Fast and Accurate Computation of Time-Domain Acoustic Scattering Problems with Exact Nonreflecting Boundary Conditions

TL;DR

This paper presents a fast, accurate method for simulating exterior wave equations using exact nonreflecting boundary conditions, involving analytic convolution kernels and a spectral-Galerkin solver, enabling efficient computation for complex scatterers.

Contribution

It introduces analytic convolution kernels for NRBCs and a boundary perturbation approach combined with a spectral-Galerkin solver for efficient wave simulation.

Findings

High-order accuracy demonstrated for NRBCs

Efficient evaluation of convolution kernels with O(N_t) complexity

Effective handling of general bounded scatterers

Abstract

This paper is concerned with fast and accurate computation of exterior wave equations truncated via exact circular or spherical nonreflecting boundary conditions (NRBCs, which are known to be nonlocal in both time and space). We first derive analytic expressions for the underlying convolution kernels, which allow for a rapid and accurate evaluation of the convolution with $O(N_t)$ operations over $N_t$ successive time steps. To handle the onlocality in space, we introduce the notion of boundary perturbation, which enables us to handle general bounded scatters by solving a sequence of wave equations in a regular domain. We propose an efficient spectral-Galerkin solver with Newmark's time integration for the truncated wave equation in the regular domain. We also provide ample numerical results to show high-order accuracy of NRBCs and efficiency of the proposed scheme.