An approximate numerical solution for the general radiation problem by combining the method of wave superposition and the singular value decomposition

Abstract

In the method of wave superposition, the field due to an arbitrarily shaped radiator is written in terms of the sum of the fields due to a finite number of simple sources enclosed within the radiator. The strengths of the sources are determined by requiring that the sum of their individual fields reproduce the radiator's normal surface velocity at a finite number of locations either exactly or in the least square sense. Through the singular value decomposition (SVD), the dipole matrix, which relates the source strengths and normal surface velocities, can be written as a product of two unitary matrices and a real, diagonal matrix. Each of the unitary matrices represents a set of mutually orthogonal mode vectors, while the diagonal matrix represents the singular values associated with these modes. This decomposition is shown to contain the first N terms of the exact multipole expansion for the solution of the associated boundary value problem.