On energy-stable and high order finite element methods for the wave equation in heterogeneous media with perfectly matched layers

2022/06/17 by Gustav Ludvigsson, Ludvigsson, Gustav, Kenneth Duru +3
Engineering · #Electromagnetic Simulation and Numerical Methods #Advanced Numerical Methods in Computational Mathematics #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2206.08507

Abstract

This paper presents a stable finite element approximation for the acoustic wave equation on second-order form, with perfectly matched layers (PML) at the boundaries. Energy estimates are derived for varying PML damping for both the discrete and the continuous case. Moreover, a priori error estimates are derived for constant PML damping. Most of the analysis is performed in Laplace space. Numerical experiments in physical space validate the theoretical results.

Related

• Efficient PML for the wave equation
• A stable decoupled perfectly matched layer for the 3D wave equation using the nodal discontinuous Galerkin method
• Perfectly matched layer for second-order time-domain elastic wave equation: formulation and stability
• Perfectly matched layers in time domain. A simple two-dimensional error analysis
• The role of numerical boundary procedures in the stability of perfectly matched layers