Reflectionless discrete perfectly matched layers for higher-order finite difference schemes

• DOI: 10.48550/arxiv.2306.13189
• Publication Date: 2023-01-01
• Authors: Vicente A. Hojas; Carlos Pérez-Aran...; Manuel A. Sánchez
• Keywords: Perfectly Matched Layer

This paper introduces discrete-holomorphic Perfectly Matched Layers (PMLs) specifically designed for high-order finite difference (FD) discretizations of the scalar wave equation. In contrast to standard PDE-based PMLs, proposed method achieves remarkable outcome completely eliminating numerical reflections at PML interface, in practice achieving errors level machine precision. Our approach builds upon ideas put forth a recent publication [Journal Computational Physics 381 (2019): 91-109] expanding scope from second-order FD arbitrary schemes. generalization uses additional localized variables accommodate larger stencils employed. We establish that solutions generated by our schemes exhibit an exponential decay rate as they propagate within domain. To showcase effectiveness method, we present variety examples, including waveguide problems. These examples highlight importance employing effectively address and minimize undesired dispersion errors, emphasizing practical advantages applicability approach.