/*===========================================================================
 
 Copyright (C) 2002-2012 Vanessa Lleras, 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.
 
===========================================================================*/
  
/**
 * Linear Elastostatic problem with a crack.
 *
 * This program is used to check that getfem++ is working. This is also 
 * a good example of use of Getfem++.
*/

#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_derivatives.h"
#include "getfem/getfem_regular_meshes.h"
#include "getfem/getfem_model_solvers.h"
#include "getfem/getfem_mesh_im_level_set.h"
#include "getfem/getfem_mesh_fem_level_set.h"
#include "getfem/getfem_mesh_fem_product.h"
#include "getfem/getfem_mesh_fem_global_function.h"
#include "getfem/getfem_spider_fem.h"
#include "getfem/getfem_mesh_fem_sum.h"
#include "getfem/getfem_Coulomb_friction.h"
#include "gmm/gmm.h"
#include "getfem/getfem_error_estimate.h"
#include "getfem/getfem_interpolated_fem.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::short_type;
using bgeot::dim_type; 
using bgeot::base_matrix; /* small dense matrix. */

/* definition of some matrix/vector types. These ones are built
 * using the predefined types in Gmm++
 */
typedef getfem::modeling_standard_sparse_vector sparse_vector;
typedef getfem::modeling_standard_sparse_matrix sparse_matrix;
typedef getfem::modeling_standard_plain_vector  plain_vector;


base_small_vector sol_f(const base_node &x) {
  // int N = x.size();
  // base_small_vector res(N); res[N-1] = x[N-1];
  return base_small_vector(x.size());
}

base_small_vector sol_F(const base_node &x) {
  int N = x.size();
  base_small_vector res(N);
  res[1] = -1.0;
  return res;
}

scalar_type young_modulus(scalar_type lambda, scalar_type mu) {
 return 4*mu*(lambda + mu)/(lambda+2*mu);
}

struct exact_solution {
  getfem::mesh_fem_global_function mf;
  getfem::base_vector U;

  exact_solution(getfem::mesh &me) : mf(me) {}
  
  void init(int mode, scalar_type lambda, scalar_type mu,
	    getfem::level_set &ls) {
    std::vector<getfem::pglobal_function> cfun(4);
    for (unsigned j=0; j < 4; ++j) {
      getfem::abstract_xy_function *s = 
	new getfem::crack_singular_xy_function(j);
      cfun[j] = getfem::global_function_on_level_set(ls, *s);
    }

    mf.set_functions(cfun);
    
    mf.set_qdim(1);
    
    U.resize(8); assert(mf.nb_dof() == 4);
    getfem::base_vector::iterator it = U.begin();
    scalar_type coeff=0.;
    switch(mode) {
      case 1: {
	scalar_type A=2+2*mu/(lambda+2*mu), B=-2*(lambda+mu)/(lambda+2*mu);
	/* "colonne" 1: ux, colonne 2: uy */
	*it++ = 0;       *it++ = A-B; /* sin(theta/2) */
	*it++ = A+B;     *it++ = 0;   /* cos(theta/2) */
	*it++ = -B;      *it++ = 0;   /* sin(theta/2)*sin(theta) */ 
	*it++ = 0;       *it++ = B;   /* cos(theta/2)*sin(theta) */
	coeff = 1./(sqrt(2*M_PI)); // * young_modulus(lambda,mu));
      } break;
      case 2: {
	scalar_type C1 = (lambda+3*mu)/(lambda+mu); 
	*it++ = C1+2-1;   *it++ = 0;
	*it++ = 0;      *it++ = -(C1-2+1);
	*it++ = 0;      *it++ = 1;
	*it++ = 1;      *it++ = 0;
	coeff = 2.*(mu+lambda)/(lambda+2*mu)/(sqrt(2*M_PI)); // * young_modulus(lambda,mu));
      } break;
      default:
	assert(0);
	break;
    }
    gmm::scale(U, coeff);
  }
};

/**************************************************************************/
/*  Structure for the crack problem.                                      */
/**************************************************************************/

struct crack_problem {

  enum { DIRICHLET_BOUNDARY_NUM = 0, NEUMANN_BOUNDARY_NUM1 = 1,
	 NEUMANN_BOUNDARY_NUM2 = 3};
  getfem::mesh mesh;  /* the mesh */
  getfem::mesh_level_set mls;       /* the integration methods.              */
  getfem::mesh_im_level_set mim;    /* the integration methods.              */
  getfem::mesh_im_level_set mimbound;  /* integration methods on the crack.  */
  getfem::mesh_fem mf_pre_u;
  getfem::mesh_fem mf_mult;
  getfem::mesh_fem_global_function mf_sing_u;
  getfem::mesh_fem_level_set mfls_u; 
  getfem::mesh_fem_sum mf_u_sum;
  exact_solution exact_sol;
  
  getfem::mesh_fem& mf_u() { return mf_u_sum; }
  
  scalar_type lambda, mu;    /* Lame coefficients.                */
  getfem::mesh_fem mf_rhs;   /* mesh_fem for the right hand side (f(x),..)   */
  
  
  double lx,ly;             /* size of the mesh */
  double F11,F12,F21,F22,F31,F32,F41,F42;       /* NEUMANN forces */

  getfem::level_set ls;      /* The two level sets defining the crack.       */
  
  scalar_type residual;      /* max residual for the iterative solvers       */
  size_type conv_max;
  unsigned dir_with_mult, option;
  
  std::string datafilename;
  bgeot::md_param PARAM;

  struct cutoff_param {
    scalar_type radius, radius1, radius0;
    size_type fun_num;
  };
  cutoff_param cutoff;

  bool adapted_refine;

  bool solve(plain_vector &U);

  void error_estimate(const plain_vector &U, plain_vector &ERR);
  
  void init(void);
  crack_problem(void) : mls(mesh), mim(mls),
			mimbound(mls, getfem::mesh_im_level_set::INTEGRATE_BOUNDARY),
			mf_pre_u(mesh), mf_mult(mesh), mf_sing_u(mesh),
			mfls_u(mls, mf_pre_u),
			mf_u_sum(mesh), exact_sol(mesh),
			mf_rhs(mesh), ls(mesh, 1, true) {}

};

/* Read parameters from the .param file, build the mesh, set finite element
 * and integration methods and selects the boundaries.
 */
void crack_problem::init(void) {
  std::string MESH_TYPE = PARAM.string_value("MESH_TYPE","Mesh type ");
  std::string FEM_TYPE  = PARAM.string_value("FEM_TYPE","FEM name");

  std::string INTEGRATION = PARAM.string_value("INTEGRATION",
					       "Name of integration method");
  std::string SIMPLEX_INTEGRATION = PARAM.string_value("SIMPLEX_INTEGRATION",
					 "Name of simplex integration method");
  std::string SINGULAR_INTEGRATION = PARAM.string_value("SINGULAR_INTEGRATION");
  option = unsigned(PARAM.int_value("OPTION", "option"));

  cout << "MESH_TYPE=" << MESH_TYPE << "\n";
  cout << "FEM_TYPE="  << FEM_TYPE << "\n";
  cout << "INTEGRATION=" << INTEGRATION << "\n";

  
  /* First step : build the mesh */
  bgeot::pgeometric_trans pgt = 
    bgeot::geometric_trans_descriptor(MESH_TYPE);
  size_type N = pgt->dim();
  std::vector<size_type> nsubdiv(N);
  size_type NX = PARAM.int_value("NX", "Number of space steps ");
  if (option == 1) NX *= 2;
  std::fill(nsubdiv.begin(),nsubdiv.end(), NX);
  getfem::regular_unit_mesh(mesh, nsubdiv, pgt,
			    PARAM.int_value("MESH_NOISED") != 0);
  if (option == 1)
    for (dal::bv_visitor i(mesh.convex_index()); !i.finished(); ++i) {
      base_node pt = gmm::mean_value(mesh.points_of_convex(i)) ;
      bool kill = true;
      for (size_type j = 0; j < N; ++j)
	if (pt[j] < 0.5) kill = false;
      if (kill) mesh.sup_convex(i, true);
    }
  
  lx = PARAM.real_value("LX", "length x'ox");
  ly = PARAM.real_value("LY", "length y'oy");
  
  bgeot::base_matrix M(2,2);
  M(0,0) = lx;   
  M(1,1) = ly;
  mesh.transformation(M);
  
  // base_small_vector tt(N); tt[0] = tt[1] = -(lx/2.);
  // mesh.translation(tt); 

  conv_max = PARAM.int_value("CONV_MAX","Maximal number of convexes in the mesh");
  adapted_refine = PARAM.int_value("ADAPTED_REFINE", "Adapted Refinement");
  
  datafilename = PARAM.string_value("ROOTFILENAME","Base name of data files.");
  residual = PARAM.real_value("RESIDUAL");
  if (residual == 0.) residual = 1e-10;
 
  mu = PARAM.real_value("MU", "Lame coefficient mu");
  lambda = PARAM.real_value("LAMBDA", "Lame coefficient lambda");
  //unsigned mode =unsigned( PARAM.int_value("MODE", "mode"));

  mf_u().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);
  getfem::pintegration_method simp_ppi = 
    getfem::int_method_descriptor(SIMPLEX_INTEGRATION);
  getfem::pintegration_method sing_ppi = (SINGULAR_INTEGRATION.size() ? getfem::int_method_descriptor(SINGULAR_INTEGRATION) : 0);
  
  mim.set_integration_method(mesh.convex_index(), ppi);
  mimbound.set_integration_method(mesh.convex_index(), ppi);
  mls.add_level_set(ls);

  mim.set_simplex_im(simp_ppi, sing_ppi);
  mimbound.set_simplex_im(simp_ppi, sing_ppi);
  mf_pre_u.set_finite_element(mesh.convex_index(), pf_u);
  mf_mult.set_finite_element(mesh.convex_index(), pf_u);
  mf_mult.set_qdim(dim_type(N));

  dir_with_mult = unsigned(PARAM.int_value("DIRICHLET_VERSION"));

  cutoff.fun_num = PARAM.int_value("CUTOFF_FUNC", "cutoff function");
  cutoff.radius = PARAM.real_value("CUTOFF", "Cutoff");
  cutoff.radius1 = PARAM.real_value("CUTOFF1", "Cutoff1");
  cutoff.radius0 = PARAM.real_value("CUTOFF0", "Cutoff0");

  /* 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(mesh.convex_index(), pf_u);
  } else {
    mf_rhs.set_finite_element(mesh.convex_index(), 
			      getfem::fem_descriptor(data_fem_name));
  }
  
  /* set boundary conditions
   * (Neuman on the upper face, Dirichlet elsewhere) */
  cout << "Selecting Neumann and Dirichlet boundaries\n";
  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);
    switch (option) {
    case 0 :
      mesh.region(DIRICHLET_BOUNDARY_NUM).add(i.cv(), i.f());
      break;
    case 1 :
      if (gmm::abs(un[N-1]-1.0) < 1.0E-7) {
	base_node pt = gmm::mean_value(mesh.points_of_face_of_convex(i.cv(), i.f()));
	if (pt[N-1] > 0.9) mesh.region(DIRICHLET_BOUNDARY_NUM).add(i.cv(), i.f());
      }
      else if (gmm::abs(un[N-1]+1.0) < 1.0E-7)
	mesh.region(NEUMANN_BOUNDARY_NUM1).add(i.cv(), i.f());
      else
	mesh.region(NEUMANN_BOUNDARY_NUM2).add(i.cv(), i.f());
      break;
    }
  }

  
  //  exact_sol.init(1,lambda,mu,ls);
}


base_small_vector ls_function(const base_node P, int option) {
  scalar_type x = P[0], y = P[1];
  base_small_vector res(2);
  switch (option) {
  case 0:
    res[0] =  y-0.5;
    res[1] =  x-0.5;
    break;
  case 1:
    //       res[0] =  2.2* x - y - 0.6;
    //       res[1] =  1.0 - (x + 2.2*y);
    res[0] =  (2.* x - y - 0.5) / sqrt(5); // crack tip on (0.375, 0.25).
    res[1] =  (7./8. - (x + 2.*y)) / sqrt(5);
    break;
  default: assert(0);
  }
  return res;
}

void crack_problem::error_estimate(const plain_vector &U, plain_vector &ERR) {


  size_type N = mesh.dim();
  size_type qdim = mf_u().get_qdim();
  gmm::clear(ERR);
  std::vector<scalar_type> coeff1, coeff2;
  base_matrix grad1(qdim, N), grad2(qdim, N), E(N, N), S1(N, N), S2(N, N);
  base_matrix hess1(qdim, N*N);
  base_matrix G1, G2;
  bgeot::geotrans_inv_convex gic;
  base_node xref2(N);
  base_small_vector up(N), jump(N);
  
  GMM_ASSERT1(!mf_u().is_reduced(), "To be adapted");

  for (dal::bv_visitor cv(mesh.convex_index()); !cv.finished(); ++cv) {
    
    getfem::mesher_level_set mmls = ls.mls_of_convex(cv, 0);
    bgeot::pgeometric_trans pgt1 = mesh.trans_of_convex(cv);
    getfem::papprox_integration pai1 = 
      get_approx_im_or_fail(mim.int_method_of_element(cv));
    getfem::pfem pf1 = mf_u().fem_of_element(cv);
    scalar_type radius = mesh.convex_radius_estimate(cv);

    bgeot::vectors_to_base_matrix(G1, mesh.points_of_convex(cv));

    coeff1.resize(mf_u().nb_basic_dof_of_element(cv));
    gmm::copy(gmm::sub_vector(U, gmm::sub_index(mf_u().ind_basic_dof_of_element(cv))), coeff1);

    getfem::fem_interpolation_context ctx1(pgt1, pf1, base_node(N), G1, cv);
     
    // Residual on the element

    for (unsigned ii=0; ii < pai1->nb_points_on_convex(); ++ii) {
      
      base_small_vector res = sol_f(pai1->point(ii));
      ctx1.set_xref(pai1->point(ii));
      pf1->interpolation_hess(ctx1, coeff1, hess1, dim_type(qdim));
      for (size_type i = 0; i < N; ++i)
	for (size_type j = 0; j < N; ++j)
	  res[i] += (lambda + mu) * hess1(j, i*N+j) + mu * hess1(i, j*N+j);
      
      // cout << "adding " << radius*radius*ctx1.J()*pai1->coeff(ii)*gmm::vect_norm2(res) << endl;
      ERR[cv] += radius*radius*ctx1.J()*pai1->coeff(ii)*gmm::vect_norm2(res);
    }

//    scalar_type ee = ERR[cv];
    if (ERR[cv] > 100)
      cout << "Erreur en résidu sur element " << cv << " : " << ERR[cv] << endl;

    // Stress on the level set.
   
    getfem::pintegration_method pim = mimbound.int_method_of_element(cv);

    if (pim->type() == getfem::IM_APPROX) {
      getfem::papprox_integration pai_crack = pim->approx_method();
      
      base_small_vector gradls;
      for (unsigned ii=0; ii < pai_crack->nb_points(); ++ii) {
	
	ctx1.set_xref(pai_crack->point(ii));
	mmls.grad(pai_crack->point(ii), gradls);
	gradls /= gmm::vect_norm2(gradls);
	gmm::mult(ctx1.B(), gradls, up);
	scalar_type norm = gmm::vect_norm2(up);
	up /= norm;
	scalar_type coefficient = pai_crack->coeff(ii)*ctx1.J(); 
	
	for (scalar_type e = -1.0; e < 2.0; e += 2.0) {
	  
	  base_node ptref = pai_crack->point(ii) + e * 1.0E-7 * gradls;
	  if (pgt1->convex_ref()->is_in(ptref) > 0.) continue;
	  ctx1.set_xref(ptref);
	  pf1->interpolation_grad(ctx1, coeff1, grad1, dim_type(qdim));
	  // cout << "coeff1 = " << coeff1 << endl;
	  // cout << "grad1 = " << grad1 << endl;
	  gmm::copy(grad1, E); gmm::add(gmm::transposed(grad1), E);
	  gmm::scale(E, 0.5);
	  // cout << "E = " << grad1 << endl;
	  scalar_type trace = gmm::mat_trace(E);
	  gmm::copy(gmm::identity_matrix(), S1);
	  gmm::scale(S1, lambda * trace);
	  gmm::add(gmm::scaled(E, 2*mu), S1);
	  // cout << "S1 = " << S1 << endl;
	  // cout << "up = " << up << endl;
	  gmm::mult(S1, up, jump);
	  // cout << "jump = " << jump << endl;
	
	  ERR[cv] += radius * coefficient * gmm::vect_norm2_sqr(jump);

// 	  if (gmm::vect_norm2(jump) > 100000) {
// 	    cout.precision(14);
// 	    cout << "gmm::vect_norm2_sqr(jump) = "
//	         << gmm::vect_norm2_sqr(jump) << " on cv " << cv
//               << " pt " << ctx1.xreal() << endl; getchar();
// 	    cout << "S1 = " << S1 << "up = " << up << endl;
// 	    cout << "jump = " << jump << endl;
// 	    cout << "point = " << ctx1.xreal() << endl;
//	  }
	}
      }
    }

    // if (ERR[cv]-ee > 100){
    //   cout << "Erreur en contrainte sur la level set sur element " << cv << " : " << ERR[cv]-ee << "  radius = " << radius << endl;
    // }
    //  ee = ERR[cv];
 
    // jump of the stress between the element ant its neighbours.
    for (short_type f1=0; f1 < mesh.structure_of_convex(cv)->nb_faces(); ++f1) {

      if (gmm::abs(mmls(mesh.trans_of_convex(cv)->convex_ref()->points_of_face(f1)[0])) < 1E-7 * radius) continue;

      size_type cvn = mesh.neighbour_of_convex(cv, f1);
      if (cvn == size_type(-1)) continue;
	
      bgeot::pgeometric_trans pgt2 = mesh.trans_of_convex(cvn);
      getfem::pfem pf2 = mf_u().fem_of_element(cvn);
      bgeot::vectors_to_base_matrix(G2, mesh.points_of_convex(cvn));
      coeff2.resize(mf_u().nb_basic_dof_of_element(cvn));
      gmm::copy(gmm::sub_vector(U, gmm::sub_index(mf_u().ind_basic_dof_of_element(cvn))), coeff2);
      getfem::fem_interpolation_context ctx2(pgt2, pf2, base_node(N), G2, cvn);
      gic.init(mesh.points_of_convex(cvn), pgt2);

      for (unsigned ii=0; ii < pai1->nb_points_on_face(f1); ++ii) {

	ctx1.set_xref(pai1->point_on_face(f1, ii));
	gmm::mult(ctx1.B(), pgt1->normals()[f1], up);
	scalar_type norm = gmm::vect_norm2(up);
	up /= norm;
	scalar_type coefficient = pai1->coeff_on_face(f1, ii) * ctx1.J() * norm; 
	
	pf1->interpolation_grad(ctx1, coeff1, grad1, dim_type(qdim));
	gmm::copy(grad1, E); gmm::add(gmm::transposed(grad1), E);
	gmm::scale(E, 0.5);
	scalar_type trace = gmm::mat_trace(E);
	gmm::copy(gmm::identity_matrix(), S1);
	gmm::scale(S1, lambda * trace);
	gmm::add(gmm::scaled(E, 2*mu), S1);

	bool converged;
	gic.invert(ctx1.xreal(), xref2, converged);
	GMM_ASSERT1(converged, "geometric transformation not well inverted ... !");
	
	ctx2.set_xref(xref2);
	pf2->interpolation_grad(ctx2, coeff2, grad2, dim_type(qdim));
	gmm::copy(grad2, E); gmm::add(gmm::transposed(grad2), E);
	gmm::scale(E, 0.5);
	trace = gmm::mat_trace(E);
	gmm::copy(gmm::identity_matrix(), S2);
	gmm::scale(S2, lambda * trace);
	gmm::add(gmm::scaled(E, 2*mu), S2);
	
	gmm::mult(S1, up, jump);
	gmm::mult_add(S2, gmm::scaled(up, -1.0), jump);

	ERR[cv] +=radius * coefficient * gmm::vect_norm2_sqr(jump);

      }
      
    }

    //   if (ERR[cv]-ee > 100)
    //   cout << "Erreur en contrainte inter element sur element " << cv << " : " << ERR[cv]-ee << endl;
      //ERR[cv] = sqrt(ERR[cv]);

  }
  
}


      
     




bool crack_problem::solve(plain_vector &U) {

  size_type N = mesh.dim();
  dal::bit_vector conv_to_refine;
  bool iteration;
  
  do {
    cout << "Number of elements : "<<  mesh.convex_index().card() << endl;
    size_type nb_dof_rhs = mf_rhs.nb_dof();
    ls.reinit();
    for (size_type d = 0; d < ls.get_mesh_fem().nb_dof(); ++d) {
      base_small_vector
	v =  ls_function(ls.get_mesh_fem().point_of_basic_dof(d), option);
      ls.values(0)[d] = v[0];
      ls.values(1)[d] = v[1];
    }
    ls.touch();
    mls.adapt();
    mim.adapt();
    mfls_u.adapt();
    mimbound.adapt();
    exact_sol.init(1,lambda, mu,ls);
   
    cout << "Setting up the singular functions for the enrichment\n";
    std::vector<getfem::pglobal_function> vfunc(4);
    for (unsigned i = 0; i < vfunc.size(); ++i) {
      /* use the singularity */
      getfem::abstract_xy_function *s = 
	new getfem::crack_singular_xy_function(i);
      getfem::abstract_xy_function *c = 
	new getfem::cutoff_xy_function(int(cutoff.fun_num),
				       cutoff.radius, 
				       cutoff.radius1, cutoff.radius0);
      s = new getfem::product_of_xy_functions(*s, *c);
      vfunc[i] = getfem::global_function_on_level_set(ls, *s);
    }
    mf_sing_u.set_functions(vfunc);


    if (PARAM.int_value("ENRICHED", "Enrichment with singular functions")) {
      cout << "enriched version\n";
      mf_u_sum.set_mesh_fems(mf_sing_u, mfls_u);
    }
    else {
      cout << "nonenriched version\n";
      mf_u_sum.set_mesh_fems(mfls_u);
    }
    
    U.resize(mf_u().nb_dof());

    getfem::mdbrick_isotropic_linearized_elasticity<>
      ELAS(mim, mf_u(), lambda, mu);
 
    // Defining the volumic source term.
    plain_vector F(nb_dof_rhs * N);
    getfem::interpolation_function(mf_rhs, F, sol_f);
    getfem::mdbrick_source_term<> VOL_F(ELAS, mf_rhs, F);

    // Defining the Neumann condition right hand side.
    getfem::interpolation_function(mf_rhs, F, sol_F, NEUMANN_BOUNDARY_NUM1);
    getfem::mdbrick_source_term<> NEUMANN(VOL_F, mf_rhs, F, NEUMANN_BOUNDARY_NUM1);
  
    // Dirichlet condition brick.
    getfem::mdbrick_Dirichlet<> DIRICHLET(NEUMANN, DIRICHLET_BOUNDARY_NUM, mf_mult);
    DIRICHLET.set_constraints_type(getfem::constraints_type(dir_with_mult));

    if (option == 0)
      DIRICHLET.rhs().set(exact_sol.mf,exact_sol.U);
     
    getfem::mdbrick_abstract<> *final_model = &DIRICHLET;

    // Generic solve.
    cout << "Total number of variables : " << final_model->nb_dof() << endl;
    getfem::standard_model_state MS(*final_model);
    gmm::iteration iter(residual, 1, 40000);
  
    getfem::standard_solve(MS, *final_model, iter);
  
  
    // Solution extraction
    //gmm::resize(U, mf_u().nb_dof());
    gmm::copy(ELAS.get_solution(MS), U);
    iteration = iter.converged();  

    conv_to_refine.clear();
    // Adapted Refinement (suivant une erreur a posteriori)
    // j=0;
    if (adapted_refine==0) {
      plain_vector ERR(mesh.convex_index().last_true()+1);
      error_estimate(U, ERR);
      cout<<"u="<<gmm::sub_vector(U,gmm::sub_interval(0,8))<<endl;
       cout<<"exact="<<exact_sol.U<<endl;
      cout << "erreur=" <<gmm::vect_norm2(ERR)<< endl;}

    if (adapted_refine && mesh.convex_index().card() < conv_max) {
      plain_vector ERR(mesh.convex_index().last_true()+1);
      error_estimate(U, ERR);
      
  cout << "erreur=" <<gmm::vect_norm2(ERR)<< endl;
  

  // getfem::error_estimate(mim, mf_u(), U, ERR);(

      // cout << "ERR = " << ERR << endl; 
    
      cout << "max = " << gmm::vect_norminf(ERR) << endl;
      scalar_type threshold = PARAM.real_value("REFINE_THRESHOLD",
					       "threshold for the refinement");
      scalar_type min_radius_elt = PARAM.real_value("MIN_RADIUS_ELT",
						  "Min radius for an element");
      scalar_type min_ = 1e18;
      conv_to_refine.clear();
      for (dal::bv_visitor i(mesh.convex_index()); !i.finished(); ++i) {
     	if (ERR[i] > threshold) {
	  if (mesh.convex_radius_estimate(i) > min_radius_elt)
	    conv_to_refine.add(i);
	  else cout << "Tried to refine elt " << i
		    << " which is too small, radius "
		    << mesh.convex_radius_estimate(i) << endl;
	}
	min_ = std::min(min_, ERR[i]);
      }
      cout << "min = " << min_ << endl;
      cout << "Refining " <<  conv_to_refine.card() << " elements..."<< endl;  
      mesh.Bank_refine(conv_to_refine);
    }

  } while(adapted_refine && conv_to_refine.card() > 0);

  mesh.write_to_file(datafilename + ".meshh");
  cout << "Refining process complete. The mesh contains now "
       <<  mesh.convex_index().card() << " convexes "<<endl;
  
  dal::bit_vector blocked_dof = mf_u().basic_dof_on_region(5);
  getfem::mesh_fem mf_printed(mesh, dim_type(N)), mf_printed_vm(mesh);
  std::string FEM_DISC = PARAM.string_value("FEM_DISC","fem disc ");
  mf_printed.set_finite_element(mesh.convex_index(),
				getfem::fem_descriptor(FEM_DISC));
  mf_printed_vm.set_finite_element(mesh.convex_index(),
				   getfem::fem_descriptor(FEM_DISC));
  plain_vector W(mf_printed.nb_dof());

  getfem::interpolation(mf_u(), mf_printed, U, W);


     
  mf_printed.write_to_file(datafilename + ".meshfem", true);
  mf_printed_vm.write_to_file(datafilename + ".meshfem_vm", true);
  gmm::vecsave(datafilename + ".U", W);
 
  plain_vector VM(mf_printed_vm.nb_dof());
  getfem::interpolation_von_mises(mf_printed, mf_printed_vm, W, VM);
  gmm::vecsave(datafilename + ".VM", VM);


  return (iteration);
}

  
/**************************************************************************/
/*  main program.                                                         */
/**************************************************************************/

int main(int argc, char *argv[]) {

  GMM_SET_EXCEPTION_DEBUG; // Exceptions make a memory fault, to debug.
  FE_ENABLE_EXCEPT;        // Enable floating point exception for Nan.

  //getfem::getfem_mesh_level_set_noisy();
try{
  crack_problem p;
  p.PARAM.read_command_line(argc, argv);
  p.init();
  p.mesh.write_to_file(p.datafilename + ".mesh");
  plain_vector U(p.mf_u().nb_dof());
  if (!p.solve(U)) GMM_ASSERT1(false, "Solve has failed");
  
  {
    getfem::mesh mcut;
    p.mls.global_cut_mesh(mcut);
    unsigned Q = p.mf_u().get_qdim();
    getfem::mesh_fem mf(mcut, dim_type(Q));
    mf.set_classical_discontinuous_finite_element(2, 0.001);
    // mf.set_finite_element
    //	(getfem::fem_descriptor("FEM_PK_DISCONTINUOUS(2, 2, 0.0001)"));
    plain_vector V(mf.nb_dof());
    
    getfem::interpolation(p.mf_u(), mf, U, V);

    
    getfem::stored_mesh_slice sl;
    getfem::mesh mcut_refined;

    
    unsigned NX = p.PARAM.int_value("NX"), nn;
    if (NX < 6) nn = 24;
    else if (NX < 12) nn = 8;
    else if (NX < 30) nn = 3;
    else nn = 1;
    
    // choose an adequate slice refinement based on the distance to
    // the crack tip
    std::vector<bgeot::short_type> nrefine(mcut.convex_index().last_true()+1);
    for (dal::bv_visitor cv(mcut.convex_index()); !cv.finished(); ++cv) {
      scalar_type dmin=0, d;
      base_node Pmin,P;
      for (unsigned i=0; i < mcut.nb_points_of_convex(cv); ++i) {
	P = mcut.points_of_convex(cv)[i];
	d = gmm::vect_norm2(ls_function(P, p.option));
	if (d < dmin || i == 0) { dmin = d; Pmin = P; }
      }
      
      if (dmin < 1e-5)
	nrefine[cv] = short_type(nn*8);
      else if (dmin < .1) 
      	nrefine[cv] = short_type(nn*2);
      else nrefine[cv] = short_type(nn);
      // nrefine[cv] = 1;
      // if (dmin < .01)
      //  cout << "cv: "<< cv << ", dmin = " << dmin << "Pmin=" << Pmin 
      //       << " " << nrefine[cv] << "\n";
    }
    
    {
      getfem::mesh_slicer slicer(mcut); 
      getfem::slicer_build_mesh bmesh(mcut_refined);
      slicer.push_back_action(bmesh);
      slicer.exec(nrefine, getfem::mesh_region::all_convexes());
    }
    
    // sl.build(mcut, 
    // getfem::slicer_build_mesh(mcut_refined), nrefine);
    
    getfem::mesh_im mim_refined(mcut_refined); 
    mim_refined.set_integration_method(getfem::int_method_descriptor
				       ("IM_TRIANGLE(6)"));
    
    getfem::mesh_fem mf_refined(mcut_refined,dim_type(Q));
    mf_refined.set_classical_discontinuous_finite_element(2, 0.0001);
    plain_vector W(mf_refined.nb_dof());
    
    getfem::interpolation(p.mf_u(), mf_refined, U, W);

 

    p.exact_sol.mf.set_qdim(dim_type(Q));
    assert(p.exact_sol.mf.nb_dof()==p.exact_sol.U.size());

     plain_vector exac(mf_refined.nb_dof());
     getfem::interpolation(p.exact_sol.mf, mf_refined, p.exact_sol.U,exac);
     plain_vector diff(exac);
     gmm::add(gmm::scaled(W,-1),diff);
    //cout<<"exact="<<p.exact_sol.U<<endl;
   // cout<<"U="<<gmm::sub_vector(U,gmm::sub_interval(0,8))<<endl;

    
    if (p.PARAM.int_value("VTK_EXPORT")) {
      getfem::mesh_fem mf_refined_vm(mcut_refined, 1);
      mf_refined_vm.set_classical_discontinuous_finite_element(1, 0.0001);
      cerr << "mf_refined_vm.nb_dof=" << mf_refined_vm.nb_dof() << "\n";
      plain_vector VM(mf_refined_vm.nb_dof());
      
      cout << "computing von mises\n";
      getfem::interpolation_von_mises(mf_refined, mf_refined_vm, W, VM);
      
      plain_vector D(mf_refined_vm.nb_dof() * Q), 
	DN(mf_refined_vm.nb_dof());


      mf_refined.write_to_file(p.datafilename + ".meshfem2", true);
      mf_refined_vm.write_to_file(p.datafilename + ".meshfem_vm2", false);
      gmm::vecsave(p.datafilename + ".U2", W);
      gmm::vecsave(p.datafilename + ".VM2", VM);
      
      
      
      cout << "export to " << p.datafilename + ".vtk" << "..\n";
      getfem::vtk_export exp(p.datafilename + ".vtk",
			     p.PARAM.int_value("VTK_EXPORT")==1);
      exp.exporting(mf_refined); 
      //exp.write_point_data(mf_refined_vm, DN, "error");
      exp.write_point_data(mf_refined_vm, VM, "von mises stress");
      exp.write_point_data(mf_refined, W, "elastostatic_displacement");
      exp.write_point_data(mf_refined,exac,"reference solution");
      cout << "export done, you can view the data file with (for example)\n"
	"mayavi2 -d " << p.datafilename << ".vtk -f "
	"WarpVector -m Surface -m Outline\n";
    }


 cout<<"L2="<<getfem::asm_L2_dist(p.mim, p.mf_u(),U,p.exact_sol.mf,p.exact_sol.U)<< endl;
cout<<"H1="<<getfem::asm_H1_dist(p.mim, p.mf_u(),U,p.exact_sol.mf,p.exact_sol.U)<< endl;

cout<<"h1="<<getfem::asm_H1_norm(mim_refined,mf_refined,diff)<< endl;
  }
  }
GMM_STANDARD_CATCH_ERROR;

  return 0; 
}



