A leap-frog meshless method with radial basis functions for simulating electromagnetic wave splitter and rotator

Abstract

In this paper, we develop a meshless method by using radial basis functions (RBFs) to solve time domain Maxwell’s equations resulting from simulating wave propagation in electromagnetic wave splitter and rotator devices. To simulate wave propagation in these devices, we introduce a perfectly matched layer (PML) to reduce the unbounded physical domain problem to a bounded domain problem. Using PML leads to a multi-physics problem with different governing equations in different subdomains, which makes the simulation quite challenging. By following the idea of leap-frog FDTD scheme, we develop the leap-frog RBF meshless method to solve these complicated coupled modeling equations. Extensive numerical results by using multiquadric RBF and Gaussian RBF are presented to demonstrate the effectiveness of our meshless method.