scholarly journals Singular Value Decompositions for Single-Curl Operators in Three-Dimensional Maxwell's Equations for Complex Media

2015 ◽  
Vol 36 (1) ◽  
pp. 203-224 ◽  
Author(s):  
Ruey-Lin Chern ◽  
Han-En Hsieh ◽  
Tsung-Ming Huang ◽  
Wen-Wei Lin ◽  
Weichung Wang
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Three Dimensional ◽  
Singular Value ◽  
Complex Media ◽  
Singular Value Decompositions ◽  
Curl Operators

scholarly journals On the Coefficients of the Singularities of the Solution of Maxwell’s Equations near Polyhedral Edges

2016 ◽  
Vol 2016 ◽  
pp. 1-17 ◽  
Author(s):  
Boniface Nkemzi
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Numerical Approximation ◽  
Three Dimensional ◽  
Physical Domain ◽  
Two Dimensional ◽  
Explicit Formulas ◽  
Nonsmooth Domains ◽  
Crack Tips ◽  
Domains With Corners

The solution fields of Maxwell’s equations are known to exhibit singularities near corners, crack tips, edges, and so forth of the physical domain. The structures of the singular fields are well known up to some undetermined coefficients. In two-dimensional domains with corners and cracks, the unknown coefficients are real constants. However, in three-dimensional domains the unknown coefficients are functions defined along the corresponding edges. This paper proposes explicit formulas for the computation of these coefficients in the case of two-dimensional domains with corners and three-dimensional domains with straight edges. The coefficients of the singular fields along straight edges of three-dimensional domains are represented in terms of Fourier series. The formulas presented are aimed at the numerical approximation of the coefficients of the singular fields. They can also be used for the construction of adaptiveH1-nodal finite-element procedures for the efficient numerical treatment of Maxwell’s equations in nonsmooth domains.

Multi-Symplectic Wavelet Collocation Method for Maxwell’s Equations

2011 ◽  
Vol 3 (6) ◽  
pp. 663-688 ◽  
Author(s):  
Huajun Zhu ◽  
Songhe Song ◽  
Yaming Chen
Keyword(s):  
Collocation Method ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Time Integration ◽  
Three Dimensional ◽  
Numerical Dispersion ◽  
Splitting Scheme ◽  
Spatial Accuracy ◽  
Symplectic Scheme ◽  
Wavelet Collocation Method

AbstractIn this paper, we develop a multi-symplectic wavelet collocation method for three-dimensional (3-D) Maxwell’s equations. For the multi-symplectic formulation of the equations, wavelet collocation method based on autocorrelation functions is applied for spatial discretization and appropriate symplectic scheme is employed for time integration. Theoretical analysis shows that the proposed method is multi-symplectic, unconditionally stable and energy-preserving under periodic boundary conditions. The numerical dispersion relation is investigated. Combined with splitting scheme, an explicit splitting symplectic wavelet collocation method is also constructed. Numerical experiments illustrate that the proposed methods are efficient, have high spatial accuracy and can preserve energy conservation laws exactly.

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