {
BOOST_PP_SEQ_FOR_EACH(SET_VIEWS, ~, TAMAAS_MODEL_TYPES);
}
#undef SET_VIEWS
search_direction = allocateGrid<true, Real>(
operation_type, model.getBoundaryDiscretization());
projected_search_direction = allocateGrid<true, Real>(
operation_type, model.getBoundaryDiscretization());
switch (variable_type) {
case gap: {
model.getBEEngine().registerDirichlet();
primal = gap_view.get();
dual = pressure_view.get();
this->functional.addFunctionalTerm(
std::make_shared<functional::ElasticFunctionalGap>(*integral_op,
this->surface));
break;
}
case pressure: {
model.getBEEngine().registerNeumann();
primal = pressure_view.get();
dual = gap_view.get();
this->functional.addFunctionalTerm(
std::make_shared<functional::ElasticFunctionalPressure>(*integral_op,
this->surface));
break;
}
}
}
/* -------------------------------------------------------------------------- */
Real PolonskyKeerRey::solve(std::vector<Real> target_v) {
// Update in case of a surface change between solves
this->surface_stddev = std::sqrt(this->surface.var());
// Printing column headers
Logger().get(LogLevel::info) << std::setw(5) << "Iter"
<< " " << std::setw(15) << "Cost_f"
<< " " << std::setw(15) << "Error" << '\n'
<< std::fixed;
const Real target = target_v.back();
// Setting uniform value if constraint
if (constraint_type == variable_type && std::abs(primal->sum()) <= 0)
*primal = target;
else if (constraint_type == variable_type)
*primal *= target / primal->mean();
else if (constraint_type != variable_type)
*primal = this->surface_stddev;
// Algorithm variables
Real Gold = 1, error = 0;
UInt n = 0;
bool delta = false;
*search_direction = 0;
do {
// Computing functional gradient
functional.computeGradF(*primal, *dual);
const Real dbar = meanOnUnsaturated(*dual);
// Enforcing dual constraint via gradient
if (constraint_type != variable_type) {
*dual += 2 * target + dbar;
} else {
// Centering dual on primal > 0
*dual -= dbar;
}
// Computing gradient norm
const Real G = computeSquaredNorm(*dual);
// Updating search direction (conjugate gradient)
updateSearchDirection(delta * G / Gold);
Gold = G;
// Computing critical step
const Real tau = computeCriticalStep(target);
// Update primal variable
delta = updatePrimal(tau);
// We should scale to constraint
if (constraint_type == variable_type)
enforceMeanValue(target);
error = computeError();
const Real cost_f = functional.computeF(*primal, *dual);
printState(n, cost_f, error);
} while (error > this->tolerance and n++ < this->max_iterations);
// Final update of dual variable
functional.computeGradF(*primal, *dual);
enforceAdmissibleState();
return error;
}
/* -------------------------------------------------------------------------- */
void PolonskyKeerRey::enforceAdmissibleState() {
/// Make dual admissible
const Real dual_min = dual->min();
*dual -= dual_min;
// Primal is pressure: need to make sure gap is positive
if (variable_type == pressure) {
*displacement_view = *dual;
*displacement_view += this->surface;
}
// Primal is gap: need to make sure dual is positive (pressure + adhesion)
else {
*displacement_view = *primal;
*displacement_view += this->surface;
integral_op->apply(*displacement_view, *pressure_view);
*pressure_view -= dual_min;
}
}
/* -------------------------------------------------------------------------- */
/**
* Computes \f$ \frac{1}{\mathrm{card}(\{p > 0\})} \sum_{\{p > 0\}}{f_i} \f$
*/
Real PolonskyKeerRey::meanOnUnsaturated(const GridBase<Real>& field) const {
// Sum on unsaturated
const Real sum = Loop::reduce<operation::plus>(
[] CUDA_LAMBDA(Real & p, const Real& f) { return (p > 0) ? f : 0; },
*primal, field);
// Number of unsaturated points
const UInt n_unsat = Loop::reduce<operation::plus>(
[] CUDA_LAMBDA(Real & p) -> UInt { return (p > 0); }, *primal);
return sum / n_unsat;
}
/* -------------------------------------------------------------------------- */
/**
* Computes \f$ \sum_{\{p > 0\}}{f_i^2} \f$
*/
Real PolonskyKeerRey::computeSquaredNorm(const GridBase<Real>& field) const {
return Loop::reduce<operation::plus>(
[] CUDA_LAMBDA(Real & p, const Real& f) { return (p > 0) ? f * f : 0; },
*primal, field);
}
/* -------------------------------------------------------------------------- */
/**
* Computes \f$ \tau = \frac{ \sum_{\{p > 0\}}{q_i't_i} }{ \sum_{\{p > 0\}}{r_i'
* t_i} } \f$
*/
Real PolonskyKeerRey::computeCriticalStep(Real target) {
integral_op->apply(*search_direction, *projected_search_direction);
const Real rbar = meanOnUnsaturated(*projected_search_direction);
if (constraint_type == variable_type)
*projected_search_direction -= rbar;
else {
*projected_search_direction += 2 * target + rbar;
}
const Real num = Loop::reduce<operation::plus>(
[] CUDA_LAMBDA(const Real& p, const Real& q, const Real& t) {
return (p > 0) ? q * t : 0;
},
*primal, *dual, *search_direction);
const Real denum = Loop::reduce<operation::plus>(
[] CUDA_LAMBDA(const Real& p, const Real& r, const Real& t) {
return (p > 0) ? r * t : 0;
},
*primal, *projected_search_direction, *search_direction);
return num / denum;
}
/* -------------------------------------------------------------------------- */
/**
* Update steps:
* 1. \f$\mathbf{p} = \mathbf{p} - \tau \mathbf{t} \f$
* 2. Truncate all \f$p\f$ negative
* 3. For all points in \f$I_\mathrm{na} = \{p = 0 \land q < 0 \}\f$ do \f$p_i =
* p_i - \tau q_i\f$
*/
bool PolonskyKeerRey::updatePrimal(Real step) {
const UInt na_num = Loop::reduce<operation::plus>(
[step] CUDA_LAMBDA(Real & p, const Real& q, const Real& t) -> UInt {
p -= step * t; // Updating primal
if (p < 0)
p = 0; // Truncating neg values
if (p == 0 && q < 0) { // If non-admissible state
p -= step * q;
return 1;
} else
return 0;
},
*primal, *dual, *search_direction);
return na_num == 0;
}
/* -------------------------------------------------------------------------- */
/**
* Error is based on \f$ \sum{p_i q_i} \f$
*/
Real PolonskyKeerRey::computeError() {
/// Making sure dual respects constraint
*dual -= dual->min();
/// Complementarity error
const Real error = primal->dot(*dual);
if (std::isnan(error))
TAMAAS_EXCEPTION("Encountered NaN in complementarity error: this may be "
"caused by a contact area of a single node.");
const Real norm = [this]() {
if (variable_type == pressure)
return std::abs(primal->sum() * this->surface_stddev);
else
return std::abs(dual->sum() * this->surface_stddev);
}();
return std::abs(error) / (norm * primal->getGlobalNbPoints());
}
/* -------------------------------------------------------------------------- */
/**
* Do \f$\mathbf{t} = \mathbf{q}' + \delta \frac{R}{R_\mathrm{old}}\mathbf{t}
* \f$
*/
void PolonskyKeerRey::updateSearchDirection(Real factor) {
Loop::loop(
[factor] CUDA_LAMBDA(Real & p, Real & q, Real & t) {
t = (p > 0) ? q + factor * t : 0;
},
*primal, *dual, *search_direction);
}
/* -------------------------------------------------------------------------- */
void PolonskyKeerRey::enforceMeanValue(Real mean) {
*primal *= mean / primal->mean();
}
} // namespace tamaas
/* -------------------------------------------------------------------------- */
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