Signal-Theoretic Characterization of Waveguide Mesh Geometries for Models of Two--Dimensional Wave Propagation in Elastic Media

TL;DR

This paper uses signal theory to compare different 2D waveguide mesh geometries, finding that triangular meshes offer the best balance of accuracy and efficiency for wave propagation modeling.

Contribution

It introduces a signal-theoretic framework to analyze and compare 2D waveguide mesh geometries based on sampling efficiency and dispersion error.

Findings

Triangular meshes outperform square and hexagonal in accuracy and cost.

Signal theory provides a new perspective for mesh geometry analysis.

Triangular geometry offers optimal tradeoffs in 2D wave propagation models.

Abstract

Waveguide Meshes are efficient and versatile models of wave propagation along a multidimensional ideal medium. The choice of the mesh geometry affects both the computational cost and the accuracy of simulations. In this paper, we focus on 2D geometries and use multidimensional sampling theory to compare the square, triangular, and hexagonal meshes in terms of sampling efficiency and dispersion error under conditions of critical sampling. The analysis shows that the triangular geometry exhibits the most desirable tradeoff between accuracy and computational cost.