Multi-Symplectic Wavelet Collocation Method for Maxwell's Equations (Advances in Applied Mathematics and Mechanics, 2021)
In 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 functionsis applied for spatial discretization and appropriate symplectic scheme is employedfor time integration. Theoretical analysis shows that the proposed method ismulti-symplectic, unconditionally stable and energy-preserving under periodicboundary conditions. The numerical dispersion relation is investigated. Combinedwith splitting scheme, an explicit splitting symplectic wavelet collocation methodis also constructed. Numerical experiments illustrate that the proposed methods areefficient, have high spatial accuracy and can preserve energy conservation laws exactly.