getfem_mesh_fem.h

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/* -*- c++ -*- (enables emacs c++ mode) */
/*===========================================================================
 
 Copyright (C) 1999-2020 Yves Renard
 
 This file is a part of GetFEM
 
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/**@file getfem_mesh_fem.h
   @author  Yves Renard <Yves.Renard@insa-lyon.fr>
   @date December 21, 1999.
   @brief Define the getfem::mesh_fem class
*/
 
#ifndef GETFEM_MESH_FEM_H__
#define GETFEM_MESH_FEM_H__
 
#include "getfem_mesh.h"
#include "getfem_fem.h"
 
 
namespace getfem {
 
  template <class CONT> struct tab_scal_to_vect_iterator {
 
    typedef typename CONT::const_iterator ITER;
    typedef typename std::iterator_traits<ITER>::value_type value_type;
    typedef typename std::iterator_traits<ITER>::pointer    pointer;
    typedef typename std::iterator_traits<ITER>::reference  reference;
    typedef typename std::iterator_traits<ITER>::difference_type
                                                            difference_type;
    typedef typename std::iterator_traits<ITER>::iterator_category
                                                            iterator_category;
    typedef size_t size_type;
    typedef tab_scal_to_vect_iterator<CONT> iterator;
 
    ITER it;
    dim_type N;
    dim_type ii;
 
    iterator &operator ++()
    { ++ii; if (ii == N) { ii = 0; ++it; } return *this; }
    iterator &operator --()
    { if (ii == 0) { ii = N; --it; } --ii; return *this; }
    iterator operator ++(int) { iterator tmp = *this; ++(*this); return tmp; }
    iterator operator --(int) { iterator tmp = *this; --(*this); return tmp; }
 
    iterator &operator +=(difference_type i)
    { it += (i+ii)/N; ii = dim_type((ii + i) % N); return *this; }
    iterator &operator -=(difference_type i)
    { it -= (i+N-ii-1)/N; ii = (ii - i + N * i) % N; return *this; }
    iterator operator +(difference_type i) const
    { iterator itt = *this; return (itt += i); }
    iterator operator -(difference_type i) const
    { iterator itt = *this; return (itt -= i); }
    difference_type operator -(const iterator &i) const
    { return (it - i.it) * N + ii - i.ii; }
 
    value_type operator *() const { return (*it) + ii; }
    value_type operator [](int i) { return *(this + i); }
 
    bool operator ==(const iterator &i) const
    { return (it == i.it) && (ii == i.ii); }
    bool operator !=(const iterator &i) const { return !(i == *this); }
    bool operator < (const iterator &i) const
    { return (it < i.it) || ((it == i.it) && (ii < i.ii)); }
    bool operator > (const iterator &i) const
    { return (it > i.it) || ((it == i.it) && (ii > i.ii)); }
    bool operator >= (const iterator &i) const
    { return (it > i.it) || ((it == i.it) && (ii >= i.ii)); }
 
    tab_scal_to_vect_iterator() {}
    tab_scal_to_vect_iterator(const ITER &iter, dim_type n, dim_type i)
      : it(iter), N(n), ii(i) { }
 
  };
 
  /** @internal @brief structure for iteration over the dofs when Qdim
      != 1 and target_dim == 1
  */
  template <class CONT> class tab_scal_to_vect {
  public :
    typedef typename CONT::const_iterator ITER;
    typedef typename std::iterator_traits<ITER>::value_type value_type;
    typedef typename std::iterator_traits<ITER>::pointer    pointer;
    typedef typename std::iterator_traits<ITER>::pointer    const_pointer;
    typedef typename std::iterator_traits<ITER>::reference  reference;
    typedef typename std::iterator_traits<ITER>::reference  const_reference;
    typedef typename std::iterator_traits<ITER>::difference_type
            difference_type;
    typedef size_t size_type;
    typedef tab_scal_to_vect_iterator<CONT> iterator;
    typedef iterator                          const_iterator;
    typedef std::reverse_iterator<const_iterator> const_reverse_iterator;
    typedef std::reverse_iterator<iterator> reverse_iterator;
 
 
  protected :
    ITER it, ite;
    dim_type N;
 
  public :
 
    bool empty() const { return it == ite; }
    size_type size() const { return (ite - it) * N; }
 
    const_iterator begin() const { return iterator(it, N, 0); }
    const_iterator end() const { return iterator(ite, N, 0); }
    const_reverse_iterator rbegin() const
    { return const_reverse_iterator(end()); }
    const_reverse_iterator rend() const
    { return const_reverse_iterator(begin()); }
 
    value_type front() const { return *begin(); }
    value_type back() const { return *(--(end())); }
 
    tab_scal_to_vect() : N(0) {}
    tab_scal_to_vect(const CONT &cc, dim_type n)
      : it(cc.begin()), ite(cc.end()), N(n) {}
 
    value_type operator [](size_type ii) const { return *(begin() + ii);}
  };
 
  /** Describe a finite element method linked to a mesh.
   *
   *  @see mesh
   *  @see mesh_im
   */
  class mesh_fem : public context_dependencies, virtual public dal::static_stored_object {
  protected :
    typedef gmm::csc_matrix<scalar_type> REDUCTION_MATRIX;
    typedef gmm::csr_matrix<scalar_type> EXTENSION_MATRIX;
 
    void copy_from(const mesh_fem &mf); /* Remember to change copy_from if
                                           adding components to mesh_fem */
 
    std::vector<pfem> f_elems;
    dal::bit_vector fe_convex;
    const mesh *linked_mesh_;
    REDUCTION_MATRIX R_;
    EXTENSION_MATRIX E_;
    mutable bgeot::mesh_structure dof_structure;
    mutable bool dof_enumeration_made;
    mutable bool is_uniform_, is_uniformly_vectorized_;
    mutable size_type nb_total_dof;
    pfem auto_add_elt_pf; /* fem for automatic addition                   */
                       /* of element option. (0 = no automatic addition)  */
    dim_type auto_add_elt_K; /* Degree of the fem for automatic addition  */
                       /* of element option. (-1 = no automatic addition) */
    bool auto_add_elt_disc, auto_add_elt_complete;
    scalar_type auto_add_elt_alpha;
    dim_type Qdim;         /* this is the "total" target_dim. */
    bgeot::multi_index mi; /* multi dimensions for matrix/tensor field. */
    // dim_type QdimM, QdimN; /* for matrix field with QdimM lines and QdimN */
    //                       /* columnsQdimM * QdimN = Qdim.                */
    std::vector<size_type> dof_partition;
    mutable gmm::uint64_type v_num_update, v_num;
    bool use_reduction;    /* A reduction matrix is applied or not.       */
 
  public :
    typedef base_node point_type;
    typedef tab_scal_to_vect<mesh::ind_cv_ct> ind_dof_ct;
    typedef tab_scal_to_vect<mesh::ind_pt_face_ct> ind_dof_face_ct;
 
    void update_from_context() const;
 
    gmm::uint64_type version_number() const
    { context_check(); return v_num; }
 
    /** Get the set of convexes where a finite element has been assigned.
     */
    inline const dal::bit_vector &convex_index() const
    { context_check(); return fe_convex; }
 
    /// Return true if a reduction matrix is applied to the dofs.
    bool is_reduced() const { return use_reduction; }
 
    /// Return the reduction matrix applied to the dofs.
    const REDUCTION_MATRIX &reduction_matrix() const { return R_; }
 
    /// Return the extension matrix corresponding to reduction applied (RE=I).
    const EXTENSION_MATRIX &extension_matrix() const { return E_; }
 
    /** Allows to set the reduction and the extension matrices.
     * Should satify (RR*EE=I). */
    template <typename MATR, typename MATE>
    void set_reduction_matrices(const MATR &RR, const MATE &EE) {
      context_check();
      GMM_ASSERT1(gmm::mat_ncols(RR) == nb_basic_dof() &&
                  gmm::mat_nrows(EE) == nb_basic_dof() &&
                  gmm::mat_nrows(RR) == gmm::mat_ncols(EE),
                  "Wrong dimension of reduction and/or extension matrices");
      R_ = REDUCTION_MATRIX(gmm::mat_nrows(RR), gmm::mat_ncols(RR));
      E_ = EXTENSION_MATRIX(gmm::mat_nrows(EE), gmm::mat_ncols(EE));
      gmm::copy(RR, R_);
      gmm::copy(EE, E_);
      use_reduction = true;
      touch(); v_num = act_counter();
    }
 
    /** Allows to set the reduction and the extension matrices in order
     *  to keep only a certain number of dof. */
    void reduce_to_basic_dof(const dal::bit_vector &kept_basic_dof);
    void reduce_to_basic_dof(const std::set<size_type> &kept_basic_dof);
 
    /// Validate or invalidate the reduction (keeping the reduction matrices).
    void set_reduction(bool r) {
      if (r != use_reduction) {
        use_reduction = r;
        if (use_reduction) {
          context_check();
          GMM_ASSERT1(gmm::mat_ncols(R_) == nb_basic_dof() &&
                      gmm::mat_nrows(E_) == nb_basic_dof() &&
                      gmm::mat_nrows(R_) == gmm::mat_ncols(E_),
                    "Wrong dimension of reduction and/or extension matrices");
        }
        touch(); v_num = act_counter();
      }
    }
 
    template<typename VECT1, typename VECT2>
    void reduce_vector(const VECT1 &V1, const VECT2 &V2) const {
      if (is_reduced()) {
        size_type qqdim = gmm::vect_size(V1) / nb_basic_dof();
        if (qqdim == 1)
          gmm::mult(reduction_matrix(), V1, const_cast<VECT2 &>(V2));
        else
          for (size_type k = 0; k < qqdim; ++k)
            gmm::mult(reduction_matrix(),
                      gmm::sub_vector(V1, gmm::sub_slice(k, nb_basic_dof(),
                                                         qqdim)),
                      gmm::sub_vector(const_cast<VECT2 &>(V2),
                                      gmm::sub_slice(k, nb_dof(),
                                                     qqdim)));
      }
      else gmm::copy(V1, const_cast<VECT2 &>(V2));
    }
 
    template<typename VECT1, typename VECT2>
    void extend_vector(const VECT1 &V1, const VECT2 &V2) const {
      size_type nbd = nb_dof();
      if (is_reduced() && nbd) {
        size_type qqdim = gmm::vect_size(V1) / nbd;
        if (qqdim == 1)
          gmm::mult(extension_matrix(), V1, const_cast<VECT2 &>(V2));
        else
          for (size_type k = 0; k < qqdim; ++k)
            gmm::mult(extension_matrix(),
                      gmm::sub_vector(V1, gmm::sub_slice(k, nb_dof(),
                                                         qqdim)),
                      gmm::sub_vector(const_cast<VECT2 &>(V2),
                                      gmm::sub_slice(k, nb_basic_dof(),
                                                     qqdim)));
      }
      else gmm::copy(V1, const_cast<VECT2 &>(V2));
    }
 
 
    /// Return a reference to the underlying mesh.
    const mesh &linked_mesh() const { return *linked_mesh_; }
 
    virtual bool is_uniform() const;
    virtual bool is_uniformly_vectorized() const;
 
    /** Set the degree of the fem for automatic addition
     *  of element option. K=-1 disables the automatic addition.
     */
    void set_auto_add(dim_type K, bool disc = false,
                      scalar_type alpha = scalar_type(0),
                      bool complete=false) {
      auto_add_elt_K = K;
      auto_add_elt_disc = disc;
      auto_add_elt_alpha = alpha;
      auto_add_elt_complete = complete;
      auto_add_elt_pf = 0;
    }
 
    /** Set the fem for automatic addition
     *  of element option. pf=0 disables the automatic addition.
     */
    void set_auto_add(pfem pf) {
      auto_add_elt_pf = pf;
      auto_add_elt_K = dim_type(-1);
      auto_add_elt_disc = false;
      auto_add_elt_alpha = scalar_type(0);
      auto_add_elt_complete = false;
    }
 
    /** Return the Q dimension. A mesh_fem used for scalar fields has
        Q=1, for vector fields, Q is typically equal to
        linked_mesh().dim().
     */
    virtual dim_type get_qdim() const { return Qdim; }
    virtual const bgeot::multi_index &get_qdims() const { return mi; }
 
    /** Change the Q dimension */
    virtual void set_qdim(dim_type q) {
      if (q != Qdim || mi.size() != 1) {
        mi.resize(1); mi[0] = q; Qdim = q;
        dof_enumeration_made = false; touch(); v_num = act_counter();
      }
    }
 
    /** Set the dimension for a matrix field. */
    virtual void set_qdim(dim_type M, dim_type N) {
      if (mi.size() != 2 || mi[0] != M || mi[1] != N) {
        mi.resize(2); mi[0] = M; mi[1] = N; Qdim = dim_type(M*N);
        dof_enumeration_made = false; touch(); v_num = act_counter();
      }
    }
 
    /** Set the dimension for a fourth order tensor field. */
    virtual void set_qdim(dim_type M, dim_type N, dim_type O, dim_type P) {
      if (mi.size() != 4 || mi[0] != M || mi[1] != N || mi[2] != O
          || mi[3] != P) {
        mi.resize(4); mi[0] = M; mi[1] = N; mi[2] = O; mi[3] = P;
        Qdim = dim_type(M*N*O*P);
        dof_enumeration_made = false; touch(); v_num = act_counter();
      }
    }
 
    /** Set the dimension for an arbitrary order tensor field. */
    virtual void set_qdim(const bgeot::multi_index &mii) {
      GMM_ASSERT1(mii.size() < 7,
                  "Tensor field are taken into account up to order 6.");
      GMM_ASSERT1(mi.size(), "Wrong sizes");
      if (!(mi.is_equal(mii))) {
        mi = mii;
        Qdim = dim_type(1);
        for (size_type i = 0; i < mi.size(); ++i)
          Qdim = dim_type(Qdim*mi[i]);
        GMM_ASSERT1(Qdim, "Wrong sizes");
        dof_enumeration_made = false; touch(); v_num = act_counter();
      }
    }
 
 
    void set_qdim_mn(dim_type M, dim_type N) IS_DEPRECATED
    { set_qdim(M,N); }
 
    /** for matrix fields, return the number of rows. */
    dim_type get_qdim_m() const IS_DEPRECATED { return dim_type(mi[0]); }
    /** for matrix fields, return the number of columns. */
    dim_type get_qdim_n() const IS_DEPRECATED { return dim_type(mi[1]); }
 
 
    /** Set the finite element method of a convex.
        @param cv the convex number.
        @param pf the finite element.
    */
    void set_finite_element(size_type cv, pfem pf);
    /** Set the finite element on a set of convexes.
        @param cvs the set of convex indexes, as a dal::bit_vector.
        @param pf the finite element, typically obtained with
        @code getfem::fem_descriptor("FEM_SOMETHING(..)")
        @endcode
    */
    void set_finite_element(const dal::bit_vector &cvs, pfem pf);
    /** shortcut for set_finite_element(linked_mesh().convex_index(),pf);
        and set_auto_add(pf). */
    void set_finite_element(pfem pf);
    /** Set a classical (i.e. lagrange polynomial) finite element on
        a convex.
        @param cv is the convex number.
        @param fem_degree the polynomial degree of the finite element.
        @param complete is a flag for excluding incomplete element
               irrespective of the element geometric transformation.
    */
    void set_classical_finite_element(size_type cv, dim_type fem_degree,
                                      bool complete=false);
    /** Set a classical (i.e. lagrange polynomial) finite element on
        a set of convexes.
        @param cvs the set of convexes, as a dal::bit_vector.
        @param fem_degree the polynomial degree of the finite element.
    */
    void set_classical_finite_element(const dal::bit_vector &cvs,
                                      dim_type fem_degree,
                                      bool complete=false);
    /** Similar to set_classical_finite_element, but uses
        discontinuous lagrange elements.
 
        @param cv the convex index.
        @param fem_degree the polynomial degree of the finite element.
        @param alpha the node inset, 0 <= alpha < 1, where 0 implies
        usual dof nodes, greater values move the nodes toward the
        center of gravity, and 1 means that all degrees of freedom
        collapse on the center of gravity.
     */
    void set_classical_discontinuous_finite_element(size_type cv,
                                                    dim_type fem_degree,
                                                    scalar_type alpha=0,
                                                    bool complete=false);
    /** Similar to set_classical_finite_element, but uses
        discontinuous lagrange elements.
 
        @param cvs the set of convexes, as a dal::bit_vector.
        @param fem_degree the polynomial degree of the finite element.
        @param alpha the node inset, 0 <= alpha < 1, where 0 implies
        usual dof nodes, greater values move the nodes toward the
        center of gravity, and 1 means that all degrees of freedom
        collapse on the center of gravity.
     */
    void set_classical_discontinuous_finite_element(const dal::bit_vector &cvs,
                                                    dim_type fem_degree,
                                                    scalar_type alpha=0,
                                                    bool complete=false);
    /** Shortcut for
     * set_classical_finite_element(linked_mesh().convex_index(),...)
     */
    void set_classical_finite_element(dim_type fem_degree,
                                      bool complete=false);
    /** Shortcut for
     *  set_classical_discontinuous_finite_element(linked_mesh().convex_index()
     *  ,...)
     */
    void set_classical_discontinuous_finite_element(dim_type fem_degree,
                                                    scalar_type alpha=0,
                                                    bool complete=false);
    /** Return the basic fem associated with an element (if no fem is
     *        associated, the function will crash! use the convex_index() of
     *  the mesh_fem to check that a fem is associated to a given
     *  convex). This fem does not take into account the optional
     *  vectorization due to qdim nor the optional reduction.
     */
    virtual pfem fem_of_element(size_type cv) const
    { return ((cv < f_elems.size()) ? f_elems[cv] : 0); }
    /** Give an array of the dof numbers a of convex.
     *  @param cv the convex number.
     *  @return a pseudo-container of the dof number.
     */
    virtual ind_dof_ct ind_basic_dof_of_element(size_type cv) const {
      context_check(); if (!dof_enumeration_made) enumerate_dof();
      return ind_dof_ct(dof_structure.ind_points_of_convex(cv),
                        dim_type(Qdim/fem_of_element(cv)->target_dim()));
    }
    ind_dof_ct ind_dof_of_element(size_type cv) const IS_DEPRECATED
    { return ind_basic_dof_of_element(cv); }
    virtual const std::vector<size_type> &
    ind_scalar_basic_dof_of_element(size_type cv) const
    { return dof_structure.ind_points_of_convex(cv); }
    /** Give an array of the dof numbers lying of a convex face (all
              degrees of freedom whose associated base function is non-zero
        on the convex face).
        @param cv the convex number.
        @param f the face number.
        @return a pseudo-container of the dof number.
    */
    virtual ind_dof_face_ct
    ind_basic_dof_of_face_of_element(size_type cv, short_type f) const {
      context_check(); if (!dof_enumeration_made) enumerate_dof();
      return ind_dof_face_ct
        (dof_structure.ind_points_of_face_of_convex(cv, f),
         dim_type(Qdim/fem_of_element(cv)->target_dim()));
    }
    ind_dof_face_ct
    ind_dof_of_face_of_element(size_type cv,short_type f) const IS_DEPRECATED
    { return ind_basic_dof_of_face_of_element(cv, f); }
    /** Return the number of dof lying on the given convex face.
        @param cv the convex number.
        @param f the face number.
    */
    virtual size_type nb_basic_dof_of_face_of_element(size_type cv,
                                                      short_type f) const {
      context_check(); if (!dof_enumeration_made) enumerate_dof();
      pfem pf = f_elems[cv];
      return dof_structure.structure_of_convex(cv)->nb_points_of_face(f)
        * Qdim / pf->target_dim();
    }
    size_type nb_dof_of_face_of_element(size_type cv,
                                        short_type f) const IS_DEPRECATED
    { return nb_basic_dof_of_face_of_element(cv, f); }
    /** Return the number of  degrees of freedom attached to a given convex.
        @param cv the convex number.
    */
    virtual size_type nb_basic_dof_of_element(size_type cv) const {
      context_check(); if (!dof_enumeration_made) enumerate_dof();
      pfem pf = f_elems[cv]; return pf->nb_dof(cv) * Qdim / pf->target_dim();
    }
    size_type nb_dof_of_element(size_type cv) const IS_DEPRECATED
    { return nb_basic_dof_of_element(cv); }
 
    /* Return the geometrical location of a degree of freedom in the
       reference convex.
        @param cv the convex number.
        @param i the local dof number.
    const base_node &reference_point_of_dof(size_type cv,size_type i) const {
      pfem pf = f_elems[cv];
      return pf->node_of_dof(cv, i * pf->target_dim() / Qdim);
    }
    */
    /** Return the geometrical location of a degree of freedom.
        @param cv the convex number.
        @param i the local dof number.
     */
    virtual base_node point_of_basic_dof(size_type cv, size_type i) const;
    base_node point_of_dof(size_type cv, size_type i) const IS_DEPRECATED
    { return point_of_basic_dof(cv, i); }
    /** Return the geometrical location of a degree of freedom.
        @param d the global dof number.
    */
    virtual base_node point_of_basic_dof(size_type d) const;
    base_node point_of_dof(size_type d) const IS_DEPRECATED
    { return point_of_basic_dof(d); }
    /** Return the dof component number (0<= x <Qdim) */
    virtual dim_type basic_dof_qdim(size_type d) const;
    dim_type dof_qdim(size_type d) const IS_DEPRECATED
    { return basic_dof_qdim(d); }
    /** Shortcut for convex_to_dof(d)[0]
         @param d the global dof number.
    */
    virtual size_type first_convex_of_basic_dof(size_type d) const;
    size_type first_convex_of_dof(size_type d) const IS_DEPRECATED
    { return first_convex_of_basic_dof(d); }
    /** Return the list of convexes attached to the specified dof
        @param d the global dof number.
        @return an array of convex numbers.
     */
    virtual const mesh::ind_cv_ct &convex_to_basic_dof(size_type d) const;
    const mesh::ind_cv_ct &convex_to_dof(size_type d) const IS_DEPRECATED
    { return convex_to_basic_dof(d); }
 
    /** Give an array that contains the global dof indices corresponding
     * to the mesh_fem dofs or size_type(-1) if a dof is not global.
     *  @param ind the returned global dof indices array.
     */
    virtual void get_global_dof_index(std::vector<size_type> &ind) const;
    /** Renumber the degrees of freedom. You should not have
     * to call this function, as it is done automatically */
    virtual void enumerate_dof() const;
 
#if GETFEM_PARA_LEVEL > 1
    void enumerate_dof_para()const;
#endif
 
    /** Return the total number of basic degrees of freedom (before the
     * optional reduction). */
    virtual size_type nb_basic_dof() const {
      context_check();
      if (!dof_enumeration_made) enumerate_dof();
      return nb_total_dof;
    }
    /// Return the total number of degrees of freedom.
    virtual size_type nb_dof() const {
      context_check();
      if (!dof_enumeration_made) enumerate_dof();
      return use_reduction ? gmm::mat_nrows(R_) : nb_total_dof;
    }
    /** Get a list of basic dof lying on a given mesh_region.
        @param b the mesh_region.
        @return the list in a dal::bit_vector.
    */
    virtual dal::bit_vector basic_dof_on_region(const mesh_region &b) const;
    /** Get a list of dof lying on a given mesh_region. For a reduced mesh_fem
        a dof is lying on a region if its potential corresponding shape
        function is nonzero on this region. The extension matrix is used
        to make the correspondence between basic and reduced dofs.
        @param b the mesh_region.
        @return the list in a dal::bit_vector.
    */
    dal::bit_vector dof_on_region(const mesh_region &b) const;
    dal::bit_vector dof_on_set(const mesh_region &b) const IS_DEPRECATED
    { return dof_on_region(b); }
 
    void set_dof_partition(size_type cv, unsigned partition_num) {
      if (dof_partition.empty() && partition_num == 0) return;
      if (dof_partition.size() < linked_mesh().nb_allocated_convex())
        dof_partition.resize(linked_mesh().nb_allocated_convex());
      if (dof_partition.at(cv) != partition_num) {
        dof_partition[cv] = partition_num;
        dof_enumeration_made = false;
      }
    }
    unsigned get_dof_partition(size_type cv) const {
      return (cv < dof_partition.size() ? unsigned(dof_partition[cv]) : 0);
    }
    void clear_dof_partition() { dof_partition.clear(); }
 
    size_type memsize() const {
      return dof_structure.memsize() +
        sizeof(mesh_fem) - sizeof(bgeot::mesh_structure) +
        f_elems.size() * sizeof(pfem) + fe_convex.memsize();
    }
    void init_with_mesh(const mesh &me, dim_type Q = 1);
    /** Build a new mesh_fem. A mesh object must be supplied.
        @param me the linked mesh.
        @param Q the Q dimension (see mesh_fem::get_qdim).
    */
    explicit mesh_fem(const mesh &me, dim_type Q = 1);
    mesh_fem();
    mesh_fem(const mesh_fem &mf);
    mesh_fem &operator=(const mesh_fem &mf);
 
    virtual ~mesh_fem();
    virtual void clear();
    /** Read the mesh_fem from a stream.
        @param ist the stream.
     */
    virtual void read_from_file(std::istream &ist);
    /** Read the mesh_fem from a file.
        @param name the file name. */
    void read_from_file(const std::string &name);
    /* internal usage. */
    void write_basic_to_file(std::ostream &ost) const;
    /* internal usage. */
    void write_reduction_matrices_to_file(std::ostream &ost) const;
    /** Write the mesh_fem to a stream. */
    virtual void write_to_file(std::ostream &ost) const;
    /** Write the mesh_fem to a file.
 
        @param name the file name
 
        @param with_mesh if set, then the linked_mesh() will also be
        saved to the file.
    */
    void write_to_file(const std::string &name, bool with_mesh=false) const;
  };
 
  /** Gives the descriptor of a classical finite element method of degree K
      on mesh.
 
      The mesh_fem won't be destroyed until its linked_mesh is
      destroyed. All the mesh_fem built by this function are stored
      in a cache, which means that calling this function twice with
      the same arguments will return the same mesh_fem object. A
      consequence is that you should NEVER modify this mesh_fem!
   */
  const mesh_fem &classical_mesh_fem(const mesh &mesh, dim_type degree,
                                     dim_type qdim=1, bool complete=false);
 
  /** Dummy mesh_fem for default parameter of functions. */
  const mesh_fem &dummy_mesh_fem();
 
 
  /** Given a mesh_fem @param mf and a vector @param vec of size equal to
   *  mf.nb_basic_dof(), the output vector @param coeff will contain the
   *  values of @param vec corresponding to the basic dofs of element
   *  @param cv. The size of @param coeff is adjusted if necessary.
   */
  template <typename VEC1, typename VEC2>
  void slice_vector_on_basic_dof_of_element(const mesh_fem &mf,
                                            const VEC1 &vec,
                                            size_type cv, VEC2 &coeff,
                                            size_type qmult1 = size_type(-1),
                                            size_type qmult2 = size_type(-1)) {
    if (qmult1 == size_type(-1)) {
      size_type nbdof = mf.nb_basic_dof();
      qmult1 = gmm::vect_size(vec) / nbdof;
      GMM_ASSERT1(gmm::vect_size(vec) == qmult1 * nbdof, "Bad dof vector size");
    }
    if (qmult2 == size_type(-1)) {
      qmult2 = mf.get_qdim();
      if (qmult2 > 1) qmult2 /= mf.fem_of_element(cv)->target_dim();
    }
    size_type qmultot = qmult1*qmult2;
    auto &ct = mf.ind_scalar_basic_dof_of_element(cv);
    gmm::resize(coeff, ct.size()*qmultot);
 
    auto it = ct.begin();
    auto itc = coeff.begin();
    if (qmultot == 1) {
      for (; it != ct.end(); ++it) *itc++ = vec[*it];
    } else {
      for (; it != ct.end(); ++it) {
        auto itv = vec.begin()+(*it)*qmult1;
        for (size_type m = 0; m < qmultot; ++m) *itc++ = *itv++;
      }
    }
  }
 
  void vectorize_base_tensor(const base_tensor &t, base_matrix &vt,
                             size_type ndof, size_type qdim, size_type N);
 
  void vectorize_grad_base_tensor(const base_tensor &t, base_tensor &vt,
                                  size_type ndof, size_type qdim, size_type N);
 
 
}  /* end of namespace getfem.                                             */
 
 
#endif /* GETFEM_MESH_FEM_H__  */