A high-order algorithm for time-domain scattering in three dimensions

The ubiquitous scattering of time-dependent waves in free-space exterior to bounded configurations is fundamental for numerous applications. Simulation of time-domain scattering in the unbounded exterior region, without artificial domain truncation, facilitates understanding of the wave propagation process in the entire exterior region. The space-time hyperbolic partial differential equation (PDE) for the unknown scalar scattered field in the free-space can be reformulated as a retarded surface integral equation (SIE) on the boundary of the configuration, using a retarded potential ansatz for the field. The unknown surface density in the ansatz satisfies the SIE, and hence the exterior scattering problem reduces to the SIE model. The weakly- or hyper-singular complexity of the SIE depends on the (Dirichlet/Neumann/Robin) condition on the boundary of the configuration in the PDE model. In this work, we develop a fully discrete high-order algorithm for efficient and stable simulation of the time-domain scattering weakly- and hyper-singular SIE models. Our algorithm is a hybrid of high-order convolution quadrature (CQ) discretization in time and spectrally accurate approximation in space. We demonstrate computational efficiency of the algorithm using a gallery of configurations with Dirichlet/Neumann/Robin boundary conditions, and compare with CQ-based benchmarks and recent results in the literature.