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/*===========================================================================
Copyright (C) 2011-2020 Yves Renard, Tomas Ligursky.
This file is a part of GetFEM
GetFEM is free software; you can redistribute it and/or modify it
under the terms of the GNU Lesser General Public License as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version along with the GCC Runtime Library
Exception either version 3.1 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 Lesser General Public
License and GCC Runtime Library Exception for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program; if not, write to the Free Software Foundation,
Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA.
===========================================================================*/
/**
@file test_continuation.cc
Continuation of solutions to the following state problem parameterized by
lambda:
-u'' + u = lambda * exp(u) in (0, 1), u'(0) = u'(1) = 0.
This program is used to check that getfem++ is working. This is also
a good example of use of GetFEM.
*/
#include "getfem/getfem_regular_meshes.h"
#include "getfem/getfem_model_solvers.h"
#include "getfem/getfem_continuation.h" /* import continuation method */
#include "gmm/gmm_inoutput.h"
using std::endl; using std::cout; using std::cerr;
using std::ends; using std::cin;
/* some GetFEM types that we will be using */
using bgeot::scalar_type; /* = double */
using bgeot::size_type; /* = unsigned long */
/* definition of a vector type; this one is built using the predefined types
in Gmm++ */
typedef getfem::modeling_standard_plain_vector plain_vector;
/*
structure for the state problem
*/
struct state_problem {
getfem::mesh mesh; /* the mesh */
getfem::mesh_fem mf_u; /* the FEM-method */
getfem::mesh_im mim; /* the integration method */
scalar_type lambda;
bgeot::md_param PARAM;
bool cont(plain_vector &U);
void init(void);
state_problem(void) : mf_u(mesh), mim(mesh) {}
};
/* Read parameters from the .param file, build the mesh, set finite element
* and integration methods.
*/
void state_problem::init(void) {
std::string FEM_TYPE = PARAM.string_value("FEM_TYPE","FEM name");
std::string INTEGRATION = PARAM.string_value("INTEGRATION",
"Name of integration method");
cout << "FEM_TYPE=" << FEM_TYPE << "\n";
cout << "INTEGRATION=" << INTEGRATION << "\n";
/* First step: build the mesh */
std::vector<getfem::size_type> nsubdiv(1);
nsubdiv[0] = PARAM.int_value("NX", "Number of space steps ");
regular_unit_mesh(mesh, nsubdiv, bgeot::simplex_geotrans(1, 1));
/* set the finite element on the mf_u */
getfem::pfem pf_u = getfem::fem_descriptor(FEM_TYPE);
getfem::pintegration_method ppi =
getfem::int_method_descriptor(INTEGRATION);
mf_u.set_finite_element(pf_u);
mim.set_integration_method(ppi);
}
/**************************************************************************/
/* Model. */
/**************************************************************************/
bool state_problem::cont(plain_vector &U) {
//Define the model
getfem::model model;
model.add_fem_variable("u", mf_u);
getfem::add_Laplacian_brick(model, mim, "u");
std::string f = "u-lambda*exp(u)", dfdu = "1-lambda*exp(u)";
model.add_fixed_size_data("lambda", 1);
getfem::add_nonlinear_term(model, mim, "(u-lambda*exp(u))*Test_u");
// Initialise the continuation
getfem::rmodel_plsolver_type ls =
getfem::default_linear_solver<getfem::model_real_sparse_matrix,
getfem::model_real_plain_vector>(model);
size_type nb_dof = mf_u.nb_dof();
scalar_type scfac = 1./ scalar_type(nb_dof);
size_type nb_step = int(PARAM.int_value("NBSTEP",
"Number of continuation steps"));
int singularities = (int) PARAM.int_value("SINGULARITIES",
"Deal with singularities?");
scalar_type h_init = PARAM.real_value("H_INIT", "h_init"),
h_max = PARAM.real_value("H_MAX", "h_max"),
h_min = PARAM.real_value("H_MIN", "h_min"),
h_inc = PARAM.real_value("H_INC", "h_inc"),
h_dec = PARAM.real_value("H_DEC", "h_dec");
size_type maxit = PARAM.int_value("MAXITER", "maxit"),
thrit = PARAM.int_value("THR_ITER", "thrit");
scalar_type maxres = PARAM.real_value("RESIDUAL", "maxres"),
maxdiff = PARAM.real_value("DIFFERENCE", "maxdiff"),
mincos = PARAM.real_value("COS", "mincos"),
maxres_solve = PARAM.real_value("RESIDUAL_SOLVE", "maxres_solve");
int noisy = (int) PARAM.int_value("NOISY", "noisy");
std::string datapath = PARAM.string_value("DATAPATH",
"Directory of data files");
gmm::set_traces_level(noisy - 1);
getfem::cont_struct_getfem_model
S(model, "lambda", scfac, ls, h_init, h_max, h_min, h_inc, h_dec, maxit,
thrit, maxres, maxdiff, mincos, maxres_solve, noisy, singularities);
std::string bp_rootfilename = PARAM.string_value("BP_ROOTFILENAME").size()
? PARAM.string_value("BP_ROOTFILENAME") : "";
scalar_type direction = PARAM.real_value("DIRECTION", "Initial direction"),
h, T_lambda;
plain_vector T_U(U), Y(nb_dof + 1);
if (bp_rootfilename.size() > 0) {
gmm::vecload(datapath + bp_rootfilename + ".Y", Y);
gmm::copy(gmm::sub_vector(Y, gmm::sub_interval(0, nb_dof)), U);
lambda = Y[nb_dof];
char s[100];
snprintf(s, 99, ".T_Y%d", (int) PARAM.int_value("IND_BRANCH", "Branch"));
gmm::vecload(datapath + bp_rootfilename + s, Y);
gmm::copy(gmm::scaled(gmm::sub_vector(Y, gmm::sub_interval(0, nb_dof)),
direction), T_U);
T_lambda = direction * Y[nb_dof];
h = S.h_init();
} else {
lambda = PARAM.real_value("LAMBDA0", "lambda0");
model.set_real_variable("lambda")[0] = lambda;
if (noisy > 0) cout << "Starting computing an initial point" << endl;
gmm::iteration iter(maxres_solve, noisy - 1, 40000);
getfem::standard_solve(model, iter);
gmm::copy(model.real_variable("u"), U);
T_lambda = direction;
S.init_Moore_Penrose_continuation(U, lambda, T_U, T_lambda, h);
}
// cout << "U = " << U << endl;
// cout << "lambda - u * exp(-u) = " << lambda - U[0] * exp(-U[0]) << endl;
// Continuation
std::string sing_label;
char s1[100], s2[100];
std::vector<std::string> sing_out;
for (size_type step = 0; step < nb_step; ++step) {
cout << endl << "Beginning of step " << step + 1 << endl;
S.Moore_Penrose_continuation(U, lambda, T_U, T_lambda, h);
if (h == 0) break;
// cout << "U = " << U << endl;
// cout << "lambda = " << lambda << endl;
// cout << "lambda - U[0] * exp(-U[0]) = "
// << lambda - U[0] * exp(-U[0]) << endl;
sing_label = S.get_sing_label();
if (sing_label.size() > 0) {
if (sing_label == "limit point")
snprintf(s1, 99, "Step %lu: %s", step + 1, sing_label.c_str());
else if (sing_label == "smooth bifurcation point") {
gmm::copy(S.get_x_sing(),
gmm::sub_vector(Y, gmm::sub_interval(0, nb_dof)));
Y[nb_dof] = S.get_gamma_sing();
snprintf(s1, 99, "continuation_step_%lu", step + 1);
gmm::vecsave(datapath + s1 + "_bp.Y", Y);
for (size_type i = 0; i < S.nb_tangent_sing(); i++) {
gmm::copy(S.get_tx_sing(i),
gmm::sub_vector(Y, gmm::sub_interval(0, nb_dof)));
Y[nb_dof] = S.get_tgamma_sing(i);
snprintf(s2, 99, "_bp.T_Y%lu", i + 1);
gmm::vecsave(datapath + s1 + s2, Y);
}
snprintf(s1, 99, "Step %lu: %s, %u branch(es) located", step + 1,
sing_label.c_str(), (unsigned int) S.nb_tangent_sing());
}
sing_out.push_back(s1);
}
cout << "End of Step n " << step + 1 << " / " << nb_step << endl;
}
if (sing_out.size() > 0) {
cout << endl
<< "------------------------------"
<< endl
<< " Detected singular points"
<< endl
<< "------------------------------"
<< endl;
for (size_type i = 0; i < sing_out.size(); i++)
cout << sing_out[i] << endl;
cout << endl;
}
return (h > 0);
}
/**************************************************************************/
/* main program. */
/**************************************************************************/
int main(int argc, char *argv[]) {
srand(7689);
GETFEM_MPI_INIT(argc, argv);
GMM_SET_EXCEPTION_DEBUG; // Exceptions make a memory fault, to debug.
FE_ENABLE_EXCEPT; // Enable floating point exception for Nan.
try {
state_problem p;
p.PARAM.read_command_line(argc, argv);
p.init();
plain_vector U(p.mf_u.nb_dof());
p.cont(U);
}
GMM_STANDARD_CATCH_ERROR;
GETFEM_MPI_FINALIZE;
return 0;
}
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