I am in the search of linear solvers for sparse matrices preferably coded in FORTRAN. For 2D calculations the use of the Finite Volume method results in solving pentadiagonal systems which can be solved by an TDMA algorithm (TriDiagonal Matrix Algorithm). Then I hope of better performances by using a GMRES method (with a preconditioning)? Thank you in advance.

Check Numerical Recipes

There is a book by Ferziger and Peric (Computational Methods for Fluid Dynamics), which deals with this (among others). The book also quotes a web-site with example codes you can get for free from the same authors (I guess you can find both in Frequently Asked Questions or similar).

Ths question was already asked a few days ago by someone else. So I can just repeat my answer again.

A good solver (in my opinion) is

http://www-fp.mcs.anl.gov/petsc/

including all kind of Krylov-subspave solvers (GMRES, BISTAB...) and Preconditioning (ILU(n)...)

It solves your equations etc.. also in parallel using MPI, if you want to do this.

A solver in Fortran is 'templates' http://www.netlib.org/linalg/html_te...Templates.html

But I heard that in the GMRES routine there was a bug, though I don't know if it was the present version.

The PETSC software can be used in combination with C and Fortran.

Frank