The meshless radial point interpolation method for time-domain electromagnetics

Abstract

Abstract-A meshless numerical technique based on radial point interpolation is introduced for electromagnetic simulations in time domain. The general class of meshless methods presents very attractive properties for addressing future challenges of electromagnetic modeling. Among the interesting aspects, the ability to handle arbitrary node distributions for conformal and multi-scale modeling can be mentioned first. Furthermore, the possibility of modifying the node distribution dynamically opens new perspectives for adaptive computations and optimization. The mathematical background of the radial point interpolation method and a two-dimensional implementation are presented here. The advantages of this meshless method are discussed and applied to a model consisting of a 90 degree H-plane waveguide bend. It is shown that solutions converge much faster using the ability of conformal modeling compared to a similar analysis in rectangular grids.

A 3-D Unconditionally Stable Laguerre-Rpim Meshless Method for Time-Domain Electromagnetic Computations

“…where r = (x, y, z) is the point of interest, r n (r) the radial basis function [9], p m (r) the monomial basis function, a n and b m the corresponding coefficients, N the number of nodes within the support domain ( Figure 1) of the interested point used for the interpolation, and M the order of the monomial basis.…”

“…After several times of transformation [9], the field quantity u(r) can be expressed by the nodal field value u n within the support domain as…”

“…where φ n (r) is the shape function of the nth node in the support domain [9]. Then the spatial derivation of the field function can be obtained…”

“…For TM-to-z waves, the time-domain Maxwell's equations can be discretized by applying (2) and (3). With the definition of E and H nodes, the field variables and corresponding spatial derivatives can be approximated while the central difference is still used to approximate the time derivatives; the resulting leapfrog meshless RPIM formulations are [9]:…”

“…It has the advantages of conformal modeling of arbitrary boundaries and capabilities of the multi-scale solutions. The RPIM meshless method was firstly applied to solving time-domain EM problems by Kaufmann et al [9]. Kaufmann et al also made detailed description of the conformal and multi-scale capabilities of the method [10,11].…”