Efficient algorithm for solution of a scattering problem

Abstract

The scattering solution of an arbitrary-shape inhomogeneous scatter can be formulated as a scattering solution of N scatterers, each of whose scattered field is approximated by M harmonics. This results in an NM unknown problem. A previously developed recursive operator algorithm, now adapted for wave scattering problems, can be used to solve this N scatterer problem. It is shown that the computational time of such an algorithm scales N2M2P where P is the number of harmonics used in the translation formulas. The scattered field from the same arbitrary shape scatterer can also be conventionally solved by the method of moments, casting it into an N linear algebraic equation. The solution of the linear algebraic equation via Gauss' elimination will involve order N3 floating-point operations. Hence, the complexity of the recursive operator algorithm is of lower order than the method of moments. It is shown that the recursive operator algorithm is more efficient than the method of moments when the number of unknowns is large.