Simulation of multiscale structures using equivalence principle algorithm with grid-robust higher order vector basis

Abstract

In this paper, equivalence principle algorithm (EPA) with grid-robust higher order vector basis (GRHOVB) is proposed to solve the multiscale problems. The EPA is a kind of domain decomposition method which transforms the interaction of objects into the interaction between virtual equivalence surfaces. Compared with traditional Curvilinear Rao–Wilton–Glisson function, GRHOVB can be used on the equivalence surface to reduce the number of unknowns and also to improve the accuracy. The tap basis is utilized to deal with current continuity when the object is intercepted by an equivalence surface. The equations are simplified further to improve the tap basis scheme. Moreover, to accelerate the solution, multilevel fast multipole algorithm is utilized in EPA. Numerical results are shown to demonstrate the accuracy and efficiency of the proposed method.