I. Introduction
Surface integral equations, such as the electric field integral equation (EFIE), magnetic field integral equation (MFIE), or combined field integral equation (CFIE), are a popular choice to solve electromagnetic scattering and radiation problems. Standard discretizations via the boundary element method (BEM) lead, however, to dense system matrices, resulting in complexity for computing and storing system matrices as well as for the cost of a single matrix-vector product, where N is the number of unknowns. To reduce the computational complexity, a plethora of so-called fast methods has been developed, such as the fast multipole method (FMM) [1], multilevel fast multipole algorithm (MLFMA) [2], [3], the adaptive integral method (AIM) [4], panel clustering [5], multilevel matrix decomposition algorithm (MLMDA) [6], [7], or precorrected-FFT [8]. For electrically small problems, a popular choice is the adaptive cross approximation (ACA) compression of -matrices, first developed for scalar problems in [9] and later investigated for the EFIE [10], because it allows to purely algebraically construct and store -matrices [11], [12], [13] in complexity by suitably sampling the rows and columns of the matrices of the well-separated interactions. Lately, the ACA is also used in the context of -matrix representations [14], [15]. For an extensive discussion of low-rank matrix factorization methods, see [16].