Title :
Highly accurate fast methods for extraction and sparsification of substrate coupling based on low-rank approximation
Author :
Kanapka, J. ; White, J.
Author_Institution :
MIT, Cambridge, MA, USA
Abstract :
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.
Keywords :
approximation theory; circuit layout CAD; circuit simulation; integrated circuit layout; integrated circuit modelling; mixed analogue-digital integrated circuits; singular value decomposition; sparse matrices; substrates; IC substrates; accurate fast methods; algorithmic structure; contact layout; extraction; hierarchical SVD algorithm; low-rank approximations; resistance matrix; sparsification; substrate coupling problems; Analog computers; Computational modeling; Conductivity; Contact resistance; Coupling circuits; Interference; Mixed analog digital integrated circuits; Permission; Signal design; Sparse matrices;
Conference_Titel :
Computer Aided Design, 2001. ICCAD 2001. IEEE/ACM International Conference on
Conference_Location :
San Jose, CA, USA
Print_ISBN :
0-7803-7247-6
DOI :
10.1109/ICCAD.2001.968661