GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Extraction of circuit models for substrate cross-talk
ICCAD '95 Proceedings of the 1995 IEEE/ACM international conference on Computer-aided design
Combined BEM/FEM substrate resistance modeling
Proceedings of the 39th annual Design Automation Conference
On Algorithms For Permuting Large Entries to the Diagonal of a Sparse Matrix
SIAM Journal on Matrix Analysis and Applications
Characterizing Substrate Coupling in Deep-Submicron Designs
IEEE Design & Test
A Novel Analytical Model for Evaluation of Substrate Crosstalk in VLSI Circuits
DELTA '02 Proceedings of the The First IEEE International Workshop on Electronic Design, Test and Applications (DELTA '02)
Substrate Coupling: Modeling, Simulation and Design Perspectives
ISQED '04 Proceedings of the 5th International Symposium on Quality Electronic Design
Substrate resistance extraction with direct boundary element method
Proceedings of the 2005 Asia and South Pacific Design Automation Conference
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Efficient techniques for accurate modeling and simulation of substrate coupling in mixed-signal IC's
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Fast and efficient parametric modeling of contact-to-substrate coupling
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
ASP-DAC '06 Proceedings of the 2006 Asia and South Pacific Design Automation Conference
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It is important to model the substrate coupling for mixed-signal circuit designs today. This paper presents an improved direct boundary element method (DBEM) for substrate resistance calculation, where only the boundary of substrate volumes is discretized and only the free-space Green function is used. At first, we discard some inessential unknowns to compress the linear system without accuracy loss. Then we make the coefficient matrix sparser. In this way, solving the linear system is greatly accelerated. Experiments on various substrates validate that DBEM is several to tens of times faster than DCT-accelerated Green's function methods and the eigendecomposition method, while preserving high accuracy. Besides, another experiment shows that this method is versatile for irregular substrates.