Acceleration of Volume Integral Equations Using Trimmed Multilevel Fast Multipole Algorithm

Abstract

The concept of trimmed tree structures for multilevel fast multipole algorithm (MLFMA), referred to as trimmed-MLFMA (T-MLFMA), is proposed for the solution of volume integral equations for the fast analysis of scattering from large, inhomogeneous objects, where the conventional MLFMA suffers from high number of iterations and matrix vector multiplication (MVM) of large matrices at each iteration. In T-MLFMA, thresholding and machine learning techniques are used to eliminate the redundant interactions as the iterations proceed. In particular, the converged basis function coefficients are estimated with a fully connected neural network and, together with the thresholding, the MLFMA tree structure is systematically pruned, and the resulting far-interaction matrix becomes sparser. As a result, both the number of iterations and the MVM time per iteration are dramatically reduced. Using only a group of small homogeneous dielectric spheres with different permittivity values at the training stage, we are able to show that scattering from large, highly inhomogeneous and fairly complex objects are solved accurately and significantly faster than the conventional MLFMA solution (up to 10 times).