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Section: Software

Keywords : parallel asynchronous sparse multifrontal solver.

MUMPS

Participants : Patrick Amestoy, Abdou Guermouche [ corresponding member ] .

In the context of PARASOL (Esprit IV Long Term Project, 1996-1999), CERFACS and ENSEEIHT-IRIT teams have initiated a parallel sparse solver MUMPS (``MUltifrontal Massively Parallel Solver''). Since the first public release of MUMPS (March 2000), this research and (also software) project is the context of a tight and fruitful collaboration with J. Y. L'Excellent (INRIA-LIP-ENS Lyon) and the INRIA project GRAAL. Recent work related to performance scalability, preprocessing of both symmetric and unsymmetric matrices, two by two pivots for symmetric indefinite matrices, and dynamic scheduling has been incorporated in the new improved version of the package (release 4.5.5 available since october 2005 at http://www.enseeiht.fr/apo/MUMPS or http://graal.ens-lyon.fr/MUMPS ).

MUMPS is a package for solving linear systems of equations Ax = b , where the matrix A is sparse and can be either unsymmetric, symmetric positive definite, or general symmetric. It uses a multifrontal technique which is a direct method based on either the LU or the LDLT factorization of the matrix. The main features of the MUMPS package include numerical pivoting during factorization, solution of the transposed system, input of the matrix in assembled format (distributed or centralized) or elemental format, error analysis, iterative refinement, scaling of the original matrix, and return of a Schur complement matrix. It also offers several built-in ordering algorithms, a tight interface to some external ordering packages such as Scotch and is available in various arithmetics (real or complex, single or double).

This year, we particularly focussed in a preliminary out-of-core functionality, where computed factors are written to disk. It has been made available to some of our users, in order to get their feedback before making this functionality more widely available. We have also been working on reducing the memory requirements for symmetric matrices (by using a packed format for temporary Schur complements) as well as for unsymmetric matrices and have modified the general memory management algorithms to allow for more flexibility in an out-of-core context.


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