A cholesky-based SGM-MLFMM for stochastic full-wave problems described by correlated random variables

In this letter, the multilevel fast multipole method (MLFMM) is combined with the polynomial chaos expansion (PCE)-based stochastic Galerkin method (SGM) to stochastically model scatterers with geometrical variations that need to be described by a set of correlated random variables (RVs). It is demonstrated how Cholesky decomposition is the appropriate choice for the RVs transformation, leading to an efficient SGM-MLFMM algorithm. The novel method is applied to the uncertainty quantification of the currents induced on a rough surface, being a classic example of a scatterer described by means of correlated RVs, and the results clearly demonstrate its superiority compared to the non-intrusive PCE methods and to the standard Monte Carlo method

A Well-Scaling Parallel Algorithm for the Computation of the Translation Operator in the MLFMA

This paper investigates the parallel, distributed-memory computation of the translation operator with L + 1 multipoles in the three-dimensional Multilevel Fast Multipole Algorithm (MLFMA). A baseline, communication-free parallel algorithm can compute such a translation operator in O(L) time, using O(L-2) processes. We propose a parallel algorithm that reduces this complexity to O(log L) time. This complexity is theoretically supported and experimentally validated up to 16 384 parallel processes. For realistic cases, the implementation of the proposed algorithm proves to be up to ten times faster than the baseline algorithm. For a large-scale parallel MLFMA simulation with 4096 parallel processes, the runtime for the computation of all translation operators during the setup stage is reduced from roughly one hour to only a few minutes