GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Mixed-signal switching noise analysis using Voronoi-tessellated substrate macromodels
DAC '95 Proceedings of the 32nd annual ACM/IEEE Design Automation Conference
Extraction of circuit models for substrate cross-talk
ICCAD '95 Proceedings of the 1995 IEEE/ACM international conference on Computer-aided design
Semi-analytical techniques for substrate characterization in the design of mixed-signal ICs
Proceedings of the 1996 IEEE/ACM international conference on Computer-aided design
Efficient techniques for accurate extraction and modeling of substrate coupling in mixed-signal IC's
DATE '99 Proceedings of the conference on Design, automation and test in Europe
A multigrid tutorial: second edition
A multigrid tutorial: second edition
Field Computation by Moment Methods
Field Computation by Moment Methods
Efficient techniques for accurate extraction and modeling of substrate coupling in mixed-signal IC's
DATE '99 Proceedings of the conference on Design, automation and test in Europe
A benchmark suite for substrate analysis
ASP-DAC '00 Proceedings of the 2000 Asia and South Pacific Design Automation Conference
On the interaction of power distribution network with substrate
ISLPED '01 Proceedings of the 2001 international symposium on Low power electronics and design
Characterizing Substrate Coupling in Deep-Submicron Designs
IEEE Design & Test
PARCOURS - Substrate Crosstalk Analysis for Complex Mixed-Signal-Circuits
PATMOS '00 Proceedings of the 10th International Workshop on Integrated Circuit Design, Power and Timing Modeling, Optimization and Simulation
Substrate model extraction using finite differences and parallel multigrid
Integration, the VLSI Journal
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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.