A near-field preconditioner preserving the low-rank representation of method of moments interaction matrices

A preconditioning methodology is proposed to preserve the low-rank representation of Method-of-Moments interaction matrix blocks in the context of multiple-scattering-based Macro Basis Function methodology. The scatterer is divided into sub-domains that can be connected with each other. A low-rank representation is obtained by employing the incomplete QR factorization without constructing the interaction matrix blocks a priori. Performing compression before preconditioning allows one to change at will the preconditioning technique. The preconditioning considered in this study is based on nearest interactions and involves auxiliary sub-domains which are immediately connected with the sub-domain of interest and partially overlap neighboring sub-domains. Low-rank representation of the interaction matrices is preserved by dealing with the auxiliary sub-domains separately. This approach comes at the cost of an overhead in terms of memory, which is directly connected with the size of the auxiliary sub-domain.