Recent advances in multiscale simulations: Wideband fast integral solver and domain decomposition method

Abstract

We propose the recent progress in fast integral multiscale simulations in our group in this contribution. Firstly, a wideband fast kernel independent fast solver is proposed. The equivalence sources on designed equivalence surface are introduced to obtain the nested low rank approximation. At the low to mid frequency, thanks to the nested low rank approximation, the computation complexity of the proposed nested equivalence source approximation is O(N), N is the number of unknowns; at the high frequency, the far interaction lists are separated into directions, in each directions, the number of equivalence sources is fixed, as a result, we can obtain O(N logN) computation complexity. Secondly, a domain decomposition method (DDM) based equivalence principle (EPA) algorithm with body of revolution (BoR) equivalence surface is proposed. Each subdomain is enclosed by the spheres, and the sphere surface is discretized with RWGs and BoR basis functions, the couplings of two subdomains can be evaluated efficiently with BoR method of moments (MoM). With the proposed DDM method, the memory can be reduced significantly, and more important, the large and ill-conditioning matrix equation can be solved efficiently.