Discontinuous Galerkin Method for the Time-domain Maxwell’s Equations

2003 ◽  
pp. 153-158
Author(s):  
Adour V. Kabakian ◽  
Vijaya Shankar ◽  
William F. Hall
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Time Domain ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
The Time Domain

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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