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

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.

Citation
Chen, L., Ozakin, M. B., Ahmed, S., & Bagci, H. (2020). A Memory-efficient Implementation of Perfectly Matched Layer with Smoothly-varying Coefficients in Discontinuous Galerkin Time-Domain Method. IEEE Transactions on Antennas and Propagation, 1–1. doi:10.1109/tap.2020.3037651

Acknowledgements
This work is supported in part by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award No 2019-CRG8-4056 and in part by the KAUST Ali I. Al-Naimi Petroleum Engineering Research Center (ANPERC). The authors would like to thank the KAUST Supercomputing Laboratory (KSL) for providing the required computational resources.

Publisher
Institute of Electrical and Electronics Engineers (IEEE)

Journal
IEEE Transactions on Antennas and Propagation

DOI
10.1109/TAP.2020.3037651

arXiv
2006.02551

Additional Links
https://ieeexplore.ieee.org/document/9263382/https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=9263382

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