Encyclopedia of Parallel Computing

2011 Edition
| Editors: David Padua

Multifrontal Method

  • 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_86

Synonyms

Definition

The multifrontal method is a direct method for solving systems of linear equations Ax = b, when A is a sparse matrix and x and b are vectors or matrices. The multifrontal method organizes the operations that take place during the factorization of sparse matrices in such a way that the entire factorization is performed through partial factorizations of a sequence of dense and small submatrices. It is guided by a tree that represents the dependencies between those partial factorizations. In the following, the multifrontal method is formulated first for finite-element analysis and later generalized to assembled sparse matrices.

The Multifrontal Method

The multifrontal method is a direct method so that if the aim is to solve the equations
$$Ax = b,$$
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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