Extracting surface macro basis functions from low-rank scattering operators with the ACA algorithm

The Adaptive Cross Approximation (ACA) algorithm has been used to compress the rank-deficient sub-blocks of the matrices that arise in the numerical solution of integral equations (IEs) with the Method of Moments. In the context of the linear embedding via Green’s operator (LEGO) method — a domain decomposition technique based on IEs — an electromagnetic problem is modelled by combining “bricks” in turn described by scattering operators which, in many situations, are singular. As a result, macro basis functions defined on the boundary of a brick can be generated by applying the ACA to a scattering operator. Said functions allow compressing the weak form of the LEGO functional equations which then use up less computer memory and are faster to invert.