Compact and Stable Modeling of Partial Inductance and Reluctance
Matrices
Compact and Stable Modeling of Partial Inductance and Reluctance
Matrices
H. Li, V. Balakrishnan, C-K. Koh, and G. Zhong
In Proc. ASPDAC, Shanghai, PRC, January 2005
Abstract:
The sparsification of the reluctance matrix L^{-1} (where L
denotes the usual inductance matrix L) has been widely used in
several recent investigations to make the problem of simulation of
interconnects tractable. Although these sparsification techniques
work well in practice, the stability of these approximations has not
been established, i.e., the sparsified reluctance and inductance
matrices are not guaranteed to be positive-definite. In this work, we
propose a band matching method that enjoys two advantages: First, we
exploit the elegant structure of the inverse of banded matrices so as
to construct an approximate inductance matrix \tilde{L} whose band
entries match the band entries of original L, and whose inverse is a
banded matrix. This approach yields a compact representation
of both inductance and reluctance matrices. Second, we establish that
the compact approximant \tilde{L} is guaranteed to be
positive-definite. Simulation results show that our approach enjoys
an approximation accuracy that is comparable to that of existing
methods.
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