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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v7.i5.40
pages 419-429

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

Franck Assous
Ariel University Center, 40700 Ariel, Israel; Bar-Ilan University, 52900 Ramat-Gan, Israel
Patrick Ciarlet, Jr.
ENSTA, 75739, Paris Cedex 15, France

ABSTRACT

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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