An efficient algorithm for time-domain acoustic scattering in three dimensions by layer potentials

In this paper, we develop a simple and fast algorithm for the time-domain acoustic scattering by a sound-soft or an impedance obstacle in three dimensions. We express the solution to the scattering problem by layer potentials, and then a time-domain boundary integral equation is derived. To numerically solve the resulting boundary integral equation, we propose a full discretization scheme by combining the convolution splines with a Galerkin method. In time, we approximate the density in a backward manner in terms of the convolution splines. In space, we project the density at each time onto the space of spherical harmonics, and then use the spatial discretization of a Nyström type on the surface of an obstacle which is homeomorphic to a sphere. A gallery of numerical examples are presented to show the efficiency of our algorithm. The stability, convergence and accuracy of the algorithm are discussed. •We develop an efficient algorithm for the time-domain acoustic obstacle scattering in three dimensions.•We propose a full discretization scheme by combining the convolution splines with a Galerkin method.•The stability, convergence and accuracy of the algorithm are discussed.