Eigenvalue branches of the perturbed Maxwell operator M+λD in a gap of σ(M)

2008 ◽  
Vol 49 (11) ◽  
pp. 113508
Author(s):  
Dong Miao
Keyword(s):  
Maxwell Operator

scholarly journals The Maxwell operator with periodic coefficients in a cylinder

2018 ◽  
Vol 29 (6) ◽  
pp. 997-1006
Author(s):  
N. Filonov ◽  
A. Prokhorov
Keyword(s):  
Periodic Coefficients ◽  
Maxwell Operator

Mixed Discontinuous Galerkin Approximation of the Maxwell Operator

2004 ◽  
Vol 42 (1) ◽  
pp. 434-459 ◽  
Author(s):  
Paul Houston ◽  
Ilaria Perugia ◽  
Dominik Schotzau
Keyword(s):  
Discontinuous Galerkin ◽  
Galerkin Approximation ◽  
Maxwell Operator

scholarly journals Analysis of a hybridizable discontinuous Galerkin method for the Maxwell operator

2019 ◽  
Vol 53 (1) ◽  
pp. 301-324 ◽  
Author(s):  
Gang Chen ◽  
Jintao Cui ◽  
Liwei Xu
Keyword(s):  
Discontinuous Galerkin ◽  
Maxwell Equations ◽  
Numerical Solutions ◽  
Special Treatment ◽  
Optimal Order ◽  
General Regularity ◽  
Maxwell Operator ◽  
Low Regularity ◽  
Hybridizable Discontinuous Galerkin ◽  
Theoretical Results

In this paper, we study a hybridizable discontinuous Galerkin (HDG) method for the Maxwell operator. The only global unknowns are defined on the inter-element boundaries, and the numerical solutions are obtained by using discontinuous polynomial approximations. The error analysis is based on a mixed curl-curl formulation for the Maxwell equations. Theoretical results are obtained under a more general regularity requirement. In particular for the low regularity case, special treatment is applied to approximate data on the boundary. The HDG method is shown to be stable and convergence in an optimal order for both high and low regularity cases. Numerical experiments with both smooth and singular analytical solutions are performed to verify the theoretical results.

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