A boundary element procedure for 3D electromagnetic transmission problems with large conductivity
Publication date
2022-04-02
Document type
Forschungsartikel
Author
Organisational unit
Publisher
MDPI
Series or journal
Mathematics
ISSN
Periodical volume
10
Periodical issue
7
Article ID
1148
Peer-reviewed
✅
Part of the university bibliography
✅
Language
English
Keyword
Boundary element
Asymptotic expansion
Skin effect
Abstract
We consider the scattering of time-periodic electromagnetic fields by metallic obstacles, or the eddy current problem. In this interface problem, different sets of Maxwell equations must be solved both in the obstacle and outside it, while the tangential components of both electric and magnetic fields are continuous across the interface. We describe an asymptotic procedure, applied for large conductivity, which reflects the skin effect in metals. The key to our method is a special integral equation procedure for the exterior boundary value problems corresponding to perfect conductors. The asymptotic procedure leads to a great reduction in complexity for the numerical solution, since it involves solving only the exterior boundary value problems. Furthermore, we introduce a FEM/BEM coupling procedure for the transmission problem and consider the implementation of Galerkin’s elements for the perfect conductor problem, and present numerical experiments.
Description
This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Version
Published version
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