An Optimized CPML Formulation for High Order FVTD Schemes for CED

Abstract

Developing an optimal perfectly matched layer (PML) formulation is crucial for efficient CED calculations. This becomes imperative for higher order CED schemes. If a PML causes spurious back-reflection of waves into the computational domain, those waves will be evolved by the higher order scheme as if they are physical. We present a PML that is conformant in its collocation and discretization with second, third and fourth order finite volume time-domain (FVTD) schemes that preserve global divergence. We present optimal PML parameters for second, third and fourth order FVTD schemes based on a careful numerically-motivated, optimization. At each order of accuracy we have to repeat the optimization study in order to get the best performance. We find that with increasing order of accuracy we can achieve greater suppression of spuriously reflected waves from the PML layer, especially at late times. Taking the finite difference time-domain (FDTD) method as a baseline, our schemes show as much as three orders of magnitude improvement in the suppression of late time reflection of waves from the PML layer. The schemes rely on several newly-invented reconstruction strategies and a very novel Implicit Taylor ADER (Arbitrary accuracy DERivatives) predictor step. Riemann solvers provide the corrector step.