2026-09-19T06:47:54Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/292362022-01-13T07:54:29Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Jacob White.
Kanapka, Joseph D. (Joseph Daniel), 1972-
Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2005-10-14T19:21:43Z
2005-10-14T19:21:43Z
2002
2002
http://hdl.handle.net/1721.1/29236
51540697
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2002.
Includes bibliographical references (p. 107-111).
Substrate coupling effects have had an increasing impact on circuit performance in recent years. As a result, there is strong demand for substrate simulation tools. Past work has concentrated on fast substrate solvers that are applied once per contact to get the dense conductance matrix G. We develop a method of using any underlying substrate solver a near-constant number of times to obtain a sparse approximate representation G [approximately equal to] QGwtQ' in a new basis. This method differs from previous matrix sparsification techniques in that it requires only a "black box" which can apply G quickly; it doesn't need an analytical representation of the underlying kernel or access to individual entries of G. The change-of-basis matrix Q is also sparse. For our largest example, with 10240 contacts, we obtained a Gwt with 130 times fewer nonzeros than the dense G (and Q more than twice as sparse as Gwt), with 20 times fewer solves than the naive method, and fewer than 4 percent of the QGwtQ' entries had relative error more than 10% compared to the exact G.
by Joseph Daniel Kanapka.
Ph.D.
111 p.
4134531 bytes
4134338 bytes
application/pdf
application/pdf
eng
Massachusetts Institute of Technology
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http://dspace.mit.edu/handle/1721.1/7582
Electrical Engineering and Computer Science.
Fast methods for extraction and sparsification of substrate coupling
Thesis
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<Abstract>Substrate coupling effects have had an increasing impact on circuit performance in recent years. As a result, there is strong demand for substrate simulation tools. Past work has concentrated on fast substrate solvers that are applied once per contact to get the dense conductance matrix G. We develop a method of using any underlying substrate solver a near-constant number of times to obtain a sparse approximate representation G [approximately equal to] QGwtQ' in a new basis. This method differs from previous matrix sparsification techniques in that it requires only a "black box" which can apply G quickly; it doesn't need an analytical representation of the underlying kernel or access to individual entries of G. The change-of-basis matrix Q is also sparse. For our largest example, with 10240 contacts, we obtained a Gwt with 130 times fewer nonzeros than the dense G (and Q more than twice as sparse as Gwt), with 20 times fewer solves than the naive method, and fewer than 4 percent of the QGwtQ' entries had relative error more than 10% compared to the exact G.</Abstract>
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