Rapid pulse responses for scattering problems

Numerical computation of the field scattered from a body in two dimensions due to an incident plane pressure pulse is considered. In particular, we examine the process of inferring the scattered field due to one incident pulse given the scattered field due to another incident pulse. The objective is to develop an indirect method that avoids the potentially expensive direct solution of the problem. Our approach is based on a formula expressing the scattered field as a convolution of a kernel with the incident pulse profile. The most straightforward generalization of this formula to the discrete version of the scatterer problem used in numerical computations does not allow the kernel to be inferred from a single numerical experiment - a difficulty we call the multi-source problem. Preprocessing the incident pulses using simple interpolation formulas overcomes the multi-source problem giving an exact algorithm for computing the kernel. Selection of a sharp incident pulse (the Kronecker pulse) for the primary numerical experiment assures stability of this algorithm and permits extremely accurate prediction of the scattered fields for secondary incident pulses.