A Memory-efficient Implementation of Perfectly Matched Layer with Smoothly-varying Coefficients in Discontinuous Galerkin Time-Domain Method

TL;DR

This paper introduces a memory-efficient implementation of PML with smoothly-varying coefficients in DGTD methods, reducing memory use while maintaining high accuracy and flexibility in wave simulations.

Contribution

It proposes a weight-adjusted approximation for mass matrices in PML, significantly lowering memory requirements without sacrificing performance.

Findings

Reduced memory footprint in DGTD PML implementation

Maintained high accuracy and low reflection in simulations

Enhanced meshing flexibility with variable coefficients

Abstract

Wrapping a computation domain with a perfectly matched layer (PML) is one of the most effective methods of imitating/approximating the radiation boundary condition in Maxwell and wave equation solvers. Many PML implementations often use a smoothly-increasing attenuation coefficient to increase the absorption for a given layer thickness, and, at the same time, to reduce the numerical reflection from the interface between the computation domain and the PML. In discontinuous Galerkin time-domain (DGTD) methods, using a PML coefficient that varies within a mesh element requires a different mass matrix to be stored for every element and therefore significantly increases the memory footprint. In this work, this bottleneck is addressed by applying a weight-adjusted approximation to these mass matrices. The resulting DGTD scheme has the same advantages as the scheme that stores individual mass matrices, namely higher accuracy (due to reduced numerical reflection) and increased meshing flexibility (since the PML does not have to be defined layer by layer) but it requires significantly less memory.