**pcg_abtb**,

**pcg_abtbc**,

**pminres_abtb**,

**pminres_abtbc** --
solvers for mixed linear problems

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");

The synopsis is the same with the pminres algorithm.

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

Preconditioned conjugate gradient algorithm on the pressure p applied to the
stabilized stokes problem:

[ A B^T ] [ u ] [ Mf ]
[ ] [ ] = [ ]
[ B -C ] [ p ] [ Mg ]

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:

inv(S1)*(B*inv(A)*B^T)*p = inv(S1)*(B*inv(A)*Mf - Mg)

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.