An Unconditionally Stable Radial Point Interpolation Meshless Method Based on the Crank–Nicolson Scheme Solution of Wave Equation

Abstract

A 2-D unconditionally stable radial point interpolation meshless method (RPIM) based on the Crank–Nicolson (CN) scheme is presented. The CN algorithm in the proposed method is applied to only one of the Maxwell equations. It leads to solving the second-order vector wave equation in the time domain. Therefore, only one electromagnetic field is implicitly updated at each iteration. Furthermore, the computational cost of the CN-RPIM scheme is lesser than the conventional RPIM. The Courant–Friedrichs–Lewy condition in the proposed vector wave equation method does not constrain the time step due to its implicit formulation. Moreover, the stability condition of the proposed method is investigated in this paper through its amplification matrix. A 2-D waveguide and a filter are used as examples to validate and to demonstrate the effectiveness and the accuracy of the proposed method. Numerical results are compared with those obtained by the explicit RPIM method and the conventional finite-difference time-domain method.