Direct Time Integration of Maxwell's Equations in 2-D Dielectric Waveguides for Propagation and Scattering of Femtosecond Electromagnetic Solitons

1993 ◽  
Author(s):  
Peter M. Goorjian ◽  
Rose M. Joseph ◽  
Allen Taflove
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Time Integration ◽  
Dielectric Waveguides ◽  
Electromagnetic Solitons

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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