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

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Abstract
In this article, the capacitance matrices of three‐dimensional conducting structures embedded in a stratified dielectric medium are computed by using the fast muitipole 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.

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