A novel high-order time-domain scheme for three-dimensional Maxwell's equations

2006 ◽  
Vol 48 (6) ◽  
pp. 1123-1125 ◽  
Author(s):  
Zhi-Xiang Huang ◽  
Wei Sha ◽  
Xian-Liang Wu ◽  
Ming-Sheng Chen
Keyword(s):  
Time Domain ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Three Dimensional ◽  
High Order ◽  
High Order Time

scholarly journals Optimized Operator-Splitting Methods in Numerical Integration of Maxwell's Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Z. X. Huang ◽  
X. L. Wu ◽  
W. E. I. Sha ◽  
B. Wu
Keyword(s):  
Numerical Integration ◽  
Time Domain ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Operator Splitting ◽  
Splitting Methods ◽  
High Order ◽  
Numerical Results ◽  
Operator Splitting Methods ◽  
The Time Domain

Optimized operator splitting methods for numerical integration of the time domain Maxwell's equations in computational electromagnetics (CEM) are proposed for the first time. The methods are based on splitting the time domain evolution operator of Maxwell's equations into suboperators, and corresponding time coefficients are obtained by reducing the norm of truncation terms to a minimum. The general high-order staggered finite difference is introduced for discretizing the three-dimensional curl operator in the spatial domain. The detail of the schemes and explicit iterated formulas are also included. Furthermore, new high-order Padé approximations are adopted to improve the efficiency of the proposed methods. Theoretical proof of the stability is also included. Numerical results are presented to demonstrate the effectiveness and efficiency of the schemes. It is found that the optimized schemes with coarse discretized grid and large Courant-Friedrichs-Lewy (CFL) number can obtain satisfactory numerical results, which in turn proves to be a promising method, with advantages of high accuracy, low computational resources and facility of large domain and long-time simulation. In addition, due to the generality, our optimized schemes can be extended to other science and engineering areas directly.

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.

Sign in / Sign up

Export Citation Format

Share Document