Wavelet-like bases for the fast solutions of second-kind integral equations
SIAM Journal on Scientific Computing
Extraction of circuit models for substrate cross-talk
ICCAD '95 Proceedings of the 1995 IEEE/ACM international conference on Computer-aided design
IES3: a fast integral equation solver for efficient 3-dimensional extraction
ICCAD '97 Proceedings of the 1997 IEEE/ACM international conference on Computer-aided design
A multiscale method for fast capacitance extraction
Proceedings of the 36th annual ACM/IEEE Design Automation Conference
Fast methods for extraction and sparsification of substrate coupling
Proceedings of the 37th Annual Design Automation Conference
Simulation Techniques and Solutions for Mixed-Signal Coupling in Integrated Circuits
Simulation Techniques and Solutions for Mixed-Signal Coupling in Integrated Circuits
A precorrected-FFT method for electrostatic analysis of complicated 3-D structures
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Comprehensive frequency-dependent substrate noise analysis using boundary element methods
Proceedings of the 2002 IEEE/ACM international conference on Computer-aided design
Model order reduction of linear networks with massive ports via frequency-dependent port packing
Proceedings of the 43rd annual Design Automation Conference
Analysis of large clock meshes via harmonic-weighted model order reduction and port sliding
Proceedings of the 2007 IEEE/ACM international conference on Computer-aided design
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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More aggressive design practices have created renewed interest in techniques for analyzing substrate coupling problems. Most previous work has focused primarily on faster techniques for extracting coupling resistances, but has offered little help for reducing the resulting resistance matrix, whose number of nonzero entries grows quadratically with the number of contacts. Wavelet-like methods have been applied to sparsifying the resistance matrix representing the substrate coupling, but the accuracy of the method is very sensitive to the particulars of the contact layout. In this paper we show that for the substrate problem it is possible to improve considerably on the wavelet-like methods by making use of the algorithmic structure common to the fast multipole and wavelet-like algorithms, but making judicious use of low-rank approximations. The approach, motivated by the hierarchical SVD algorithm, can achieve more than an order of magnitude better accuracy for commensurate sparsity, or can achieve much better sparsity at commensurate accuracy, when compared to the wavelet-like algorithm.