Explicit finite-difference time-domain method with perfectly matched layers for transient low-frequency eddy-current analysis

Abstract

The finite-difference time-domain (FDTD) method is a robust algorithm for the solution of high-frequency electromagnetic problems, but, unfortunately, the method has no counterpart in eddy-current analysis. Hence, the extension of FDTD to power frequencies is an attractive theoretical problem that could give rise to an entirely new methodology for low-frequency electromagnetics. In this paper, we introduce a general explicit FDTD algorithm for transient eddy-current problems. We perform a theoretical investigation of a nonstandard difference scheme, including the issues of stability and consistency. The study provides a class of explicit methods with varying properties and computational complexity. From these, we chose the DuFort-Frankel algorithm for its simplicity and efficiency. However, the most intricate issue for the application of an explicit scheme is the solution of the open boundary problem. Unlike conventional integral equation or forced truncation approaches, the free-space problem is successfully treated by using a specially designed perfectly matched layer (PML) for eddy currents. The explicit scheme within the conductors is, finally, efficiently combined with the free space-PML equations via the interface conditions.

Computational analysis of power frequency devices by a novel hybrid quasi-static finite difference–finite element technique

“…The power frequency counterpart of the, very effective in high frequencies, finite difference time domain method, i.e. the Dufort-Frankel finite difference scheme, appears to be quite attractive [5,6]. In contrast to Yee's algorithm, which discretizes Maxwell's curl equations and is based upon their symmetry, the Dufort-Frankel scheme directly applies non-standard finite difference approximations to the diffusion equation.…”

Explicit time integration of transient eddy current problems

“…Here, in the nonconductive regions the boundary element method (BEM) is applied for computing the air parts of the solution, corresponding to a magnetostatic Poisson problem [3]. As an alternative to the BEM, the use of an adapted Perfectly Matched Layer (PML) is proposed in [4]. In [5] and [6], the conductive and nonconductive regions are also treated differently.…”

Uma proposta para análise otimizada de correntes transitórias em materiais condutores.

“…Em [16] o autor apresenta um método explicito baseado no método das diferenças finitas no domínio do tempo fazendo uso da metodologia "Perfectly Matched Layers" (PML) para análise de transitórios de correntes induzidas em baixas freqüências. É feito um estudo sobre condições de estabilidade e consistência e também é analisada a aplicação do método em problemas 2-D e 3-D com auxílio do algoritmo DuFort-Frankel.…”