Sparse Gaussian elimination with controlled fill-in on a shared memory multiprocessor
- Colorado Univ., Denver, CO (USA). Dept. of Electrical and Computer Engineering
- Colorado Univ., Boulder, CO (USA). Dept. of Electrical and Computer Engineering
During LU decomposition of a sparse matrix, it is possible to perform computation on many diagonal elements simultaneously. Pivots that can be processed in parallel are related by a compatibility relation and are grouped in a compatible set. The collection of all maximal compatibles yields different maximum sized sets of pivots that can be processed in parallel. Generation of the maximal compatibles is based on the construction of an incompatible table which gives information about pairs of incompatible pivots. The algorithm to generate all maximal compatibles involves a binary tree search and is exponential in the order of the matrix. A technique to obtain an ordered compatible set directly from the ordered incompatible table is given. The ordering is based on the Markowitz number of the pivot candidates. This technique generates a set of compatible pivots with the property of generating few fills. A new heuristic algorithm is presented that combines the idea of an ordered compatible set with a limited binary tree search to generate several sets of compatible pivots in linear time. An elimination set to reduce the matrix is generated and selected on the basis of a minimum Markowitz sum number. The parallel pivoting technique presented is a stepwise algorithm and can be applied to any submatrix of the original matrix. Parameters are suggested to obtain a balance between parallelism and fill-ins. Result of applying the proposed algorithms on several large application matrices using the HEP multiprocessor are presented and analyzed.
- OSTI ID:
- 5242913
- Journal Information:
- IEEE (Institute of Electrical and Electronics Engineers) Transactions on Computers; (USA), Journal Name: IEEE (Institute of Electrical and Electronics Engineers) Transactions on Computers; (USA) Vol. 38:11; ISSN ITCOB; ISSN 0018-9340
- Country of Publication:
- United States
- Language:
- English
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