An Adaptive Radial Point Interpolation Meshless Method for Simulation of Electromagnetic and Optical Fields

Abstract

This paper is going to handle an adaptive meshless method by which a wide range of microwave problems in terms of frequency are numerically solved whose accuracy and computational time are acceptable with respect to some other numerical schemes. As the origin, in the process of imposing the conventional radial point interpolation method (CRPIM) to laser problems, a special function was found, which results in a well-behaved basis function for CRPIM. This basis function possesses two fundamental advantages in view of meshless methods. At first, and in contradiction with conventional basis functions, the shape parameters are deterministic, which results in a higher accuracy than conventional basis functions. Second, it will construct the shape functions without any need for the middle matrix inversion step. Also, the adaptive basis function inherits the fundamental properties of fields. Hence, the computational time is reduced, approximately by half, comparing with the conventional basis functions. To investigate the proposed adaptive method named quantum radial point interpolation method in different areas of interest, it has been employed to solve three classes of partial differential equations in computational electromagnetics, i.e., Schrodinger's equation in a quantum wave laser, Laplace and electromagnetic wave equations. The results are more accurate and faster than the CRPIM and the finite-element method.