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An efficient analyse phase for element problems
Author(s) -
Hogg Jonathan D.,
Scott Jennifer A.
Publication year - 2013
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.1810
Subject(s) - solver , matrix (chemical analysis) , sparse matrix , factorization , finite element method , element (criminal law) , phase (matter) , computer science , linear system , algorithm , mathematics , algebra over a field , computational science , mathematical optimization , mathematical analysis , pure mathematics , computational chemistry , chemistry , materials science , physics , organic chemistry , political science , law , composite material , gaussian , thermodynamics
SUMMARY The analyse phase of a sparse direct solver for symmetrically structured linear systems of equations is used to determine the sparsity pattern of the matrix factor. This allows the subsequent numerical factorisation and solve phases to be executed efficiently. Many direct solvers require the system matrix to be in assembled form. For problems arising from finite element applications, assembling and then using the system matrix can be costly in terms of both time and memory. This paper describes and implements a variant of the work of Gilbert, Ng and Peyton for matrices in elemental form. The proposed variant works with an equivalent matrix that avoids explicitly assembling the system matrix and exploits supervariables. Numerical experiments using problems from practical applications are used to demonstrate the significant advantages of working directly with the elemental form. Copyright © 2012 John Wiley & Sons, Ltd.