MUMPS
Solver for Large Linear Systems

MUMPS: examples which illustrate the use of MUMPS, which is a package for the solution of large linear systems.

Features include

• treatment of symmetric positive definite matrices;
• treatement of general symmetric matrices;
• treatment of general unsymmetric matrices;
• Real or complex arithmetic (single or double precision);
• Parallel factorization and solve phases (uniprocessor version also available);
• Out of core numerical phases;
• Iterative refinement and backward error analysis;
• Various matrix input formats: assembled, distributed, elemental format;
• Partial factorization and Schur complement matrix (centralized or 2D block-cyclic) with reduced/ condensed right-hand side;
• Interfaces to MUMPS: Fortran, C, Matlab and Scilab;
• Several reorderings interfaced: AMD, QAMD, AMF, PORD, METIS, PARMETIS, SCOTCH, PT-SCOTCH;
• Symmetric indefinite matrices: preprocesssing and 2-by-2 pivots;
• Parallel analysis and matrix scaling;
• Computation of the determinant (with an option to discard factors);
• Forward elimination during factorization.

MUMPS is typical of modern software in being extraordinarily powerful, but also complex, reliant on numerous other packages, tricky to install, and somewhat awkward to use.

Web Site:

http://mumps.enseeiht.fr/.

Related Data and Programs:

EIGEN, examples which illustrate the use of EIGEN, a C++ template library for linear algebra, including natural and usable definitions of vectors and matrices, norms, factorizations, solution of linear systems, evaluation of eigenvalues, and many standard linear algebra algorithms for dense and sparse matrices.

SCALAPACK, examples which illustrate the use of SCALAPACK, which is a library for the configuration, distribution, and solution of linear algebra problems using distributed memory and parallel processing.

SUPERLU, C programs which illustrate how to use the SUPERLU library, which applies a fast direct solution method to solve sparse linear systems, by James Demmel, John Gilbert, and Xiaoye Li.

UMFPACK, C programs which illustrate how to solve a sparse linear system by calling the C library UMFPACK, by Timothy Davis.

Reference:

1. P R Amestoy, Ian Duff, J-Y l'Excellent,
   Multifrontal parallel distributed symmetric and unsymmetric solvers,
   Computer Methods in Applied Mechanics and Engineering,
   Volume 184, Number 2–4, pages 501–520, 2000.

Examples and Tests:

• dsimpletest.F, the real double precision version of the test example.
• input_simpletest_real, an input file needed to run the example.
• dsimpletest.sh, a shell script which compiles, loads and runs the example under MPI. Since I do not use the recommended Makefile, I have to define a number of environment variables.
• dsimpletest.txt, the output file.

You can go up one level to the EXAMPLES directory.