Encyclopedia of Parallel Computing

2011 Edition
| Editors: David Padua

Mumps

  • Patrick Amestoy
  • Alfredo Buttari
  • Iain Duff
  • Abdou Guermouche
  • Jean-Yves L’Excellent
  • Bora Uçar
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-09766-4_204

Synonyms

 MUMPS

Definition

MUMPS (MUltifrontal Massively Parallel Solver) is a parallel library for the solution of sparse linear equations. It primarily targets parallel platforms with distributed memory, where the message passing paradigm MPI is used. MUMPS is a direct code, based on Gaussian elimination. It will solve sparse linear systems with a real unsymmetric, symmetric positive definite, or symmetric indefinite coefficient matrix and will solve complex systems where the matrix is unsymmetric or complex symmetric. MUMPS has a large number of options, some to enhance functionality and some to improve performance or core memory usage. Whereas most direct solvers for distributed memory environments rely on static approaches where the computational tasks are known and assigned to the processors in advance, one of the main originalities of MUMPS is its ability to perform dynamic pivoting in order to guarantee numerical stability, leading to dynamic data structures and non-fully...

This is a preview of subscription content, log in to check access.

Bibliography

  1. 1.
    Agullo E (2008) On the out-of-core factorization of large sparse matrices. PhD thesis, École Normale Supérieure de Lyon, France, November 2008Google Scholar
  2. 2.
    Agullo E, Guermouche A, L’Excellent J-Y (2008) A parallel out-of-core multifrontal method: storage of factors on disk and analysis of models for an out-of-core active memory. Parallel Comput 34(6–8):296–317MathSciNetCrossRefGoogle Scholar
  3. 3.
    Agullo E, Guermouche A, L’Excellent J-Y (2009) Reducing the I/O volume in sparse out-of-core multifrontal methods. SIAM J Sci Comput, to appearGoogle Scholar
  4. 4.
    Amestoy P, Duff I, Guermouche A, Slavova T (2009) Analysis of the solution phase of a parallel multifrontal approach. Parallel Comput 2009. doi: 10.1016/j.parco.2009.06.001Google Scholar
  5. 5.
    Amestoy PR (1991) Factorization of large sparse matrices based on a multifrontal approach in a multiprocessor environment. INPT PhD thesis TH/PA/91/2, CERFACS, Toulouse, FranceGoogle Scholar
  6. 6.
    Amestoy PR, Buttari A, L’Excellent J-Y (2008) Towards a parallel analysis phase for a multifrontal sparse solver. June 2008. Presentation at the 5th International workshop on Parallel Matrix Algorithms and Applications (PMAA’08)Google Scholar
  7. 7.
    Amestoy PR, Duff IS, L’Excellent J-Y (1998) Multifrontal solvers within the PARASOL environment. In: Kågström B, Dongarra J, Elmroth E, Waśniewski J (eds) Applied parallel computing, PARA’98, Lecture Notes in Computer Science, No. 1541, pp 7–11, 1998. Springer, BerlinGoogle Scholar
  8. 8.
    Amestoy PR, Duff IS, L’Excellent J-Y, Koster J (2001) A fully asynchronous multifrontal solver using distributed dynamic scheduling. SIAM J Matrix Anal A 23(1):15–41zbMATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    Amestoy PR, Duff IS, Vömel C (2005) Task scheduling in an asynchronous distributed memory multifrontal solver. SIAM J Matrix Anal A 26:544–565zbMATHCrossRefGoogle Scholar
  10. 10.
    Amestoy PR, Guermouche A, L’Excellent J-Y, Pralet S (2006) Hybrid scheduling for the parallel solution of linear systems. Parallel Comput 32(2):136–156MathSciNetCrossRefGoogle Scholar
  11. 11.
    Duff IS (1986) Parallel implementation of multifrontal schemes. Parallel Comput 3:193–204zbMATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    Duff IS, Pralet S (2007) Strategies for scaling and pivoting for sparse symmetric indefinite problems. SIAM J Matrix Anal A 27(2):313–340MathSciNetCrossRefGoogle Scholar
  13. 13.
    Duff IS Pralet S (2007) Towards stable mixed pivoting strategies for the sequential and parallel solution of sparse symmetric indefinite systems. SIAM J Matrix Anal A 29(3): 1007–1024zbMATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    Duff IS, Reid JK (1984) The multifrontal solution of unsymmetric sets of linear systems. SIAM J Sci Stat Comput 5:633–641zbMATHMathSciNetCrossRefGoogle Scholar
  15. 15.
    Espirat V (1996) Développement d’une approche multifrontale pour machines a mémoire distribuée et réseau hétérogène de stations de travail. Technical Report Master thesis, ENSEEIHT-IRITGoogle Scholar
  16. 16.
    Guermouche A (2004) Études et optimisation du comportement mémoire dans les méthodes parallèles de factorisation de matrices creuses. PhD thesis, ENS Lyon, FranceGoogle Scholar
  17. 17.
    Guermouche A, L’Excellent J-Y (2005) A study of various load information exchange mechanisms for a distributed application using dynamic scheduling. In: 19th International Parallel and Distributed Processing Symposium (IPDPS’05)Google Scholar
  18. 18.
    Guermouche A, L’Excellent J-Y (2006) Constructing memoryminimizing schedules for multifrontal methods. ACM T Math Software 32(1):17–32MathSciNetCrossRefGoogle Scholar
  19. 19.
    Guermouche A, L’Excellent J-Y, Utard G (2003) Impact of reordering on the memory of a multifrontal solver. Parallel Comput 29(9):1191–1218MathSciNetCrossRefGoogle Scholar
  20. 20.
    Liu JWH (1986) On the storage requirement in the out-of-core multifrontal method for sparse factorization. ACM T Math Software 12(3):249–264zbMATHCrossRefGoogle Scholar
  21. 21.
    Pralet S (2004) Constrained orderings and scheduling for parallel sparse linear algebra. Phd thesis, Institut National Polytechnique de Toulouse, September 2004. CERFACS Technical Report, TH/PA/04/105Google Scholar
  22. 22.
    Slavova Tz (2009) Parallel triangular solution in the out-of-core multifrontal approach for solving large sparse linear system. PhD thesis, Institut National Polytechnique de Toulouse, 2009. CERFACS Technical Report, TH/PA/09/59Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Patrick Amestoy
    • 1
  • Alfredo Buttari
    • 2
  • Iain Duff
    • 3
  • Abdou Guermouche
    • 4
  • Jean-Yves L’Excellent
    • 5
  • Bora Uçar
    • 6
  1. 1.INPTUniversité de Toulouse ENSEEIHT-IRITToulouse cedex 7France
  2. 2.CNRSUniversité de ToulouseToulouse cedex 7France
  3. 3.Rutherford Appleton LaboratoryScience & Technology Facilities CouncilDidcotUK
  4. 4.LaBRIUniversité de BordeauxTalenceFrance
  5. 5.INRIAENS LyonLyonFrance
  6. 6.CNRSENS LyonLyonFrance