Integral methods for the solution of eddy current problems are very appealing since they avoid the meshing of the insulating regions. Yet, their main shortcoming is that they require the assembly and storage of a fully populated stiffness matrix K. To reduce the memory footprint and to enable a fast matrix construction, low-rank approximations techniques-like the Adaptive Cross Approximation (ACA)-have been considered a major breakthrough in the field. This paper presents a novel family of compression techniques that is enabled by a novel explicit factorization of the inductance matrix. Such a novel family exhibits orders of magnitude speedup and memory consumption with respect to state-of-the-art techniques. In particular, the aim of this paper is to compare for the first time the memory occupation, computation time and accuracy of the solution obtained with different compression techniques.
