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An efficient out‐of‐core multifrontal solver for large‐scale unsymmetric element problems
Author(s) -
Reid J. K.,
Scott J. A.
Publication year - 2008
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2437
Subject(s) - solver , computer science , parallel computing , computational science , code (set theory) , finite element method , sparse matrix , factorization , linear algebra , matrix (chemical analysis) , linear system , interface (matter) , multi core processor , algorithm , theoretical computer science , mathematics , programming language , mathematical analysis , physics , geometry , materials science , set (abstract data type) , bubble , quantum mechanics , maximum bubble pressure method , gaussian , composite material , thermodynamics
In many applications where the efficient solution of large sparse linear systems of equations is required, a direct method is frequently the method of choice. Unfortunately, direct methods have a potentially severe limitation: as the problem size grows, the memory needed generally increases rapidly. However, the in‐core memory requirements can be limited by storing the matrix and its factors externally, allowing the solver to be used for very large problems. We have designed a new out‐of‐core package for the large sparse unsymmetric systems that arise from finite‐element problems. The code, which is called HSL _ MA78 , implements a multifrontal algorithm and achieves efficiency through the use of specially designed code for handling the input/output operations and efficient dense linear algebra kernels. These kernels, which are available as a separate package called HSL _ MA74 , use high‐level BLAS to perform the partial factorization of the frontal matrices and offer both threshold partial and rook pivoting. In this paper, we describe the design of HSL _ MA78 and explain its user interface and the options it offers. We also describe the algorithms used by HSL _ MA74 and illustrate the performance of our new codes using problems from a range of practical applications. Copyright © 2008 John Wiley & Sons, Ltd.