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Local interaction simulation approach for the acoustic wave equation with perfectly matched layer

Tao Yu, Tailong Jin, Yanfeng Shen, Lei Zhang

Abstract

Simulation of the acoustic wave equation plays an important role in various applications, including audio engineering, medical imaging, and fluid dynamics. However, the complexity of the propagation medium can pose challenges, such as the infinite computing region and the interface conditions between different media. In this paper, we construct a method for simulating acoustic wave propagation based on the local interaction simulation approach (LISA) and the perfectly matched layer (PML). This method can simulate wave propagation in a finite computing region and overcome the smoothing process at the interface between different media. Numerical examples demonstrate the effectiveness of this approach.

Local interaction simulation approach for the acoustic wave equation with perfectly matched layer

Abstract

Simulation of the acoustic wave equation plays an important role in various applications, including audio engineering, medical imaging, and fluid dynamics. However, the complexity of the propagation medium can pose challenges, such as the infinite computing region and the interface conditions between different media. In this paper, we construct a method for simulating acoustic wave propagation based on the local interaction simulation approach (LISA) and the perfectly matched layer (PML). This method can simulate wave propagation in a finite computing region and overcome the smoothing process at the interface between different media. Numerical examples demonstrate the effectiveness of this approach.

Paper Structure

This paper contains 11 sections, 66 equations, 3 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Local Interaction Simulation Approach
  3. Continuity condition I:
  4. Continuity condition II:
  5. Perfectly Matched Layer
  6. PML formulation
  7. PML equation for $v$:
  8. PML equation for $u$
  9. PML system
  10. Second Order PML Method
  11. Numerical Experiments

Figures (3)

  • Figure 1: Graphical illustration of the cross point $P$ and other auxiliary points used in the derivation of LISA.
  • Figure 2: The snapshot of wave propagation without interface
  • Figure 3: The snapshot of wave propagation with interface

Theorems & Definitions (2)

  • Remark 1
  • Remark 2