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#ifndef _SKIT_SOLVER_ABTB_H
#define _SKIT_SOLVER_ABTB_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/solver.h"
#include "rheolef/mixed_solver.h"
#include "rheolef/csr.h"

namespace rheolef {

/*Class:solver_abtb
NAME: @code{solver_abtb} -- direct or iterative solver iterface for mixed linear systems
@cindex mixed linear problem
@cindex conjugate gradien algorithm
@cindex finite element method
@cindex stabilized mixed finite element method
@cindex Stokes problem
@cindex incompresible elasticity
SYNOPSIS:
  @example
    solver_abtb stokes     (a,b,mp); 
    solver_abtb elasticity (a,b,c,mp); 
  @end example
DESCRIPTION:
  @noindent
  The @code{solver_abtb} class provides direct or iterative algorithms for some mixed problem:
  @example
       [ A  B^T ] [ u ]    [ Mf ]
       [        ] [   ]  = [    ]
       [ B  -C  ] [ p ]    [ Mg ]
  @end example
  where A is symmetric positive definite and C is symmetric positive.
  By default, iterative algorithms are considered for tridimensional problems
  and direct methods otherwise.
  Such mixed linear problems appears for instance with the discretization
  of Stokes problems.
  The C matrix can be zero and then the corresponding argument can be omitted
  when invoking the constructor.
  Non-zero C matrix appears for of Stokes problems with stabilized P1-P1 element,
  or for nearly incompressible elasticity problems.
DIRECT ALGORITHM:
  When the kernel of @code{B^T} is not reduced to zero, then the pressure p is defined up to a constant
  and the system is singular. In the case of iterative methods, this is not a problem.
  But when using direct method, the system is then completed to impose a constraint on the pressure term
  and the whole matrix is factored one time for all.
ITERATIVE ALGORITHM:
  The preconditionned conjugate gradient algorithm is used, where the @code{mp} matrix
  is used as preconditionner. See @pxref{mixed_solver algorithm}.
EXAMPLES:
  See the user's manual for practical examples for the nearly incompressible
  elasticity, the Stokes and the Navier-Stokes problems.
AUTHOR:
   | Pierre.Saramito@imag.fr
    LJK-IMAG, 38041 Grenoble cedex 9, France
DATE:  19 january 2012
METHODS: @mixed_solver
End:
*/
//<solver_abtb:
template <class T, class M = rheo_default_memory_model>
class solver_abtb_basic {
public:

// typedefs:

  typedef typename csr<T,M>::size_type size_type;

// allocators:

  solver_abtb_basic ();
  solver_abtb_basic (const csr<T,M>& a, const csr<T,M>& b, const csr<T,M>& mp,
       const solver_option_type& opt = solver_option_type());
  solver_abtb_basic (const csr<T,M>& a, const csr<T,M>& b, const csr<T,M>& c, const csr<T,M>& mp,
       const solver_option_type& opt = solver_option_type());

// accessors:

  void solve (const vec<T,M>& f, const vec<T,M>& g, vec<T,M>& u, vec<T,M>& p) const;

protected:
// internal
  void init();
// data:
  mutable solver_option_type _opt;
  csr<T,M>          _a;
  csr<T,M>          _b;
  csr<T,M>          _c;
  csr<T,M>          _mp;
  solver_basic<T,M> _sA;
  solver_basic<T,M> _sa;
  solver_basic<T,M> _smp;
  bool              _need_constraint;
};
typedef solver_abtb_basic<Float,rheo_default_memory_model> solver_abtb;
//>solver_abtb:

} // namespace rheolef
#endif // _SKIT_SOLVER_ABTB_H