Volume 8, Issue 1
A High-Order Discontinuous Galerkin Method for the Two-Dimensional Time-Domain Maxwell’s Equations on Curved Mesh

Hongqiang Lu, Yida Xu, Yukun Gao, Wanglong Qin & Qiang Sun

Adv. Appl. Math. Mech., 8 (2016), pp. 104-116.

Published online: 2018-05

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  • Abstract

In this paper, a DG (Discontinuous Galerkin) method which has been widely employed in CFD (Computational Fluid Dynamics) is used to solve the twodimensional time-domain Maxwell’s equations for complex geometries on unstructured mesh. The element interfaces on solid boundary are treated in both curved way and straight way. Numerical tests are performed for both benchmark problems and complex cases with varying orders on a series of grids, where the high-order convergence in accuracy can be observed. Both the curved and the straight solid boundary implementation can give accurate RCS (Radar Cross-Section) results with sufficiently small mesh size, but the curved solid boundary implementation can significantly improve the accuracy when using relatively large mesh size. More importantly, this CFD-based high-order DG method for the Maxwell’s equations is very suitable for complex geometries.

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@Article{AAMM-8-104, author = {Hongqiang Lu, Yida Xu, Yukun Gao, Wanglong Qin and Qiang Sun}, title = {A High-Order Discontinuous Galerkin Method for the Two-Dimensional Time-Domain Maxwell’s Equations on Curved Mesh}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {8}, number = {1}, pages = {104--116}, abstract = {

In this paper, a DG (Discontinuous Galerkin) method which has been widely employed in CFD (Computational Fluid Dynamics) is used to solve the twodimensional time-domain Maxwell’s equations for complex geometries on unstructured mesh. The element interfaces on solid boundary are treated in both curved way and straight way. Numerical tests are performed for both benchmark problems and complex cases with varying orders on a series of grids, where the high-order convergence in accuracy can be observed. Both the curved and the straight solid boundary implementation can give accurate RCS (Radar Cross-Section) results with sufficiently small mesh size, but the curved solid boundary implementation can significantly improve the accuracy when using relatively large mesh size. More importantly, this CFD-based high-order DG method for the Maxwell’s equations is very suitable for complex geometries.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2014.m642}, url = {http://global-sci.org/intro/article_detail/aamm/12079.html} }
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