A two-dimensional leapfrog node-based radial point interpolation meshless method for modeling nonmagnetized plasma

Abstract

In this paper, we introduce a two-dimensional (2-D) Node-based Meshless Radial Point Interpolation Method (RPIM) for modeling nonmagnetized plasma. The problem domain is firstly discretized by a set of electric field nodes (E-nodes) and a set of magnetic field nodes (H-nodes). E-nodes and H-nodes are defined in a manner similar to the point-matched time-domain finite-element method. With the RPIM scheme, the field variable at the node is interpolated by a scalar expansion function which combines radial basis function with monomial basis function. After some mathematical manipulations, the shape function of the node in the support domain is obtained. The field variables and corresponding spatial derivatives in field equations can be obtained analytically and the central finite-difference is used to approximate the time derivatives. The leapfrog RPIM meshless method formulations are then obtained. TM wave propagation in isotropic nonmagnetized plasma is simulated to validate the accuracy and efficiency of the proposed method.