A spatial high-order hexahedral discontinuous Galerkin method to solve Maxwell’s equations in time domain

2006 ◽  
Vol 217 (2) ◽  
pp. 340-363 ◽  
Author(s):  
G. Cohen ◽  
X. Ferrieres ◽  
S. Pernet
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Time Domain ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
High Order

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

2015 ◽  
Vol 8 (1) ◽  
pp. 104-116
Author(s):  
Hongqiang Lu ◽  
Yida Xu ◽  
Yukun Gao ◽  
Wanglong Qin ◽  
Qiang Sun
Keyword(s):  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Time Domain ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Mesh Size ◽  
High Order ◽  
Solid Boundary ◽  
Complex Geometries ◽  
Two Dimensional

AbstractIn this paper, a DG (Discontinuous Galerkin) method which has been widely employed in CFD (Computational Fluid Dynamics) is used to solve the two-dimensional 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.

Implicit DG Method for Time Domain Maxwell’s Equations Involving Metamaterials

2015 ◽  
Vol 7 (6) ◽  
pp. 796-817 ◽  
Author(s):  
Jiangxing Wang ◽  
Ziqing Xie ◽  
Chuanmiao Chen
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Time Domain ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Fully Discrete ◽  
Integral Differential Equations ◽  
The Time Domain ◽  
Spatial Approximation

AbstractAn implicit discontinuous Galerkin method is introduced to solve the time-domain Maxwell’s equations in metamaterials. The Maxwell’s equations in metamaterials are represented by integral-differential equations. Our scheme is based on discontinuous Galerkin method in spatial domain and Crank-Nicolson method in temporal domain. The fully discrete numerical scheme is proved to be unconditionally stable. When polynomial of degree at most p is used for spatial approximation, our scheme is verified to converge at a rate of O(τ2+hp+1/2). Numerical results in both 2D and 3D are provided to validate our theoretical prediction.

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