A direct integral-equation solver of linear complexity for large-scale 3D capacitance and impedance extraction

Authors

Wenwen Chai
Dan Jiao
Cheng-Kok Koh

Abstract

State-of-the-art integral-equation-based solvers rely on techniques that can perform a matrix-vector multiplication in O(N) complexity. In this work, a fast inverse of linear complexity was developed to solve a dense system of linear equations directly for the capacitance extraction of any arbitrary shaped 3D structure. The proposed direct solver has demonstrated clear advantages over state-of-the-art solvers such as FastCap and HiCap; with fast CPU time and modest memory consumption, and without sacrificing accuracy. It successfully inverts a dense matrix that involves more than one million unknowns associated with a large-scale on-chip 3D interconnect embedded in inhomogeneous materials. Moreover, we have successfully applied the proposed solver to full-wave extraction.

Comments

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Keywords

Capacitance, Computer aided design, Digital integrated circuits, Multiprocessing systems, Three dimensional

Date of this Version

January 2009

Published in:

Proceedings - Design Automation Conference (2009) 752-757;