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Multilevel integral equation methods for the extraction of substrate coupling parameters in mixed-signal IC's

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2 Author(s)
Chou, M. ; Dept. of Electr. Eng. & Comput. Sci., MIT, Cambridge, MA, USA ; White, J.

The extraction of substrate coupling resistances can be formulated as a first-kind integral equation, which requires only discretization of the two-dimensional contacts. However, the result is a dense matrix problem which is too expensive to store or to factor directly. Instead, we present a novel, multigrid iterative method which converges more rapidly than previously applied Krylov-subspace methods. At each level in the multigrid hierarchy, we avoid dense matrix-vector multiplication by using moment-matching approximations and a sparsification algorithm based on eigendecomposition. Results on realistic examples demonstrate that the combined approach is up to an order of magnitude faster than a Krylov-subspace method with sparsification, and orders of magnitude faster than not using sparsification at all.

Published in:

Design Automation Conference, 1998. Proceedings

Date of Conference:

19-19 June 1998