MUMPS : a parallel sparse direct solver

Sparse matrix graph

MUMPS Main Features

  • Solution of large linear systems with
      symmetric positive definite matrices
      general symmetric matrices
      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
SAMCEF Field software, by courtesy of SAMTECH

Recent features

  • Detection of null pivots, null space basis estimate
  • Sparse multiple right-hand side, distributed solution; Exploitation of sparsity in the right-hand sides
  • Computation of selected entries in the inverse of a matrix
  • Block Low Rank (BLR) factorization and solve
  • Selective 64-bit integer feature for matrices with more than 2 billion nonzeros
Vampir trace
A fully asynchronous distributed solver (VAMPIR trace)

Implementation

  • Distributed Multifrontal Solver (Fortran 95, MPI) using shared-memory parallelism (OpenMP, multithreaded BLAS) within each MPI process;
  • Dynamic Distributed Scheduling to accomodate numerical fill-in, load balancing and multi-user environment;
  • Use of BLAS, BLACS, ScaLAPACK.
PARASOL
Partially funded by CEC ESPRIT IV long-term research project -- No. 20160 (PARASOL)