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Parallel solution techniques for sparse linear systems in circuit simulation. (English) Zbl 1060.65036

Schilders, Wilhelmus H. A. (ed.) et al., Scientific computing in electrical engineering. Proceedings of the SCEE 2002 Conference, Eindhoven, The Netherlands, June 23–28, 2002. Berlin: Springer (ISBN 3-540-21372-4/hbk). Mathematics in Industry 4. The European Consortium for Mathematics in Industry., 112-119 (2004).
Summary: For solving sparse linear systems from circuit simulation whose coefficient matrices include a few dense rows and columns, a parallel Bi-CGSTAB algorithm with distributed Schur complement preconditioning is presented. The parallel efficiency of the solver is increased by transforming the equation system into a problem without dense rows and columns as well as by exploitation of parallel graph partitioning methods. The costs of local, incomplete LU decompositions are decreased by fill-in reducing reordering methods of the matrix and a threshold strategy for the factorization. The efficiency of the parallel solver is demonstrated with real circuit simulation problems on a PC cluster.
For the entire collection see [Zbl 1046.78001].

MSC:

65F10 Iterative numerical methods for linear systems
65F35 Numerical computation of matrix norms, conditioning, scaling
65Y05 Parallel numerical computation
65F50 Computational methods for sparse matrices
94C05 Analytic circuit theory
94C15 Applications of graph theory to circuits and networks

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