A Low-Memory Implementation of Perfectly Matched Layers with Smooth-Varying Coefficients in Discontinuous Galerkin Time Domain Methods

Abstract

The perfectly matched layer (PML) is one of the most popular domain truncation techniques used in differential-equation based wave-type equation solvers. Practical implementations of PMLs often use smooth-varying attenuation coefficients to reduce the numerical reflection from PMLs and to reduce the thickness required for reaching a certain level of absorption. In discontinuous Galerkin time-domain (DGTD) methods, assigning smooth-varying coefficients calls for storing individual mass matrices for each mesh element, which significantly increases the memory-cost. This work proposes a memory-efficient implementation of smooth-varying PMLs in DGTD. A weight-adjusted approximation is applied to the mass matrices involved in the PML formulation, which yields a low memory-cost algorithm and maintains the high-order accuracy of DGTD. The proposed scheme has the same accuracy as the implementation of storing local mass matrices of each element, and provides a higher mesh flexibility and a smaller reflection than using a constant coefficient in each element.