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DOI 10.5286/raltr.2008016
Persistent URL http://purl.org/net/epubs/work/43758
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Record Id 43758
Title Scaling and pivoting in an out-of-core sparse direct solver
Abstract Out-of-core sparse direct solvers reduce the amount of main memory needed to factorise and solve large sparse linear systems of equations by holding the matrix data, the computed factrors and some of the work arrays in files on disk. The efficiency of the factorization and solution phases is dependent upon the number of entries in the factors. For a given pivot sequence, the level of fill in the factors beyond that predicted on the basis of the sparsity pattern alone depends on the number of pivots that are delayed (that is, the number of pivots that are used later than expected because of numerical stability considerations). Our aim is to limit the number of delayed pivots, whilst maintaining robustness and accuracy. In this paper, we consider a new out-of-core multifrontal solver that is designed to solve efficiently the system of linear equations that arise from finite element applications. We consider how equilibration can be built into the solver without requiring the system matrix to be held in main memory. We also examine the effects of different pivoting startegies, including threashold partial pivoting, threashold rook pivoting and static pivoting. Numerical experiments are reported for problems arising from a range of practical applications.
Organisation CSE , CSE-NAG , STFC
Keywords scaling , partial pivoting , large sparse unsymmetric linear systems , element problems , multifrontal , out-of-core solver , rook pivoting
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Language English (EN)
Type Details URI(s) Local file(s) Year
Report RAL Technical Reports RAL-TR-2008-016. STFC, 2008. sRAL2008016.pdf 2008