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国际多尺度计算工程期刊

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ISSN 打印: 1543-1649

ISSN 在线: 1940-4352

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Solving the 3D Maxwell Equations Near Conical Singularities by a Multiscale Strategy

卷 7, 册 5, 2009, pp. 419-429
DOI: 10.1615/IntJMultCompEng.v7.i5.40
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摘要

This article is concerned with the numerical solution of the time-dependent Maxwell equations in a three-dimensional domain that contains (sharp metallic) conical protuberances. These conical inclusions on the internal boundary of the domain, typically a waveguide, are geometrical singularities that generate, in their neighborhood, strong electromagnetic fields. Based on recent theoretical and practical developments on curl-free singular fields, we propose a method to compute the instationary electromagnetic field, including the effects of these conical vertices. The principle is based on a splitting of the spaces of solutions into a regular part and a singular part. The regular part is computed by a continuous finite element method, whereas the singular part involves a multiscale representation of the solution, written in the vicinity of the geometrical singularities. As an illustration, numerical results in a rectangular waveguide and comparisons with an axisymmetric problem are shown.

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