Title: Space-time domain solutions of the wave equation by a non-singular boundary integral method and Fourier transform,
Abstract: The general space-time evolution of the scattering of an incident acoustic
plane wave pulse by an arbitrary configuration of targets is treated by
employing a recently developed non-singular boundary integral method to solve
the Helmholtz equation in the frequency domain from which the fast Fourier
transform is used to obtain the full space-time solution of the wave equation.
The non-singular boundary integral solution can enforce the radiation boundary
condition at infinity exactly and can account for multiple scattering effects
at all spacings between scatterers without adverse effects on the numerical
precision. More generally, the absence of singular kernels in the non-singular
integral equation confers high numerical stability and precision for smaller
numbers of degrees of freedom. The use of fast Fourier transform to obtain the
time dependence is not constrained to discrete time steps and is particularly
efficient for studying the response to different incident pulses by the same
configuration of scatterers. The precision that can be attained using a smaller
number of Fourier components is also quantified.