The Optimal Spatially-Smoothed Source Patterns for the Pseudospectral Time-Domain Method

TL;DR

This paper derives explicit conditions for optimal spatially-smoothed source patterns in the PSTD method, reducing aliasing errors by aligning with Pascal's triangle, and validates their effectiveness through multi-dimensional simulations.

Contribution

It introduces a novel analytical framework for designing optimal source patterns in PSTD, linking aliasing errors to Pascal's triangle for the first time.

Findings

Optimal source patterns significantly reduce aliasing errors.

Simulation results confirm the superior performance of the proposed patterns.

The method is effective in 1-D, 2-D, and 3-D PSTD simulations.

Abstract

Spatially-smoothed sources are often utilized in the pseudospectral time-domain (PSTD) method to suppress the associated aliasing errors to levels as low as possible. In this work, the explicit conditions of the optimal source patterns for these spanning sources are presented based on the fact that the aliasing errors are mainly attributed to the high spatial-frequency parts of the time-stepped source items and subsequently demonstrated to be exactly corresponding to the normalized rows of Pascal's triangle. The outstanding performance of these optimal sources is verified by the practical 1-D, 2-D and 3-D PSTD simulations and compared with that of non-optimal sources.