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A templated parallel C++ implementation of the minres algorithm.

MINRES is a Krylov subspace iterative method for the solution of large sparse
symmetric (possibly indefinite) linear systems.

MINRES was first proposed by C.C. Paige and M.A. Saunders (1975).

It is based on Lanczos tridiagonalization.
A symmetric positive definite preconditioner can be specified.

The present C++ implementation is based on the matlab code by
Michael Saunders (SOL, Stanford University) and Sou Cheng Choi (SCCM, Stanford University)
available at

http://www.stanford.edu/group/SOL/software/minres.html

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The aim of tminres is to provide an efficient and portable implementation of 
the minres algorithm.

tminres supports user-defined parallel and serial data structure for the 
description of vectors, linear operators, and preconditioners.

The abstract classes Vector_trait and Operator_trait define the signatures of
the methods that the user-defined classes should provide.

Users can decide whenever to use static (templates) or dynamic (derivated classes)
polymorphism in order to provide such interfaces.

Two concrete implementations of Vector_trait and Operator_trait are included in the code:

  1)  Serial code: A VectorSimple class implements the methods required by minres.
  2)  Parallel code: A VectorEpetraAdapter shows how to wrap parallel data structures
      in Trilinos (http://trilinos.sandia.gov/) to be used with tminres.
      
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DOCUMENTATION

To create the documentation

$ doxygen Doxyfile.in

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EXAMPLES

SerialExample:
- In ex1 we solve a linear system with a diagonal operator
  (half of the entries are positive, half are negative).
  No preconditioner is used.

- In ex2 we solve a linear system arising from a finite volume discretization
  of the Stokes system in a square.
  A diagonal precondtioner is used.

To compile and execute the serial examples:

$ cd SerialExample
$ make
$ ./ex1
$ ./ex2
$ make clean


TrilinosExample:

In this example we show how to use Trilinos parallel vectors and matrices
(Epetra_MultiVector and Epetra_CrsMatrix) with our minres code.

We consider a finite element discretization of the Stokes system in a cube.
An algebraic multigrid block preconditioner is used.

To compile this examples you need to have a working installation of Trilinos (10.8 or above).
The following packages of Trilinos are required: Epetra, EpetraExt, ML, Teuchos.
The installation of Trilinos may require additional external libraries, such as Blas, Lapack, Metis.

To compile and execute the Trilinos examples you first need to edit the Makefile.in according to
your system configuration and Trilinos compiling options.

$ cd TrilinosExample
$ vi Makefile.in
$ make
$ mpirun -n XX ./ex1.exe
$ make clean