3D Interpolation in Wave-Based Acoustic Simulation

In any acoustics simulation setting relying on computation over a spatial grid, interpolation of the acoustic field is essential in order to accurately model source and receiver positions. Most available approaches to 3D interpolation, such as those used in computer graphics or medical imaging, are based on polynomial or windowed-sinc designs. In this short contribution, it is shown that highly accurate optimised designs are available if particular features of acoustic wave propagation and numerical scheme design are incorporated: performance can be tuned to an acoustic wavenumber range of interest, taking into account numerical dispersion artefacts, and the interdependence of the solution to the acoustic wave equation at neighbouring time steps can be further exploited, leading to extremely compact locally-defined interpolation designs. Numerical results are presented.

I. Introduction

Wave-based acoustic simulation refers to the numerical solution of the acoustic wave equation over an enclosure. For volumetric time-domain methods, the acoustic field is represented over a grid in three dimensions. The finite difference time domain method (FDTD) is the most well-known method [1]–[4], but there are many other varieties [5]–[8]. Such methods are heavily used in virtual room and architectural acoustics [5], [7]–[11], environmental acoustics [12], and in ultrasound applications [13]–[15]. In most practical settings, the grid is chosen to be regular (often Cartesian), allowing for simplified algorithm design and opportunities for massive parallelisation.