librheolef-dev 6.5-1+b1 / usr / include / rheolef / field.h

# ifndef _RHEOLEF_FIELD_H
# define _RHEOLEF_FIELD_H
///
/// This file is part of Rheolef.
///
/// Copyright (C) 2000-2009 Pierre Saramito <Pierre.Saramito@imag.fr>
///
/// Rheolef is free software; you can redistribute it and/or modify
/// it under the terms of the GNU General Public License as published by
/// the Free Software Foundation; either version 2 of the License, or
/// (at your option) any later version.
///
/// Rheolef 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 General Public License for more details.
///
/// You should have received a copy of the GNU General Public License
/// along with Rheolef; if not, write to the Free Software
/// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
/// 
/// =========================================================================

#include "rheolef/skit.h"
#include "rheolef/space.h"
#include "rheolef/undeterminated.h"
#include "rheolef/misc_algo.h" // copy_n
#include "rheolef/quadrature.h"

namespace rheolef {

// forward declaration:
template <class Expr> struct field_expr;
template <class T, class M> class field_indirect;
template <class T, class M> class field_indirect_const;
template <class T, class M> class field_component;
template <class T, class M> class field_component_const;
template <class T, class M> class field_concat_value;
template <class T, class M> class band_basic;

//<field:  
/*Class:field
NAME:  @code{field} - piecewise polynomial finite element field
DESCRIPTION:       
  @noindent
  Store degrees of freedom associated to a mesh and
  a piecewise polynomial approximation, with respect
  to the numbering defined by the underlying @ref{space class}.

  @noindent
  This class contains two vectors, namely unknown and blocked
  degrees of freedoms, and the associated finite element space.
  Blocked and unknown degrees of freedom can be set by using
  domain name indexation:
  @example
        geo omega ("circle");
        space Xh (omega, "P1");
        Xh.block ("boundary");
        field uh (Xh);
        uh ["boundary"] = 0;
  @end example

@findex interpolate
INTERPOLATION:
  Interpolation of a function @code{u} in a field @code{uh} with respect to 
  the interpolation writes:
  @example
        Float u (const point& x) @{ return x[0]*x[1]; @}
        ...
        field uh = interpolate (Xh, u);
  @end example

@findex dual
LINEAR ALGEBRA:
  Linear algebra, such as @code{uh+vh}, @code{uh-vh} and @code{lambda*uh + mu*vh}, 
  where @code{lambda} and @code{mu} are of type @code{Float}, are supported.
  The duality product between two fields @code{lh} and @code{vh}
  writes simply @code{dual(lh,vh)}: for discrete fields, it corresponds to a simple Euclidian dot
  product in @code{IR^n}.
  The application of a bilinear form (@pxref{form class})
  writes @code{m(uh,vh)} and is equivalent to @code{dual(m*uh,vh)}. 

NON-LINEAR ALGEBRA:
  Non-linear operations, such as @code{sqrt(uh)} or @code{1/uh} are also available.
  Notice that non-linear operations do not returns in general picewise polynomials:
  the value returned by @code{sqrt(uh)} may be filtered by @code{interpolate},
  @example
        field vh = interpolate (Xh, sqrt(uh));
  @end example
  the Lagrange interpolant, to becomes a piecewise polynomial:
  All standard unary and binary math functions @code{abs, cos, sin}... are available
  on fields. Also @code{sqr(uh)}, the square of a field, and @code{min(uh,vh)}, @code{max(uh,vh)}
  are provided. Binary functions can be used also with a scalar, as in
  @example
        field vh = interpolate (Xh, max (abs(uh), 0));
        field wh = interpolate (Xh, pow (abs(uh), 1./3));
  @end example
  For applying a user-provided function to a field, use
  the @code{compose} function:
@example
        field vh = interpolate(Xh, compose(f, uh));
        field wh = interpolate(Xh, compose(f, uh, vh));
@end example
  The composition supports also general unary and binary class-functions.
  Also, the multiplication @code{uh*vh} and the division @code{uh/vh}
  returns a result that is not in the same discrete finite element space:
  its result may be filtered by the @code{interpolate} operator:
@example
        field wh = interpolate(Xh, uh*vh);
@end example
  Any function or class function can be used in nonlinear expressions:
  the function is interpolated in the specified finite element space.

@findex normal
  There is a special predefined class-function named @code{normal} that represents the 
  outer unnit normal vector on a boundary domain or surfacic mesh:
@example
        size_t k = omega.order();
        string n_approx = "P" + itos(k-1) + "d";
        space Nh (omega["boundary"], n_approx, "vector");
        field nh = interpolate(Nh, normal());
@end example
  The normal() function could appear in any nonlinear field expression:
  it is evaluated on the fly, based on the current mesh.
  Notice that when using isoparametric elements, the normal vector is no more
  constant along any face of the mesh.
  Also, on general curved domains, the unit normal vector is discontinuous
  accross boundary element interfaces.

ACCESS BY DOMAIN:
  The restriction of a field to a geometric domain, says @code{"boundary"}
  writes @code{uh["boundary"]}: it represents the trace of the field on
  the boundary:
  @example
        space Xh (omega, "P1");
        uh["boundary"] = 0;
  @end example
  Extraction of the trace as a field is also possible:
  @example
        field wh = uh["boundary"];
  @end example
  The space associated to the trace writes @code{wh.get_space()} and
  is equivalent to @code{space(omega["boundary"], "P1")}.
  See @pxref{space class}.

VECTOR VALUED FIELD:
  A vector-valued field contains several components, as:
  @example
        space Xh (omega, "P2", "vector");
        field uh (Xh);
        field vh = uh[0] - uh[1];
        field nh = norm (uh);
  @end example
  The @code{norm} function returns the euclidian norm of the vector-valuated 
  field at each degree of freedom: its result is a scalar field.

TENSOR VALUED FIELD:
  A tensor-valued field can be constructed and used as:
  @example
        space Th (omega, "P1d", "tensor");
        field sigma_h (Xh);
        field trace_h = sigma(0,0) + sigma_h(1,1);
        field nh = norm (sigma_h);
  @end example
  The @code{norm} function returns the euclidian norm of the tensor-valuated 
  field at each degree of freedom: its result is a scalar field. 
  Notice that, as tensor-valued fields are symmetric, extra-diagonals are counted twice.

GENERAL MULTI-COMPONENT INTERFACE:
  A general multi-component field writes:
  @example
        space Th (omega, "P1d", "tensor");
        space Vh (omega, "P2", "vector");
        space Qh (omega, "P1");
        space Xh = Th*Vh*Qh;
        field xh (Xh);
        field tau_h = xh[0]; // tensor-valued
        field uh    = xh[1]; // vector-valued
        field qh    = xh[2]; // scalar
  @end example
  Remark the hierarchical multi-component field structure:
  the first-component is tensor-valued and the second-one is vector-valued.
  There is no limitation upon the hierarchical number of levels in use.

  For any field @code{xh}, the string @code{xh.valued()} returns @code{"scalar"}
  for a scalar field and @code{"vector"} for a vector-valued one. Other possible
  valued are @code{"tensor"} and @code{"other"}.
  The @code{xh.size()} returns the number of field components.
  When the field is scalar, it returns zero by convention, and @code{xh[0]} is undefined.
  A vector-valued field has @code{d} components, where @code{d=omega.dimension()}.
  A tensor-valued field has @code{d*(d+1)/2} components, where @code{d=omega.dimension()}.

BLOCKED AND UNBLOCKED ARRAYS:
  The field class contains two arrays of degrees-of-freedom (dof) associated
  respectively to blocked and unknown dofs. Blocked dofs corresponds to
  Dirichlet boundary conditions, as specified by space (See @pxref{space class}).
  For simpliity, direct public access to these array is allowed, as @code{uh.b} and @code{uh.u}:
  see @pxref{vec class}.

LOW-LEVEL DEGREE-OF-FREEDOM ACCESS:
  The field class provides a STL-like container interface for accessing the degrees-of-freedom
  (dof) of a finite element field @code{uh}. The number of dofs is @code{uh.ndof()}
  and any dof can be accessed via @code{uh.dof(idof)}.
  A non-local dof at the partition interface can be obtain via @code{uh.dis_dof(dis_idof)}
  where @code{dis_idof} is the (global) distribued index assoiated to the
  distribution @code{uh.ownership()}.

  For performances, a STL-like iterator interface is available, with 
  @code{uh.begin_dof()} and @code{uh.end_dof()} returns iterators to the
  arrays of dofs on the current processor.
  See @pxref{array class} for more about distributed arrays.

  For convenience, @code{uh.max()}, @code{uh.min()} and @code{uh.max_abs()} 
  retuns respectively the maximum, minimum and maximum of the absolute value
  of the degrees of freedom.

FILE FORMAT:
  TODO

IMPLEMENTATION NOTE:
  The field expression use the expression template technics in
  order to avoid temporaries when evaluating complex expressions.
AUTHOR: Pierre.Saramito@imag.fr
DATE:   23 february 2011
End:
*/
//<field:
template <class T, class M = rheo_default_memory_model>
class field_basic : public std::unary_function<point_basic<typename scalar_traits<T>::type>,T> {
public :
// typedefs:

    typedef typename std::size_t            size_type;
    typedef M                               memory_type;
    typedef T                               scalar_type;
    typedef typename float_traits<T>::type  float_type;
//  typedef undeterminated_basic<T>         value_type; // TODO
    typedef T                               value_type; // TO_CLEAN
    typedef space_constant::valued_type     valued_type;
    typedef geo_basic  <float_type,M>       geo_type;
    typedef space_basic<float_type,M>       space_type;
    class iterator;
    class const_iterator;

// allocator/deallocator:
  
    field_basic();

    explicit field_basic (
	const space_type& V, 
	const T& init_value = std::numeric_limits<T>::max());
   
    void resize (
	const space_type& V, 
	const T& init_value = std::numeric_limits<T>::max());

    field_basic                   (const field_indirect<T,M>&);
    field_basic<T, M>& operator=  (const field_indirect<T,M>&);
    field_basic                   (const field_indirect_const<T,M>&);
    field_basic<T, M>& operator=  (const field_indirect_const<T,M>&);
    field_basic                   (const field_component<T,M>&);
    field_basic<T, M>& operator=  (const field_component<T,M>&);
    field_basic                   (const field_component_const<T,M>&);
    field_basic<T, M>& operator=  (const field_component_const<T,M>&);
    template <class Expr> field_basic                   (const field_expr<Expr>&);
    template <class Expr> field_basic<T, M>& operator=  (const field_expr<Expr>&);
    field_basic<T, M>& operator=  (const T&);

// initializer list (c++ 2011):

#ifdef _RHEOLEF_HAVE_STD_INITIALIZER_LIST
    field_basic (const std::initializer_list<field_concat_value<T,M> >& init_list);
    field_basic<T,M>& operator= (const std::initializer_list<field_concat_value<T,M> >& init_list);
#endif // _RHEOLEF_HAVE_STD_INITIALIZER_LIST

// accessors:

    const space_type&  get_space()  const { return _V; }
    const geo_type&    get_geo()    const { return _V.get_geo(); }
    std::string        stamp()      const { return _V.stamp(); }
    std::string        get_approx() const { return _V.get_approx(); }
    valued_type        valued_tag() const { return _V.valued_tag(); }
    const std::string& valued()     const { return _V.valued(); }

// accessors & modifiers to unknown & blocked parts:

    const vec<T,M>&     u() const { dis_dof_update_needed(); return _u; }
    const vec<T,M>&     b() const { dis_dof_update_needed(); return _b; }
          vec<T,M>& set_u()       { return _u; }
          vec<T,M>& set_b()       { return _b; }

// accessors to extremas:

    T min() const;
    T max() const;
    T max_abs() const;
    T min_abs() const;

// accessors by domains:

    field_indirect<T,M>        operator[] (const geo_basic<T,M>& dom);
    field_indirect_const<T,M>  operator[] (const geo_basic<T,M>& dom) const;
    field_indirect<T,M>        operator[] (std::string dom_name);
    field_indirect_const<T,M>  operator[] (std::string dom_name) const;

// accessors by components:

    size_type size() const { return _V.size(); }
    field_component<T,M>       operator[] (size_type i_comp);
    field_component_const<T,M> operator[] (size_type i_comp) const;
    field_component<T,M>       operator() (size_type i_comp, size_type j_comp);
    field_component_const<T,M> operator() (size_type i_comp, size_type j_comp) const;

// accessors by degrees-of-freedom (dof):

    const distributor& ownership() const { return get_space().ownership(); }
    const communicator& comm() const { return ownership().comm(); }
    size_type     ndof() const { return ownership().size(); }
    size_type dis_ndof() const { return ownership().dis_size(); }
          T& dof (size_type idof);
    const T& dof (size_type idof) const;
    const T& dis_dof (size_type dis_idof) const;
    iterator begin_dof();
    iterator end_dof();
    const_iterator begin_dof() const;
    const_iterator end_dof() const;

// input/output:

    idiststream& get (idiststream& ips);
    odiststream& put (odiststream& ops) const;
    odiststream& put_field (odiststream& ops) const;

// evaluate uh(x) where x is given locally as hat_x in K:

    T dis_evaluate (const point_basic<T>& x, size_type i_comp = 0) const;
    T operator()   (const point_basic<T>& x) const { return dis_evaluate (x,0); }
    point_basic<T> dis_vector_evaluate (const point_basic<T>& x) const;

// internals:
public:

    // evaluate uh(x) where x is given locally as hat_x in K:
    // requiers to call field::dis_dof_upgrade() before.
    T evaluate (const geo_element& K, const point_basic<T>& hat_xq, size_type i_comp = 0) const;

    // propagate changed values shared at partition boundaries to others procs
    void dis_dof_update() const;

    template <class Expr>
    void assembly_internal (
        const geo_basic<T,M>&         dom,
        const geo_basic<T,M>&         band,
        const band_basic<T,M>&        gh,
        const Expr&                   expr,
        const quadrature_option_type& qopt,
        bool                          is_on_band);
    template <class Expr>
    void assembly (
        const geo_basic<T,M>&         domain,
        const Expr&                   expr,
        const quadrature_option_type& qopt);
    template <class Expr>
    void assembly (
        const band_basic<T,M>&        gh,
        const Expr&                   expr,
        const quadrature_option_type& qopt);

protected:
    void dis_dof_update_internal() const;
    void dis_dof_update_needed() const;

// data:
    space_type   _V;
    vec<T,M>     _u;
    vec<T,M>     _b;
    mutable bool _dis_dof_update_needed;
};
template <class T, class M>
idiststream& operator >> (odiststream& ips, field_basic<T,M>& u);

template <class T, class M>
odiststream& operator << (odiststream& ops, const field_basic<T,M>& uh);

typedef field_basic<Float> field;
typedef field_basic<Float,sequential> field_sequential;
//>field:

// =================================================================================
// field::iterator
// =================================================================================
template <class T, class M>
class field_basic<T,M>::iterator {
protected:
  typedef typename vec<T,M>::iterator                       data_t; // random acess
  typedef typename array<space_pair_type,M>::const_iterator iter_t; // forward access
public:

// typedefs:

  typedef std::forward_iterator_tag         iterator_category; // TODO: not fully random yet
  typedef typename vec<T,M>::size_type      size_type;
  typedef T                                 value_type;
  typedef T&                                reference;
  typedef T*                                pointer;
  typedef std::ptrdiff_t                    difference_type;

// allocators:

  iterator ()
    : _blk_iub_iter(), _u(), _b()
    {}
  iterator (iter_t blk_iub_iter, data_t u, data_t b)
    : _blk_iub_iter(blk_iub_iter), _u(u), _b(b)
    {}

// accessors & modifiers:

  reference operator* () const { 
      size_type iub = (*_blk_iub_iter).iub();
      size_type blk = (*_blk_iub_iter).is_blocked();
      if (!blk) return _u[iub]; else return _b[iub];
  }
  iterator& operator++ () { _blk_iub_iter++; return *this; }
  iterator  operator++ (int) { iterator tmp = *this; operator++(); return *this; }
  iterator& operator+= (difference_type n) { _blk_iub_iter += n; return *this; }
  iterator  operator+  (difference_type n) const { iterator tmp = *this; return tmp += n; }
  reference operator[] (size_type n) const { return *(*this + n); }

// comparators:

  bool operator== (const iterator& j) const { return _blk_iub_iter == j._blk_iub_iter; }
  bool operator!= (const iterator& j) const { return ! operator== (j); }
protected:
  template <class T1, class M1> friend class field_basic<T1,M1>::const_iterator;
// data:
  iter_t _blk_iub_iter;
  data_t _u;
  data_t _b;
};
template <class T, class M>
inline
typename field_basic<T,M>::iterator
field_basic<T,M>::begin_dof ()
{
  dis_dof_update_needed();
  return iterator (_V.data()._idof2blk_iub.begin(), _u.begin(), _b.begin());
}
template <class T, class M>
inline
typename field_basic<T,M>::iterator
field_basic<T,M>::end_dof ()
{
  dis_dof_update_needed();
  return iterator (_V.data()._idof2blk_iub.end(), _u.begin(), _b.begin());
}
// =================================================================================
// field::const_iterator
// =================================================================================
template <class T, class M>
class field_basic<T,M>::const_iterator {
protected:
  typedef typename vec<T,M>::const_iterator                 data_t;
  typedef typename array<space_pair_type,M>::const_iterator iter_t;
public:

// typedefs:

  typedef std::forward_iterator_tag         iterator_category;
  typedef typename vec<T,M>::size_type      size_type;
  typedef T                                 value_type;
  typedef const T&                          reference;
  typedef const T*                          pointer;
  typedef std::ptrdiff_t                    difference_type;

// allocators:

  const_iterator ()
    : _blk_iub_iter(), _u(), _b()
    {}
  const_iterator (iter_t blk_iub_iter, data_t u, data_t b)
    : _blk_iub_iter(blk_iub_iter), _u(u), _b(b)
    {}
  const_iterator (iterator i)
    : _blk_iub_iter(i._blk_iub_iter), _u(i._u), _b(i._b)
    {}

// accessors & modifiers:

  reference operator* () const { 
      size_type iub = (*_blk_iub_iter).iub();
      size_type blk = (*_blk_iub_iter).is_blocked();
      if (!blk) return _u[iub]; else return _b[iub];
  }
  const_iterator& operator++ () { _blk_iub_iter++; return *this; }
  const_iterator  operator++ (int) { const_iterator tmp = *this; operator++(); return *this; }
  const_iterator& operator+= (difference_type n) { _blk_iub_iter += n; return *this; }
  const_iterator  operator+  (difference_type n) const { const_iterator tmp = *this; return tmp += n; }
  reference operator[] (size_type n) const { return *(*this + n); }

// comparators:

  bool operator== (const const_iterator& j) const { return _blk_iub_iter == j._blk_iub_iter; }
  bool operator!= (const const_iterator& j) const { return ! operator== (j); }
protected:
// data:
  iter_t _blk_iub_iter;
  data_t _u;
  data_t _b;
};
template <class T, class M>
inline
typename field_basic<T,M>::const_iterator
field_basic<T,M>::begin_dof () const
{
    return const_iterator (_V.data()._idof2blk_iub.begin(), _u.begin(), _b.begin());
}
template <class T, class M>
inline
typename field_basic<T,M>::const_iterator
field_basic<T,M>::end_dof () const
{
    return const_iterator (_V.data()._idof2blk_iub.end(), _u.begin(), _b.begin());
}
// =================================================================================
// field: inlined
// =================================================================================
template <class T, class M>
inline
field_basic<T,M>::field_basic ()
 : _V(),
   _u(),
   _b(),
   _dis_dof_update_needed(true)
{
}
template <class T, class M>
void
field_basic<T,M>::dis_dof_update_needed() const
{
  _dis_dof_update_needed = true;
}
template <class T, class M>
void
field_basic<T,M>::dis_dof_update() const
{
  if (!_dis_dof_update_needed) return; 
  _dis_dof_update_needed = false;
  if (is_distributed<M>::value) dis_dof_update_internal();
}
template<class T, class M>
inline
field_basic<T,M>&
field_basic<T,M>::operator=  (const T& value)
{
  check_macro (stamp() != "", "field=constant : uninitialized field in affectation");
  std::fill (begin_dof(), end_dof(), value);
  dis_dof_update_needed();
  return *this;
}
template <class T, class M>
inline
T& 
field_basic<T,M>::dof (size_type idof)
{
  dis_dof_update_needed();
  if (! _V.is_blocked(idof)) {
    return _u [_V.iub(idof)]; 
  } else {
    return _b [_V.iub(idof)];
  }
}
template <class T, class M>
inline
const T&
field_basic<T,M>::dof (size_type idof) const
{
  if (! _V.is_blocked(idof)) {
    return _u [_V.iub(idof)];
  } else {
    return _b [_V.iub(idof)];
  }
}
template <class T, class M>
inline
T
field_basic<T,M>::min () const
{
  T val = std::numeric_limits<T>::max();
  for (const_iterator iter = begin_dof(), last = end_dof(); iter != last; iter++) {
    val = std::min(val, *iter);
  }
#ifdef _RHEOLEF_HAVE_MPI
  if (is_distributed<M>::value) {
    val = mpi::all_reduce (comm(), val, mpi::minimum<T>());
  }
#endif // _RHEOLEF_HAVE_MPI
  return val;
}
template <class T, class M>
inline
T
field_basic<T,M>::max () const
{
  T val = std::numeric_limits<T>::min();
  for (const_iterator iter = begin_dof(), last = end_dof(); iter != last; iter++) {
    val = std::max(val, *iter);
  }
#ifdef _RHEOLEF_HAVE_MPI
  if (is_distributed<M>::value) {
    val = mpi::all_reduce (comm(), val, mpi::maximum<T>());
  }
#endif // _RHEOLEF_HAVE_MPI
  return val;
}
template <class T, class M>
inline
T
field_basic<T,M>::min_abs () const
{
  T val = std::numeric_limits<T>::max();
  for (const_iterator iter = begin_dof(), last = end_dof(); iter != last; iter++) {
    val = std::min(val, abs(*iter));
  }
#ifdef _RHEOLEF_HAVE_MPI
  if (is_distributed<M>::value) {
    val = mpi::all_reduce (comm(), val, mpi::minimum<T>());
  }
#endif // _RHEOLEF_HAVE_MPI
  return val;
}
template <class T, class M>
inline
T
field_basic<T,M>::max_abs () const
{
  T val = 0;
  for (const_iterator iter = begin_dof(), last = end_dof(); iter != last; iter++) {
    val = std::max(val, abs(*iter));
  }
#ifdef _RHEOLEF_HAVE_MPI
  if (is_distributed<M>::value) {
    val = mpi::all_reduce (comm(), val, mpi::maximum<T>());
  }
#endif // _RHEOLEF_HAVE_MPI
  return val;
}
template <class T, class M>
inline
idiststream&
operator >> (idiststream& ips, field_basic<T,M>& uh)
{
  return uh.get (ips);
}
template <class T, class M>
inline
odiststream&
operator << (odiststream& ops, const field_basic<T,M>& uh)
{
  return uh.put (ops);
}
#ifdef TO_CLEAN
template <class T, class M>
inline
field_basic<T,M>
norm (const field_basic<T,M>& uh)
{
  return sqrt(norm2(uh));
}
#endif // TO_CLEAN

}// namespace rheolef
# endif /* _RHEOLEF_FIELD_H */