elastostatic.cc

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/*===========================================================================
 
 Copyright (C) 2002-2020 Yves Renard, Julien Pommier.
 
 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 elastostatic.cc
   @brief Linear Elastostatic problem. A dummy linear
   elastotatic problem is solved on a regular mesh, and is compared to
   the analytical solution.
 
   This program is used to check that getfem++ is working. This is also 
   a good example of use of GetFEM.
 
   @see laplacian.cc
   @see nonlinear_elastostatic.cc
*/
 
#include "getfem/getfem_config.h"
#include "getfem/getfem_assembling.h" /* import assembly methods (and norms comp.) */
#include "getfem/getfem_export.h"   /* export functions (save solution in a file)  */
#include "getfem/getfem_regular_meshes.h"
#include "getfem/getfem_model_solvers.h"
#include "gmm/gmm.h"
#include "getfem/getfem_interpolation.h"
#include "getfem/getfem_error_estimate.h"
#include "getfem/getfem_import.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::base_small_vector; /* special class for small (dim<16) vectors */
using bgeot::base_node;  /* geometrical nodes(derived from base_small_vector)*/
using bgeot::scalar_type; /* = double */
using bgeot::size_type;   /* = unsigned long */
using bgeot::dim_type;
using bgeot::base_matrix; /* small dense matrix. */
 
/* definition of some matrix/vector types. 
 * default types of getfem_model_solvers.h
 */
typedef getfem::modeling_standard_sparse_vector sparse_vector;
typedef getfem::modeling_standard_sparse_matrix sparse_matrix;
typedef getfem::modeling_standard_plain_vector  plain_vector;
 
/**************************************************************************/
/*  Exact solution.                                                       */
/**************************************************************************/
 
gmm::row_matrix<base_small_vector> sol_K;
static scalar_type sol_lambda, sol_mu, alph = 0.3;
int sol_sing;
 
base_small_vector sol_u(const base_node &x) {
  int N = x.size(); base_small_vector res(N);
  switch(sol_sing) {
    case 0 :
      for (int i = 0; i < N; ++i)
        res[i] = alph * sin(gmm::vect_sp(sol_K.row(i), x));
      break;
    case 1 :
      {
        base_small_vector trans(x.size());
        gmm::fill(trans,  M_PI / 10.0);
        base_node y = x - trans;
        scalar_type a = gmm::vect_norm2(y);
        for (int i = 0; i < N; ++i) res[i] = a;
        break;
      }
    case 2 :
      {
        base_small_vector trans(x.size());
        gmm::fill(trans,  M_PI / 10.0);
        base_node y = x - trans;
        scalar_type a = gmm::sqrt(gmm::vect_norm2(y));
        for (int i = 0; i < N; ++i) res[i] = a;
        break;
      }
  }
  return res;
}
 
base_small_vector sol_f(const base_node &x) {
  int N = x.size();
  base_small_vector res(N);
  switch (sol_sing) {
    case 0 :
      for (int i = 0; i < N; i++) {
        res[i] = alph * ( sol_mu * gmm::vect_sp(sol_K.row(i), sol_K.row(i)) )
          * sin(gmm::vect_sp(sol_K.row(i), x));
        for (int j = 0; j < N; j++)
          res[i] += alph * ( (sol_lambda + sol_mu) * sol_K(j,j) * sol_K(j,i))
            * sin(gmm::vect_sp(sol_K.row(j), x));
      }
      break;
    case 1 :
      {
        base_small_vector trans(x.size());
        gmm::fill(trans,  M_PI / 10.0);
        base_node y = x - trans;
        scalar_type r = gmm::vect_norm2(y) + 1e-100;
        scalar_type r2 = r*r;
        scalar_type tr(0); tr = std::accumulate(y.begin(), y.end(), tr);
 
        for (int i = 0; i < N; i++)
          res[i] = sol_lambda * (y[i]*tr / r2 - 1.0) / r
            + sol_mu * (y[i]*tr/r2 - N) / r;
      }
      break;
    case 2 :
      {
        base_small_vector trans(x.size());
        gmm::fill(trans,  M_PI / 10.0);
        base_node y = x - trans;
        
        scalar_type r = gmm::vect_norm2(y) + 1e-100;
        scalar_type a = gmm::sqrt(1.0/r); 
        scalar_type b = a*a*a, c = b*b*a; 
        scalar_type tr(0); tr = std::accumulate(y.begin(), y.end(), tr);
        for (int i = 0; i < N; ++i)
          res[i] -= b * (sol_lambda + sol_mu * (N+1-3.0/2.0)) * 0.5
            - c * 3.0 * (sol_lambda + sol_mu) * (y[i]*tr) / 4.0;
      }
      break;
  }
  return res;
}
 
base_matrix sol_sigma(const base_node &x) {
  int N = x.size();
  base_matrix res(N,N);
  switch (sol_sing) {
    case 0 :
      for (int i = 0; i < N; i++)
        for (int j = 0; j <= i; j++) {
          res(j,i) = res(i,j) = alph * sol_mu *
            ( sol_K(i,j) * cos(gmm::vect_sp(sol_K.row(i), x))
              +  sol_K(j,i) * cos(gmm::vect_sp(sol_K.row(j), x))
              );
          if (i == j)
            for (int k = 0; k < N; k++)
              res(i,j) += alph * sol_lambda * sol_K(k,k)
                * cos(gmm::vect_sp(sol_K.row(k), x));
        }
      break;
    case 1 :
      {
        base_small_vector trans(x.size());
        gmm::fill(trans,  M_PI / 10.0);
        base_node y = x - trans;
        scalar_type r = gmm::vect_norm2(y) + 1e-100;
        scalar_type tr(0); tr = std::accumulate(y.begin(), y.end(), tr);
        for (int i = 0; i < N; i++) {
          res(i, i) += sol_lambda * tr / r;
          for (int j = 0; j < N; j++)
            res(i, j) += sol_mu * (y[i] + y[j]) / r;
        }
      }
 
      break;
    case 2 :
      {
        base_small_vector trans(x.size());
        gmm::fill(trans,  M_PI / 10.0);
        base_node y = x - trans;
        scalar_type r = gmm::vect_norm2(y) + 1e-100;
        scalar_type a = gmm::sqrt(1.0/r); 
        scalar_type b = a*a*a;
        scalar_type tr(0); tr = std::accumulate(y.begin(), y.end(), tr);
        for (int i = 0; i < N; i++) {
          res(i, i) += sol_lambda * tr * b * 0.5;
          for (int j = 0; j < N; j++)
            res(i, j) += sol_mu * b * (y[i] + y[j]) * 0.5;
        }
      }
  }
 
  return res;
}
 
/*
  structure for the elastostatic problem
*/
struct elastostatic_problem {
 
  enum { DIRICHLET_BOUNDARY_NUM = 0, NEUMANN_BOUNDARY_NUM = 1};
  getfem::mesh mesh;  /* the mesh */
  getfem::mesh_im mim;       /* the integration methods.                     */
  getfem::mesh_fem mf_u;     /* main mesh_fem, for the elastostatic solution */
  getfem::mesh_fem mf_mult;  /* mesh_fem for the Dirichlet condition.        */
  getfem::mesh_fem mf_rhs;   /* mesh_fem for the right hand side (f(x),..)   */
  getfem::mesh_fem mf_p;     /* mesh_fem for the pressure for mixed form     */
  scalar_type lambda, mu;    /* Lam� coefficients.                           */
 
  scalar_type residual;       /* max residual for iterative solvers          */
  bool mixed_pressure, refine;
  size_type dirichlet_version;
 
  std::string datafilename;
  bgeot::md_param PARAM;
  
  void select_boundaries(void);
  bool solve(plain_vector &U);
  void init(void);
  void compute_error(plain_vector &U);
  elastostatic_problem(void) : mim(mesh),mf_u(mesh), mf_mult(mesh),
                               mf_rhs(mesh),mf_p(mesh) {}
};
 
/* Selects the boundaries */
 
void elastostatic_problem::select_boundaries(void) {
  size_type N = mesh.dim();
  getfem::mesh_region border_faces;
  getfem::outer_faces_of_mesh(mesh, border_faces);
  for (getfem::mr_visitor i(border_faces); !i.finished(); ++i) {
    base_node un = mesh.normal_of_face_of_convex(i.cv(), i.f());
    un /= gmm::vect_norm2(un);
    if (gmm::abs(un[N-1] - 1.0) < 0.5) { // new Neumann face
      mesh.region(NEUMANN_BOUNDARY_NUM).add(i.cv(), i.f());
    } else {
      mesh.region(DIRICHLET_BOUNDARY_NUM).add(i.cv(), i.f());
    }
  }
}
 
 
/* Read parameters from the .param file, build the mesh, set finite element
 * and integration methods and selects the boundaries.
 */
void elastostatic_problem::init(void) {
  std::string MESH_FILE = PARAM.string_value("MESH_FILE", "Mesh file");
  std::string FEM_TYPE  = PARAM.string_value("FEM_TYPE","FEM name");
  std::string INTEGRATION = PARAM.string_value("INTEGRATION",
                                               "Name of integration method");
 
  cout << "MESH_FILE=" << MESH_FILE << "\n";
  cout << "FEM_TYPE="  << FEM_TYPE << "\n";
  cout << "INTEGRATION=" << INTEGRATION << "\n";
 
#if GETFEM_PARA_LEVEL > 1
  double t_init=MPI_Wtime();
#endif
 
  size_type NX = PARAM.int_value("NX");
  size_type N = PARAM.int_value("N");
  std::stringstream filename; filename << MESH_FILE;
  if ((MESH_FILE.compare(0,11,"structured:") == 0) && NX > 0) {
    filename << ";NSUBDIV=[" << NX;
    for (size_type i = 1; i < N; ++i) filename << "," << NX;
    filename << "];";
  }
  getfem::import_mesh(filename.str(), mesh);
  
  GMM_ASSERT1(N == mesh.dim(), "The mesh has not the right dimension");
 
#if GETFEM_PARA_LEVEL > 1
  cout<<"temps creation maillage "<< MPI_Wtime()-t_init<<endl;
#endif
 
  dirichlet_version
    = size_type(PARAM.int_value("DIRICHLET_VERSION",
                                               "Dirichlet version"));
  datafilename = PARAM.string_value("ROOTFILENAME","Base name of data files.");
  scalar_type FT = PARAM.real_value("FT", "parameter for exact solution");
  residual = PARAM.real_value("RESIDUAL");
  if (residual == 0.) residual = 1e-10;
  gmm::resize(sol_K, N, N);
  for (size_type i = 0; i < N; i++)
    for (size_type j = 0; j < N; j++)
      sol_K(i,j) = (i == j) ? FT : -FT;
 
  mu = PARAM.real_value("MU", "Lam� coefficient mu");
  lambda = PARAM.real_value("LAMBDA", "Lam� coefficient lambda");
  sol_sing = int(PARAM.int_value("SOL_SING", "Optional singular solution"));
  refine = (PARAM.int_value("REFINE", "Optional refinement") != 0);
  sol_lambda = lambda; sol_mu = mu;
  mf_u.set_qdim(dim_type(N));
  mf_mult.set_qdim(dim_type(N));
 
  /* 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);
 
  mim.set_integration_method(ppi);
  mf_u.set_finite_element(pf_u);
 
  std::string dirichlet_fem_name = PARAM.string_value("DIRICHLET_FEM_TYPE");
  if (dirichlet_fem_name.size() == 0)
    mf_mult.set_finite_element(pf_u);
  else {
    cout << "DIRICHLET_FEM_TYPE="  << dirichlet_fem_name << "\n";
    mf_mult.set_finite_element(getfem::fem_descriptor(dirichlet_fem_name));
  }
 
  mixed_pressure =
    (PARAM.int_value("MIXED_PRESSURE","Mixed version or not.") != 0);
  if (mixed_pressure) {
    std::string FEM_TYPE_P  = PARAM.string_value("FEM_TYPE_P","FEM name P");
    mf_p.set_finite_element(getfem::fem_descriptor(FEM_TYPE_P));
  }
 
  /* set the finite element on mf_rhs (same as mf_u is DATA_FEM_TYPE is
     not used in the .param file */
  std::string data_fem_name = PARAM.string_value("DATA_FEM_TYPE");
  if (data_fem_name.size() == 0) {
    GMM_ASSERT1(pf_u->is_lagrange(), "You are using a non-lagrange FEM. "
                << "In that case you need to set "
                << "DATA_FEM_TYPE in the .param file");
    mf_rhs.set_finite_element(pf_u);
  } else {
    mf_rhs.set_finite_element(getfem::fem_descriptor(data_fem_name));
  }
  
  /* set boundary conditions
   * (Neuman on the upper face, Dirichlet elsewhere) */
  cout << "Selecting Neumann and Dirichlet boundaries\n";
  select_boundaries();
 
#if GETFEM_PARA_LEVEL > 1
  
  
  t_init = MPI_Wtime();
  
  mf_u.nb_dof(); mf_rhs.nb_dof(); mf_mult.nb_dof();
 
  cout<<"enumerate dof time "<< MPI_Wtime()-t_init<<endl;
#else
  double t_init = gmm::uclock_sec();
  mf_u.nb_dof(); mf_rhs.nb_dof(); mf_mult.nb_dof();
  cout << "enumerate dof time " << gmm::uclock_sec() - t_init << endl;
#endif
}
 
/* compute the error with respect to the exact solution */
void elastostatic_problem::compute_error(plain_vector &U) {
  size_type N = mesh.dim();
  std::vector<scalar_type> V(mf_rhs.nb_basic_dof()*N);
  getfem::interpolation(mf_u, mf_rhs, U, V);
  for (size_type i = 0; i < mf_rhs.nb_basic_dof(); ++i) {
    gmm::add(gmm::scaled(sol_u(mf_rhs.point_of_basic_dof(i)), -1.0),
             gmm::sub_vector(V, gmm::sub_interval(i*N, N)));
  }
 
  
 
  cout.precision(16);
  mf_rhs.set_qdim(dim_type(N));
  scalar_type l2 = getfem::asm_L2_norm(mim, mf_rhs, V);
  scalar_type h1 = getfem::asm_H1_norm(mim, mf_rhs, V);
 
  if (getfem::MPI_IS_MASTER())
    cout << "L2 error = " << l2 << endl
         << "H1 error = " << h1 << endl
         << "Linfty error = " << gmm::vect_norminf(V) << endl;
  
/*   getfem::vtk_export exp(datafilename + "_err.vtk", */
/*                       PARAM.int_value("VTK_EXPORT")==1); */
/*   exp.exporting(mf_rhs);  */
/*   exp.write_point_data(mf_rhs, V, "elastostatic_displacement"); */
 
  mf_rhs.set_qdim(1);
}
 
/**************************************************************************/
/*  Model.                                                                */
/**************************************************************************/
 
 
bool elastostatic_problem::solve(plain_vector &U) {
 
  size_type N = mesh.dim();
 
  if (mixed_pressure) cout << "Number of dof for P: " << mf_p.nb_dof() << endl;
  cout << "Number of dof for u: " << mf_u.nb_dof() << endl;
 
  getfem::model model;
 
  // Main unknown of the problem.
  model.add_fem_variable("u", mf_u);
 
  // Linearized elasticity brick.
  model.add_initialized_scalar_data("lambda", mixed_pressure ? 0.0 : lambda);
  model.add_initialized_scalar_data("mu", mu);
  getfem::add_isotropic_linearized_elasticity_brick
    (model, mim, "u", "lambda", "mu");
 
  // Linearized incompressibility condition brick.
  if (mixed_pressure) {
    model.add_initialized_scalar_data("incomp_coeff", 1.0/lambda);
    model.add_fem_variable("p", mf_p); // Adding the pressure as a variable
    add_linear_incompressibility
      (model, mim, "u", "p", size_type(-1), "incomp_coeff");
  }
 
  // Volumic source term.
  std::vector<scalar_type> F(mf_rhs.nb_dof()*N);
  getfem::interpolation_function(mf_rhs, F, sol_f);
  model.add_initialized_fem_data("VolumicData", mf_rhs, F);
  getfem::add_source_term_brick(model, mim, "u", "VolumicData");
    
  // Neumann condition.
  gmm::resize(F, mf_rhs.nb_dof()*N*N);
  getfem::interpolation_function(mf_rhs, F, sol_sigma, NEUMANN_BOUNDARY_NUM);
  model.add_initialized_fem_data("NeumannData", mf_rhs, F);
  getfem::add_normal_source_term_brick
    (model, mim, "u", "NeumannData", NEUMANN_BOUNDARY_NUM);
 
  // Dirichlet condition.
  gmm::resize(F, mf_rhs.nb_dof()*N);
  getfem::interpolation_function(mf_rhs, F, sol_u);
  model.add_initialized_fem_data("DirichletData", mf_rhs, F);
  getfem::add_Dirichlet_condition_with_multipliers
    (model, mim, "u", mf_u, DIRICHLET_BOUNDARY_NUM, "DirichletData");
 
  gmm::iteration iter(residual, 1, 40000);
#if GETFEM_PARA_LEVEL > 1
  double t_init=MPI_Wtime();
#endif
  dal::bit_vector cvref;
  
  do { // solve with optional refinement
    
    cout << "Total number of variables : " << model.nb_dof() << endl;
 
    // Defining the volumic source term.
    size_type nb_dof_rhs = mf_rhs.nb_dof();
    gmm::resize(F, nb_dof_rhs * N);
    getfem::interpolation_function(mf_rhs, F, sol_f);
    gmm::copy(F, model.set_real_variable("VolumicData"));
 
    // Defining the Neumann source term.
    gmm::resize(F, nb_dof_rhs * N * N);
    getfem::interpolation_function(mf_rhs, F, sol_sigma, NEUMANN_BOUNDARY_NUM);
    gmm::copy(F, model.set_real_variable("NeumannData"));
 
    // Defining the Dirichlet condition value.
    gmm::resize(F, nb_dof_rhs * N);
    getfem::interpolation_function(mf_rhs, F, sol_u, DIRICHLET_BOUNDARY_NUM);
    gmm::copy(F, model.set_real_variable("DirichletData"));
    
    iter.init();
    getfem::standard_solve(model, iter);
    gmm::resize(U, mf_u.nb_dof());
    gmm::copy(model.real_variable("u"), U);
 
    if (refine) {
      plain_vector ERR(mesh.convex_index().last_true()+1);
      getfem::error_estimate(mim, mf_u, U, ERR);
      
      cout << "max = " << gmm::vect_norminf(ERR) << endl;
      // scalar_type threshold = gmm::vect_norminf(ERR) * 0.7;
      scalar_type threshold = 0.0001, min_ = 1e18;
      cvref.clear();
      for (dal::bv_visitor i(mesh.convex_index()); !i.finished(); ++i) {
        if (ERR[i] > threshold) cvref.add(i);
        min_ = std::min(min_, ERR[i]);
      }
      cout << "min = " << min_ << endl;
      cout << "Nb elt to be refined : " << cvref.card() << endl;
     
      mesh.Bank_refine(cvref);
    }
 
  } while (refine && cvref.card() > 0);
 
#if GETFEM_PARA_LEVEL > 1
    cout<<"temps standard solve "<< MPI_Wtime()-t_init<<endl;
#endif
 
 
  return (iter.converged());
}
  
/**************************************************************************/
/*  main program.                                                         */
/**************************************************************************/
 
int main(int argc, char *argv[]) {
 
  GETFEM_MPI_INIT(argc, argv); // For parallelized version
 
  GMM_SET_EXCEPTION_DEBUG; // Exceptions make a memory fault, to debug.
  FE_ENABLE_EXCEPT;        // Enable floating point exception for Nan.
 
  //  try {
 
 
 
    elastostatic_problem p;
    p.PARAM.read_command_line(argc, argv);
#if GETFEM_PARA_LEVEL > 1
    double t_ref=MPI_Wtime();
#endif
    p.init();
#if GETFEM_PARA_LEVEL > 1
    cout << "temps init "<< MPI_Wtime()-t_ref << endl;
#endif
    if (getfem::MPI_IS_MASTER())
      p.mesh.write_to_file(p.datafilename + ".mesh");
 
    plain_vector U;
 
#if GETFEM_PARA_LEVEL > 1
    t_ref=MPI_Wtime();
    cout<<"begining resol"<<endl;
#endif
    if (!p.solve(U)) GMM_ASSERT1(false, "Solve has failed");
 
#if GETFEM_PARA_LEVEL > 1
    cout << "temps Resol "<< MPI_Wtime()-t_ref << endl;
    t_ref = MPI_Wtime();
#endif
    p.compute_error(U);
#if GETFEM_PARA_LEVEL > 1
    cout << "temps error "<< MPI_Wtime()-t_ref << endl;
    t_ref = MPI_Wtime();
#endif
 
    // if (getfem::MPI_IS_MASTER()) { p.mesh.write_to_file("toto.mesh"); }
 
    if (p.PARAM.int_value("VTK_EXPORT") && getfem::MPI_IS_MASTER()) {
      cout << "export to " << p.datafilename + ".vtk" << "..\n";
      getfem::vtk_export exp(p.datafilename + ".vtk",
                             p.PARAM.int_value("VTK_EXPORT")==1);
      exp.exporting(p.mf_u); 
      exp.write_point_data(p.mf_u, U, "elastostatic_displacement");
      cout << "export done, you can view the data file with (for example)\n"
        "mayavi2 -d " << p.datafilename << ".vtk -f ExtractVectorNorm -f "
        "WarpVector -m Surface -m Outline\n";
    }
 
    //  } GMM_STANDARD_CATCH_ERROR;
 
  GETFEM_MPI_FINALIZE;
 
  return 0; 
}