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# ifndef _RHEO_MIXED_SOLVER_H
# define _RHEO_MIXED_SOLVER_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 "puzawa.h"
#include "pcg.h"
#include "pminres.h"
namespace rheolef { 

template <class Matrix, class Vector, class Solver>
struct abtbc_schur_complement { // S = B*inv(A)*B^T + C
  Solver iA;
  Matrix B, C;
  abtbc_schur_complement (const Solver& iA1,const Matrix& B1, const Matrix& C1) : iA(iA1), B(B1), C(C1) {}
  Vector operator* (const Vector& p) const {
    Vector v = iA.solve(B.trans_mult(p));
    return B*v + C*p;
  }
};
template <class Matrix, class Vector, class Solver>
struct abtb_schur_complement { // S = B*inv(A)*B^T
  Solver iA;
  Matrix B;
  abtb_schur_complement (const Solver& iA1,const Matrix& B1) : iA(iA1), B(B1) {}
  Vector operator* (const Vector& p) const {
    Vector v = iA.solve(B.trans_mult(p));
    return B*v;
  }
};
template <class Matrix, class Vector, class Solver, class Preconditioner, class Size, class Real>
int puzawa_abtbc (const Matrix& A, const Matrix& B, const Matrix& C, Vector& u, Vector& p,
  const Vector& Mf, const Vector& Mg, const Preconditioner& S1,
  const Solver& inner_solver_A, Size& max_iter, Real& tol, const Float& rho,
  odiststream *p_derr = 0, std::string label = "puzawa_abtbc")
{
  abtbc_schur_complement<Matrix,Vector,Solver> S (inner_solver_A, B, C);
  Vector v = inner_solver_A.solve (Mf);
  Vector Mh = B*v - Mg;
  int status = puzawa(S, p, Mh, S1, max_iter, tol, rho, p_derr, label);
  u = inner_solver_A.solve (Mf - B.trans_mult(p));
  return status;
}
template <class Matrix, class Vector, class Solver, class Preconditioner, class Size, class Real>
int puzawa_abtb (const Matrix& A, const Matrix& B, Vector& u, Vector& p,
  const Vector& Mf, const Vector& Mg, const Preconditioner& S1,
  const Solver& inner_solver_A, Size& max_iter, Real& tol, const Float& rho,
  odiststream *p_derr = 0, std::string label = "puzawa_abtb")
{
  abtb_schur_complement<Matrix,Vector,Solver> S (inner_solver_A, B);
  Vector v = inner_solver_A.solve (Mf);
  Vector Mh = B*v - Mg;
  int status = puzawa(S, p, Mh, S1, max_iter, tol, rho, p_derr, label);
  u = inner_solver_A.solve (Mf - B.trans_mult(p));
  return status;
}
/*Class:mixed_solver
NAME: @code{pcg_abtb}, @code{pcg_abtbc}, @code{pminres_abtb}, @code{pminres_abtbc} -- solvers for mixed linear problems
@findex pcg
@findex pminres
@findex pcg\_abtb
@findex pcg\_abtbc
@findex pminres\_abtb
@findex pminres\_abtbc
@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
    template <class Matrix, class Vector, class Solver, class Preconditioner, class Size, class Real>
    int pcg_abtb (const Matrix& A, const Matrix& B, Vector& u, Vector& p,
      const Vector& Mf, const Vector& Mg, const Preconditioner& S1,
      const Solver& inner_solver_A, Size& max_iter, Real& tol,
      odiststream *p_derr = 0, std::string label = "pcg_abtb");

    template <class Matrix, class Vector, class Solver, class Preconditioner, class Size, class Real>
    int pcg_abtbc (const Matrix& A, const Matrix& B, const Matrix& C, Vector& u, Vector& p,
      const Vector& Mf, const Vector& Mg, const Preconditioner& S1,
      const Solver& inner_solver_A, Size& max_iter, Real& tol,
      odiststream *p_derr = 0, std::string label = "pcg_abtbc");
  @end example
  The synopsis is the same with the pminres algorithm.

EXAMPLES:
  See the user's manual for practical examples for the nearly incompressible
  elasticity, the Stokes and the Navier-Stokes problems.

DESCRIPTION: 
  @noindent
  Preconditioned conjugate gradient algorithm on the pressure p applied to 
  the stabilized stokes problem:
  @example
       [ A  B^T ] [ u ]    [ Mf ]
       [        ] [   ]  = [    ]
       [ B  -C  ] [ p ]    [ Mg ]
  @end example
  where A is symmetric positive definite and C is symmetric positive
  and semi-definite.
  Such mixed linear problems appears for instance with the discretization
  of Stokes problems with stabilized P1-P1 element, or with nearly
  incompressible elasticity.
  Formaly u = inv(A)*(Mf - B^T*p) and the reduced system writes for
  all non-singular matrix S1:
  @example
     inv(S1)*(B*inv(A)*B^T)*p = inv(S1)*(B*inv(A)*Mf - Mg)
  @end example
  Uzawa or conjugate gradient algorithms are considered on the
  reduced problem.
  Here, S1 is some preconditioner for the Schur complement S=B*inv(A)*B^T.
  Both direct or iterative solvers for S1*q = t are supported.
  Application of inv(A) is performed via a call to a solver
  for systems such as A*v = b.
  This last system may be solved either by direct or iterative algorithms,
  thus, a general matrix solver class is submitted to the algorithm.
  For most applications, such as the Stokes problem, 
  the mass matrix for the p variable is a good S1 preconditioner
  for the Schur complement.
  The stoping criteria is expressed using the S1 matrix, i.e. in L2 norm
  when this choice is considered.
  It is scaled by the L2 norm of the right-hand side of the reduced system,
  also in S1 norm.
AUTHOR: 
   | Pierre.Saramito@imag.fr
    LJK-IMAG, 38041 Grenoble cedex 9, France
DATE:   15 april 2009
METHODS: @mixed_solver
End:
*/

template <class Matrix, class Vector, class VectorExpr1, class VectorExpr2,
  class Solver, class Preconditioner, class Size, class Real>
int pcg_abtbc (const Matrix& A, const Matrix& B, const Matrix& C, Vector& u, Vector& p,
  const VectorExpr1& Mf, const VectorExpr2& Mg, const Preconditioner& S1,
  const Solver& inner_solver_A, Size& max_iter, Real& tol,
  odiststream *p_derr = 0, std::string label = "pcg_abtbc")
{
  abtbc_schur_complement<Matrix,Vector,Solver> S (inner_solver_A, B, C);
  Vector v = inner_solver_A.solve (Mf);
  Vector Mh = B*v - Mg;
  int status = pcg(S, p, Mh, S1, max_iter, tol, p_derr, label);
  u = inner_solver_A.solve (Mf - B.trans_mult(p));
  return status;
}
template <class Matrix, class Vector, class VectorExpr1, class VectorExpr2,
  class Solver, class Preconditioner, class Size, class Real>
int pcg_abtb (const Matrix& A, const Matrix& B, Vector& u, Vector& p,
  const VectorExpr1& Mf, const VectorExpr2& Mg, const Preconditioner& S1,
  const Solver& inner_solver_A, Size& max_iter, Real& tol,
  odiststream *p_derr = 0, std::string label = "pcg_abtb")
{
  abtb_schur_complement<Matrix,Vector,Solver> S (inner_solver_A, B);
  Vector v = inner_solver_A.solve (Mf);
  Vector Mh = B*v - Mg;
  int status = pcg(S, p, Mh, S1, max_iter, tol, p_derr, label);
  u = inner_solver_A.solve (Mf - B.trans_mult(p));
  return status;
}
template <class Matrix, class Vector, class Solver, class Preconditioner, class Size, class Real>
int pminres_abtbc (const Matrix& A, const Matrix& B, const Matrix& C, Vector& u, Vector& p,
  const Vector& Mf, const Vector& Mg, const Preconditioner& S1,
  const Solver& inner_solver_A, Size& max_iter, Real& tol,
  odiststream *p_derr = 0, std::string label = "pminres_abtbc")
{
  abtbc_schur_complement<Matrix,Vector,Solver> S (inner_solver_A, B, C);
  Vector v = inner_solver_A.solve (Mf);
  Vector Mh = B*v - Mg;
  int status = pminres(S, p, Mh, S1, max_iter, tol, p_derr, label);
  u = inner_solver_A.solve (Mf - B.trans_mult(p));
  return status;
}
template <class Matrix, class Vector, class Solver, class Preconditioner, class Size, class Real>
int pminres_abtb (const Matrix& A, const Matrix& B, Vector& u, Vector& p,
  const Vector& Mf, const Vector& Mg, const Preconditioner& S1,
  const Solver& inner_solver_A, Size& max_iter, Real& tol,
  odiststream *p_derr = 0, std::string label = "pminres_abtb")
{
  abtb_schur_complement<Matrix,Vector,Solver> S (inner_solver_A, B);
  Vector v = inner_solver_A.solve (Mf);
  Vector Mh = B*v - Mg;
  int status = pminres(S, p, Mh, S1, max_iter, tol, p_derr, label);
  u = inner_solver_A.solve (Mf - B.trans_mult(p));
  return status;
}
}// namespace rheolef
# endif // _RHEO_MIXED_SOLVER_H