Developing and Analyzing New Unconditionally Stable Finite Element Schemes for Maxwell’s Equations in Complex Media

2021 ◽  
Vol 86 (3) ◽  
Author(s):  
Yunqing Huang ◽  
Meng Chen ◽  
Jichun Li
Keyword(s):  
Finite Element ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Complex Media ◽  
Unconditionally Stable ◽  
Finite Element Schemes

Finite Element Analysis of Maxwell’s Equations in Dispersive Lossy Bi-Isotropic Media

2013 ◽  
Vol 5 (04) ◽  
pp. 494-509 ◽  
Author(s):  
Yunqing Huang ◽  
Jichun Li ◽  
Yanping Lin
Keyword(s):  
Finite Element ◽  
Existence And Uniqueness ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Practical Implementation ◽  
Element Analysis ◽  
Fully Discrete ◽  
Isotropic Media ◽  
Discrete Finite Element ◽  
Finite Element Schemes

AbstractIn this paper, the time-dependent Maxwell’s equations used to modeling wave propagation in dispersive lossy bi-isotropic media are investigated. Existence and uniqueness of the modeling equations are proved. Two fully discrete finite element schemes are proposed, and their practical implementation and stability are discussed.

scholarly journals Finite elements in computational electromagnetism

Acta Numerica ◽  
2002 ◽  
Vol 11 ◽  
pp. 237-339 ◽  
Author(s):  
R. Hiptmair
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Linear Model ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Differential Forms ◽  
Asymptotic Convergence ◽  
Discrete Differential Forms ◽  
Computational Electromagnetism ◽  
Finite Element Schemes

This article discusses finite element Galerkin schemes for a number of linear model problems in electromagnetism. The finite element schemes are introduced as discrete differential forms, matching the coordinate-independent statement of Maxwell's equations in the calculus of differential forms. The asymptotic convergence of discrete solutions is investigated theoretically. As discrete differential forms represent a genuine generalization of conventional Lagrangian finite elements, the analysis is based upon a judicious adaptation of established techniques in the theory of finite elements. Risks and difficulties haunting finite element schemes that do not fit the framework of discrete differential forms are highlighted.

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