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.