Perfectly matched anisotropic layer for the numerical analysis of unbounded eddy-current problems

Abstract

An extension of the perfectly matched layer (PML) technique in quasi-static fields is developed. The new lowfrequency PML is based on a fictitious medium with diagonal tensor anisotropy. On the basis of a theoretical investigation, the material properties of the anisotropic layer are specified, so that it will be reflectionless for an arbitrary eddy-current field that may exist in free space. Furthermore, the PML is designed in such a way that outgoing eddy-current fields are sufficiently absorbed. The effectiveness of the low-frequency PML is validated by the implementation of the finite-element solution of a simple two-dimensional eddy-current problem as well as a more complicated three-dimensional one.Index Terms-Eddy currents, edge elements, numerical methods, perfectly matched layers.

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

“…However, we can easily prove that both schemes are also inconsistent. Using (5) and (7), the coefficient of the wave term in the DuFort-Frankel case is proven to be (14) whereas a more severe inconsistency is observed in the case of the SSI method, i.e., (15) This indicates that the inclusion of the nonstandard difference terms in the SSI method has not been done in a way that improves its performance, since it aggravates rather than alleviates the inconsistency effect. This fact is graphically shown in Fig.…”

“…For larger problems, though, the method's robustness becomes questionable due to the presence of the dense matrix, which raises the computational requirements in a far-fromlinear manner as its size increases. In this study, we propose an algorithm based entirely on a differential equation formulation, making use of the PML for eddy-current problems [15]. In this case, a free-space buffer is required between the conductive domains and the PML, which inevitably gives rise to an exterior static problem and a corresponding sparse matrix solution.…”

“…2), is a diagonally anisotropic medium [15] with its relative magnetic permeability tensor given by (18) In finite-difference schemes, it is essential to reduce numerical dispersion introduced by abrupt material changes. For this reason, the smooth polynomial profile (19) is introduced for the PML coefficient, where is the PML's width, the -coordinate of its interface with free space, and the maximum transverse permeability value, which is to be appropriately chosen.…”

“…However, the most remarkable feature of the proposed technique, which facilitates its application to more realistic computational studies, is the development and employment of a specially designed perfectly matched layer (PML) for eddy-current problems. An anisotropic layer of this kind has been introduced in a recent paper [15] in conjunction with a finite-element method, while it seems that in this particular context of explicit methods, the PML attains its full potential, as demonstrated by the numerical applications-both two-and three-dimensional (2-D and 3-D).…”

Near-field performance analysis of locally-conformal perfectly matched absorbers via Monte Carlo simulations

“…The PML approach, based on either the Berenger's formulation or the anisotropic formulation, has been successfully applied in many other fields, e.g. acoustics [8,9]; elasticity [10,11]; linearized Euler equations [12,13]; eddy current problems [14]; and wave propagation in poroelastic media [15].…”