Skip to main content

Mumps

  • Reference work entry

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 via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   1,600.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   1,799.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Bibliography

  1. Agullo E (2008) On the out-of-core factorization of large sparse matrices. PhD thesis, École Normale Supérieure de Lyon, France, November 2008

    Google Scholar 

  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):296–317

    Article  MathSciNet  Google Scholar 

  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 appear

    Google Scholar 

  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.2009.06.001

    Google Scholar 

  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, France

    Google Scholar 

  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. 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, Berlin

    Google Scholar 

  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):15–41

    Article  MATH  MathSciNet  Google Scholar 

  9. Amestoy PR, Duff IS, Vömel C (2005) Task scheduling in an asynchronous distributed memory multifrontal solver. SIAM J Matrix Anal A 26:544–565

    Article  MATH  Google Scholar 

  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):136–156

    Article  MathSciNet  Google Scholar 

  11. Duff IS (1986) Parallel implementation of multifrontal schemes. Parallel Comput 3:193–204

    Article  MATH  MathSciNet  Google Scholar 

  12. Duff IS, Pralet S (2007) Strategies for scaling and pivoting for sparse symmetric indefinite problems. SIAM J Matrix Anal A 27(2):313–340

    Article  MathSciNet  Google Scholar 

  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): 1007–1024

    Article  MATH  MathSciNet  Google Scholar 

  14. Duff IS, Reid JK (1984) The multifrontal solution of unsymmetric sets of linear systems. SIAM J Sci Stat Comput 5:633–641

    Article  MATH  MathSciNet  Google Scholar 

  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-IRIT

    Google Scholar 

  16. Guermouche A (2004) Études et optimisation du comportement mémoire dans les méthodes parallèles de factorisation de matrices creuses. PhD thesis, ENS Lyon, France

    Google Scholar 

  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. Guermouche A, L’Excellent J-Y (2006) Constructing memoryminimizing schedules for multifrontal methods. ACM T Math Software 32(1):17–32

    Article  MathSciNet  Google Scholar 

  19. Guermouche A, L’Excellent J-Y, Utard G (2003) Impact of reordering on the memory of a multifrontal solver. Parallel Comput 29(9):1191–1218

    Article  MathSciNet  Google Scholar 

  20. Liu JWH (1986) On the storage requirement in the out-of-core multifrontal method for sparse factorization. ACM T Math Software 12(3):249–264

    Article  MATH  Google Scholar 

  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/04/105

    Google Scholar 

  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/09/59

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media, LLC

About this entry

Cite this entry

Amestoy, P., Buttari, A., Duff, I., Guermouche, A., L’Excellent, JY., Uçar, B. (2011). Mumps. In: Padua, D. (eds) Encyclopedia of Parallel Computing. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-09766-4_204

Download citation

Publish with us

Policies and ethics