Parallel solution of sparse linear systems on a vector multiprocessor computer. Master's thesis, August 1988-August 1990
This paper describes an efficient approach for solving sparse linear systems using direct method on a shared-memory vector multiprocessor computer. The direct method is divided into three steps: LU factorization, forward substitution and backward substitution. If the size of the linear system is large, LU factorization is a very time-consuming step, so that concurrency and vectorization are exploited to reduce execution time. Parallelism of LU factorization is obtained by partitioning the matrix using multilevel node-tearing techniques. The partitioned matrix is reordered into a NBBD (Nested Bordered-Block Diagonal) form. A nested-block data structure is used to store the sparse matrix, enabling the use of vectorization as well as multiprocessing to achieve high performance. This approach is suitable for many applications that require the repeated direct solution of sparse linear systems with identical matrix structure, such as circuit simulation. The approach has been implemented in a program that runs on an ALLIANT FX/8 vector multiprocessor with shared memory. Speedups in execution time compared to conventional serial computation with no vectorization are up to 20 using eight processors.
- Research Organization:
- Illinois Univ., Urbana, IL (USA). Coordinated Science Lab.
- OSTI ID:
- 6204751
- Report Number(s):
- AD-A-225377/1/XAB; UILU-ENG-90-2227; CNN: N00014-84-C-0149
- Resource Relation:
- Other Information: Thesis
- Country of Publication:
- United States
- Language:
- English
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