Local Interaction Simulation Approach for the Acoustic Wave Equation with Perfectly Matched Layer

Abstract

The simulation of the acoustic wave equation is essential for a wide range of applications, but the complexity of the propagation medium presents significant challenges. These include addressing the infinite computational domain, which can be managed using absorbing boundary conditions, and handling interface conditions between different media. In this paper, we utilize the Local Interaction Simulation Approach (LISA) to simulate acoustic wave propagation, which is designed to accommodate complex interface geometries on a regular grid. In engineering applications, absorbing boundary conditions in LISA are typically implemented using the ALID method, which introduces a damping term that increases in the absorbing layer. Here, we propose integrating the Perfectly Matched Layer (PML) with LISA, a novel combination that has not been previously explored in the literature. We demonstrate that, despite the added complexity of PML due to its requirement for multiple auxiliary equations within the absorbing layer, it delivers superior performance and outperforms the ALID method in terms of effectiveness.