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A 3-D Discontinuous Spectral Element Time-Domain Method for Maxwell's Equations

A discontinuous spectral element time-domain method is proposed to analyze transient electromagnetic properties of general 3-D structures. This method is advantageous in that its mass matrices are block-diagonal due to the Gauss-Lobatto-Legendre polynomials, and it allows different orders of basis functions for each subdomain. The Riemann solver is employed in the boundary integral terms to communicate fields between adjacent subdomains. Perfectly matched layers are utilized to truncate the computational domain. Galerkin method is used for spatial discretization, and a fourth-order Runge-Kutta scheme is employed for the time integration. The validity of the proposed approach is demonstrated through several numerical examples of initial value problems and scattering problems.