Multipole‐accelerated capacitance computation for 3‐D structures in a stratified dielectric medium using a closed‐form Green's function

Abstract

In this article, the capacitance matrices of three-dimensional conducting structures embedded in a stratified dielectric medium are computed by using the fast multipole method in conjunction with a closed-form approximation of the appropriate Green's function. Image charges that result from the employment of this Green's function are incorporated into the fast multipole method. This technique is used to accelerate the iterative generalized minimal residual-based solution of the system of equations generated by the method of moments. This yields the charge distributions on the conductors and thereby the required capacitance matrix. It is shown that the use of this technique typically results in a speedup of more than an order of magnitude over iterative and direct methods without a compromise of the numerical accuracy. 0 1995 John Wiley & Sons, Inc.

Forward‐backward method with a spectral acceleration algorithm for capacitance extraction of planar structures on a single‐layered medium

“…Lu et al presented active inductors for the circuit implementation to realize area reduction [6]. Scardelletti et al proposed a miniaturized power divider and quarter-wave transmission line was shortened using capacitive loading [7]. Based on the method of Scardelletti et al, a miniaturized power divider using capacitive loading has been designed, fabricated, and tested in our group [8,9].…”

“…The capacitance extraction problems in three-dimensional (3-D) planar structures have been studied extensively [1][2][3][4][5][6][7][8][9][10]. The method of moments (MM) has been employed directly in the capacitance calculation of conducting plates locating on a single-layered substrate [1].…”

The Fast Multipole Algorithm for Analysis of Large-Scale Microstrip Antenna Arrays

“…The other approach is to combine FMM with DCIM [10][11][12][13]. In [10] and [11], which treat the static and two-dimensional (2-D) problems, the equivalent problem is set up by adding images at the corresponding complex coordinates, and therefore, represented by basis functions. In the FMM implementation, the translation is different for different images.…”

Fast Capacitance Extraction for Finite Planar Periodic Structures Using the Generalized Forward-Backward and Novel Spectral Acceleration Method

“…There are several methods to accelerate the calculation of these problems [3][4][5][6][7][8][9][10][11][12][13][14]. One of them is the forward-backward (FB) method [12] illustrating an O(N 2 ) matrixvector multiplication calculation time per iteration, where N is the number of unknowns.…”

“…Capacitance extraction problems in three-dimensional structures have been studied extensively [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. There are several methods to accelerate the calculation of these problems [3][4][5][6][7][8][9][10][11][12][13][14].…”