Monte Carlo Methods for Partial Differential Equations With Applications to Electronic Design Automation by Wenjian Yu & Michael Mascagni

Author:Wenjian Yu & Michael Mascagni
Language: eng
Format: epub
ISBN: 9789811932502
Publisher: Springer Nature Singapore

7.2 Background

7.2.1 Review of the FRW Algorithm for Capacitance Extraction

The FRW method for calculating electrostatic capacitance is originated from expressing the electric potential of a point r as an integral of the potential on surface S enclosing r (Coz and Iverson 1992; Yu et al. 2013):

(7.1)

where P(r, r(1)) is called surface Green’s function and can be regarded as a probability density function with non-negative value. Therefore, is the statistical mean of , and can be calculated with a Monte Carlo (MC) procedure sampling S. The domain enclosed by S is called transition domain, and usually r is the center of the transition domain.

The problem of capacitance extraction is to calculate the capacitances related to a specified conductor (called master conductor). For master conductor i, a Gaussian surface Gi is constructed to enclose it. According to the Gauss theorem, the charge of conductor i

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