Fast-factorization acceleration of MoM domain-decomposition: SFX-AIM and general

Domain-decomposition (DD) for Integral Equation can be achieved by aggregating standard basis functions into specialized basis functions on each sub-domain; this results in a strong compression of the MoM matrix, which allows an iteration-free (e.g. LU decomposition) solution also for electrically large problems. Fast matrix-vector product algorithms can be used in the matrix filling and compression process of the employed aggregate-functions approach. In this paper we propose and demonstrate the use of the Adaptive Integral Method (AIM) fast factorization to accelerate the Synthetic Function eXpansion (SFX) DD approach. The method remains iteration-free, with a significant boost in memory and time performances, with analytical predictions of complexity scalings confirmed by numerical results. At a more general level, the complexity scaling of both stand-alone DD and its combined use with fast MoM is addressed analytically and discussed with respect to known literature accounts of various implementations of the DD paradigm, with non-obvious results and practical indications.