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/* -*- c++ -*- (enables emacs c++ mode) */
/*===========================================================================
Copyright (C) 2004-2017 Yves Renard
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.
As a special exception, you may use this file as it is a part of a free
software library without restriction. Specifically, if other files
instantiate templates or use macros or inline functions from this file,
or you compile this file and link it with other files to produce an
executable, this file does not by itself cause the resulting executable
to be covered by the GNU Lesser General Public License. This exception
does not however invalidate any other reasons why the executable file
might be covered by the GNU Lesser General Public License.
===========================================================================*/
/**@file getfem_spider_fem.h
@author Yves Renard <Yves.Renard@insa-lyon.fr>
@date October 29, 2004.
@brief work in progress...
*/
#ifndef GETFEM_SPIDER_FEM_H__
#define GETFEM_SPIDER_FEM_H__
#include "getfem/getfem_interpolated_fem.h"
#include "getfem_Xfem.h"
#include "getfem/getfem_regular_meshes.h"
namespace getfem {
struct Xfem_sqrtr : public virtual_Xfem_func {
virtual scalar_type val(const Xfem_func_context &c)
{ return ::sqrt(c.xreal[0]); }
// { return ::sqrt(c.xreal[0])*cos(log(c.xreal[0])); }
virtual base_small_vector grad(const Xfem_func_context &c)
{ base_small_vector V(2);
V[0] = 1. / (2.* ::sqrt(c.xreal[0])); return V; }
// V[0] = (1./::sqrt(c.xreal[0]))( (cos(log(::sqrt(c.xreal[0])^2)))/2. - sin(log(::sqrt(c.xreal[0])^2)) ); return V; }
virtual base_matrix hess(const Xfem_func_context &c) {
base_matrix m(2,2);
m(0,0) = 1. / (4.* ::sqrt(c.xreal[0])*c.xreal[0]);
//m(0,0) = ((1./::sqrt(c.xreal[0]))^(3))( (3. * cos(log(::sqrt(c.xreal[0])^2)))/4. - sin(log(::sqrt(c.xreal[0])^2)));
return m;
}
};
struct Xfem_sqrtrcos : public virtual_Xfem_func {
scalar_type eps;
virtual scalar_type val(const Xfem_func_context &c) {
return ::sqrt(c.xreal[0]) * cos( eps*log(c.xreal[0]) );
}
virtual base_small_vector grad(const Xfem_func_context &c) {
base_small_vector V(2);
V[0] = ( 1./::sqrt( c.xreal[0]) ) * ( cos( eps*log(c.xreal[0]) )/2. - eps*sin( eps*log(c.xreal[0]) ) );
return V;
}
virtual base_matrix hess(const Xfem_func_context &c) {
base_matrix m(2,2);
m(0,0) = (1./::pow(sqrt(c.xreal[0]),3.)) * ( ((-1./4.) - ::pow(eps,2.)) * cos( eps*log(c.xreal[0]) ) );
return m;
}
};
struct Xfem_sqrtrsin : public virtual_Xfem_func {
scalar_type eps;
virtual scalar_type val(const Xfem_func_context &c) {
return ::sqrt(c.xreal[0]) * sin( eps*log(c.xreal[0]) );
}
virtual base_small_vector grad(const Xfem_func_context &c) {
base_small_vector V(2);
V[0] = ( 1./::sqrt(c.xreal[0]) ) * ( sin( eps*log(c.xreal[0]) )/2. + eps*cos( eps*log(c.xreal[0]) ) );
return V;
}
virtual base_matrix hess(const Xfem_func_context &c) {
base_matrix m(2,2);
m(0,0) = (1./::pow(sqrt(c.xreal[0]),3.)) * ( ((-1./4.) - ::pow(eps,2.)) * sin( eps*log(c.xreal[0]) ) );
return m;
}
};
/*
struct Xfem_sqrtr : public virtual_Xfem_func {
virtual scalar_type val(const Xfem_func_context &c)
{ return 1; }
virtual base_small_vector grad(const Xfem_func_context &c)
{ base_small_vector V(2); return V; }
virtual base_matrix hess(const Xfem_func_context &c) {
base_matrix m(2,2); return m;
}
};
*/
struct interpolated_transformation : public virtual_interpolated_func{
/* Polar transformation and its gradient. */
base_small_vector trans;
scalar_type theta0;
virtual void val(const base_node &xreal, base_node &v) const {
base_node w = xreal - trans;
v[0] = gmm::vect_norm2(w);
v[1] = atan2(w[1], w[0]) - theta0;
}
virtual void grad(const base_small_vector &xreal, base_matrix &m) const {
base_node w = xreal - trans;
scalar_type r = gmm::vect_norm2(w); assert(gmm::abs(r)>1e-30);
m(0,0) = w[0] / r; m(0,1) = w[1] / r;
m(1,0) = -w[1] / gmm::sqr(r); m(1,1) = w[0] / gmm::sqr(r);
}
virtual void hess(const base_node &, base_matrix &) const
{ GMM_ASSERT1(false, "this interpolated_func has no hessian"); }
virtual ~interpolated_transformation() {}
};
DAL_SIMPLE_KEY(special_cartesianfem_key, pfem);
class spider_fem {
protected :
mesh cartesian;
mesh_fem cartesian_fem;
pfem Qk;
std::shared_ptr<Xfem> penriched_Qk;
scalar_type R;
unsigned Nr, Ntheta, K;
Xfem_sqrtr Sqrtr;
Xfem_sqrtrcos Sqrtrcos;
Xfem_sqrtrsin Sqrtrsin;
int bimat_enrichment;
scalar_type epsilon;
pfem final_fem;
interpolated_transformation itt;
public :
pfem get_pfem(void) { return final_fem; }
~spider_fem () {
pfem pf(penriched_Qk);
dal::del_stored_object(pf);
if (final_fem) del_interpolated_fem(final_fem);
}
spider_fem(scalar_type R_, mesh_im &mim, unsigned Nr_, unsigned Ntheta_,
unsigned K_, base_small_vector translation, scalar_type theta0,
int bimat_enrichment_ = 0, scalar_type epsilon_ = scalar_type(0))
: cartesian_fem(cartesian), R(R_), Nr(Nr_),
Ntheta(Ntheta_), K(K_), bimat_enrichment(bimat_enrichment_), epsilon(epsilon_), final_fem(0) {
itt.trans = translation;
itt.theta0 = theta0;
/* make the cartesian mesh */
bgeot::pgeometric_trans pgt =
bgeot::geometric_trans_descriptor("GT_LINEAR_QK(2)");
std::vector<size_type> nsubdiv(2);
nsubdiv[0] = Nr; nsubdiv[1] = Ntheta;
getfem::regular_unit_mesh(cartesian, nsubdiv, pgt, false);
bgeot::base_matrix M(2,2);
M(0,0) = R;
M(1,1) = 2. * M_PI;
cartesian.transformation(M);
bgeot::base_small_vector V(2);
V[1] = -M_PI;
cartesian.translation(V);
getfem::mesh_region border_faces;
getfem::outer_faces_of_mesh(cartesian, border_faces);
for (getfem::mr_visitor it(border_faces); !it.finished(); ++it) {
base_node un = cartesian.normal_of_face_of_convex(it.cv(), it.f());
un /= gmm::vect_norm2(un);
if (un[0] >= 0.8) cartesian.region(0).add(it.cv(), it.f());
}
std::stringstream Qkname;
Qkname << "FEM_QK(2," << K << ")";
Qk = fem_descriptor(Qkname.str());
penriched_Qk = std::make_shared<Xfem>(pfem());
if(bimat_enrichment == 0){
cout << "Using SpiderFem homogenuous isotropic enrichment [sqrt(r)]..." << endl;
penriched_Qk->add_func(Qk, &Sqrtr);
}
else {
cout << "Using SpiderFem bimaterial enrichement..." << endl;
Sqrtrcos.eps = epsilon;
Sqrtrsin.eps = epsilon;
//cout << "epsilon = " << epsilon << endl;
penriched_Qk->add_func(Qk, &Sqrtrcos);
penriched_Qk->add_func(Qk, &Sqrtrsin);
}
penriched_Qk->valid();
pfem pf(penriched_Qk);
dal::pstatic_stored_object_key
pk = std::make_shared<special_cartesianfem_key>(pf);
dal::add_stored_object(pk, pf, pf->ref_convex(0), pf->node_tab(0));
cartesian_fem.set_finite_element(cartesian.convex_index(), pf);
GMM_ASSERT1(!cartesian_fem.is_reduced(), "To be adapted");
dal::bit_vector blocked_dof = cartesian_fem.basic_dof_on_region(0);
// cout << "blocked dofs = " << blocked_dof << endl;
final_fem = new_interpolated_fem(cartesian_fem, mim,&itt,blocked_dof, false);
}
void check() {
const interpolated_fem &ife = dynamic_cast<const interpolated_fem&>(*final_fem);
dal::bit_vector bv = ife.interpolated_convexes();
cerr << "interpolated_convexes: nb=" << bv.card() << "; " << bv << "\n";
unsigned ming, maxg;
scalar_type meang;
ife.gauss_pts_stats(ming,maxg,meang);
cerr << " gauss pts in interpolated mesh_fem convexes: min=" << ming << ", max=" << maxg << ", meang=" << meang << "\n";
if (bv.card() != cartesian.convex_index().card()) {
cerr << cartesian.convex_index().card() - bv.card() <<
"convexes missed by interpolated_fem, increase the "
"number of integration points";
GMM_ASSERT3(false, "");
}
}
};
} /* end of namespace getfem. */
#endif
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