Development of Discontinuous-Galerkin-Based TSETD With Second-Order CFS-PML Scheme for Electromagnetic Simulations

This study presents a numerical approach for solving Maxwell's equations by combining the Discontinuous Galerkin Tetrahedral Spectral Element Time-Domain (DG-TSETD) method with a second-order complex frequency-shifted perfectly matched layer (2nd CFS-PML), facilitating electromagnetic wave simulations in 3D unstructured tetrahedral meshes and reducing the impact of wave reflections. Leveraging the DG-TSETD framework, this study utilizes high-order basis functions derived from Jacobi polynomials and transformations between tetrahedral and hexahedral elements to enable efficient integration-free calculations based on a central approximation that constructs optimized interpolation nodes to form a well-conditioned Vandermonde matrix, coupled with explicit time integration via a third-order Runge-Kutta scheme. Numerical simulations with an ellipsoid model demonstrate that the second-order CFS-PML outperforms the first-order CFS-PML in attenuating reflected waves for varying basis function orders. Additionally, we compare the computational expenses of first and second-order PMLs across various basis function orders, developing an effective computational strategy through performance trade-off analysis, offering theoretical and practical insights for time-domain electromagnetic simulations in 3D space.