A fast hierarchical algorithm for three-dimensional capacitanceextraction
Weiping Shi; Jianguo Liu; Kakani, N.; Tiejun Yu
Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on
Volume 21, Issue 3, Mar 2002 Page(s):330 - 336
Digital Object Identifier 10.1109/43.986426
Summary:The authors present a new algorithm for computing the capacitance
of three-dimensional electrical conductors of complex structures. The
new algorithm is significantly faster and uses much less memory than
previous best algorithms and is kernel independent. The new algorithm is
based on a hierarchical algorithm for the n-body problem and is an
acceleration of the boundary element method (BEM) for solving the
integral equation associated with the capacitance extraction problem.
The algorithm first adaptively subdivides the conductor surfaces into
panels according to an estimation of the potential coefficients and a
user-supplied error bound. The algorithm stores the potential
coefficient matrix in a hierarchical data structure of size O(n),
although the matrix is size n2 if expanded explicitly, where
n is the number of panels. The hierarchical data structure allows the
multiplication of the coefficient matrix with any vector in O (n) time.
Finally, a generalized minimal residual algorithm is used to solve m
linear systems each of size n × n in O(mn) time, where m is the
number of conductors. The new algorithm is implemented and the
performance is compared with previous best algorithms for the k ×
k bus example. The new algorithm is 60 times faster than FastCap and
uses 1/80 of the memory used by FastCap. The results computed by the new
algorithm are within 2.5% from that computed by FastCap. The new
algorithm is 5 to 150 times faster than the commercial software QuickCap
with the same accuracy
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