# High-order discretization of a stable time-domain integral equation for 3D acoustic scattering

## TL;DR

This paper introduces a high-order explicit time-domain integral equation method for 3D acoustic scattering, combining advanced spatial discretization and convolution splines to achieve high accuracy and stability.

## Contribution

It presents a novel high-order discretization scheme using Nyström methods and convolution splines for stable, accurate 3D acoustic scattering simulations.

## Key findings

- Achieved 5-9 digit accuracy in simulations
- Demonstrated stability up to 8th order
- Validated parameters for combined field formulation

## Abstract

We develop a high-order, explicit method for acoustic scattering in three space dimensions based on a combined-field time-domain integral equation. The spatial discretization, of Nystr\"om type, uses Gaussian quadrature on panels combined with a special treatment of the weakly singular kernels arising in near-neighbor interactions. In time, a new class of convolution splines is used in a predictor-corrector algorithm. Experiments on a torus and a perturbed torus are used to explore the stability and accuracy of the proposed scheme. This involved around one thousand solver runs, at up to 8th order and up to around 20,000 spatial unknowns, demonstrating 5-9 digits of accuracy. In addition we show that parameters in the combined field formulation, chosen on the basis of analysis for the sphere and other convex scatterers, work well in these cases.