A New Formulation for the Radiation Operator: Application to the Fast Computation of the Singular Value Decomposition

This paper proposes a new formula for the operator K given by the product of the radiation operator by its adjoint. The formula expresses K by means of a surface integral, extended to the boundary of the source domain, rather than a volume integral, extended to the whole source domain, as entailed by its mathematical definition. As a result, the computation of K becomes much less onerous than the computation based on its mathematical definition. An immediate application of the derived formula is the fast computation of the singular value decomposition of the radiation operator, through to the fast computation of K. Some possible implications of the derived formula for K are also discussed. Finally, numerical examples are provided as proof of the validity and effectiveness of the formula.