A Novel Coupling Algorithm for Perfectly Matched Layer With Wave Equation-Based Discontinuous Galerkin Time-Domain Method

Abstract

The second-order wave equation-based discontinuous Galerkin time-domain (DGTD) methods typically employ the first-order absorbing boundary condition for modeling open problems. To improve the modeling accuracy, this paper proposes a novel coupling algorithm of the well-posed perfectly matched layer (PML) for wave equation-based DGTD methods. Based on the domain decomposition technique, the proposed coupling algorithm divides the computational domain into two regions, that is, the physical and PML regions, whose meshes can be nonconformal with each other. Instead of introducing time convolution terms, the new coupling scheme is implemented through employing different DGTD frameworks for the two regions. Specifically, the physical region employs the wave equation-based DGTD framework, while the PML region employs the first-order Maxwell’s curl equations-based DGTD framework. To facilitate modeling of electrically small problems, the implicit Newmark-beta time integration is used for the physical region. To conveniently couple with the physical region, the implicit Crank–Nicolson algorithm is used for the PML region. Numerical results are shown to examine the accuracy and efficiency of the proposed coupling algorithm for modeling electrically small problems.