Application of a meshless method in electromagnetics

Abstract

Abstract-An improved meshless method is presented with an emphasis on the detailed description of this new computational technique and its numerical implementations by investigating the usefulness of a commonly neglected parameter in this paper. Two approaches to enforce essential boundary conditions are also thoroughly investigated. Numerical tests on a mathematical function is carried out as a means of validating the proposed method. It will be seen that the proposed method is more robust than the conventional ones. Applications in solving electromagnetic problems are also presented.Index Terms-Lagrange multiplier method, least squares method, meshless method, moving-least square approximants.

A Meshless Collocation Method Based on Radial Basis Functions and Wavelets

“…In regions and , the interpolation of the solution variable is the standard form of (4) and (1), respectively. To develop a general interpolation formula in region for the solution variable using both RBF's and wavelets, one begins with (6) To ensure that the required mathematical properties of the entire bases such as consistency and linear independence are retained, the bridging scale concept is used to modify the wavelets [5]. Thus, in region , (6) becomes (7) where is the modified wavelet based on bridging scales and is defined as (8) where .…”

“…2, is selected as the numerical example to validate and to demonstrate the advantages and shortcomings of the proposed method. The governing equations are (15) Three different methods, i.e., the proposed one, the element-free Galerkin (EFG) method [6], and the FE method are used to study this problem. For the convenience of performance comparisons, the same node distribution with a total number of 1236 nodes is used for all three methods.…”

The meshless radial point interpolation method for time-domain electromagnetics

“…In computational mechanics, RPIM was introduced in [3] and applied to electro-or magnetostatics, e.g. [4], [5]. An implementation for the collocation method in conjunction with wavelets was presented in [6].…”

Refinement computations of electromagnetic fields using FE and meshless methods

“…Therefore, it is highly desirable to explore methods which will alleviate, at least partly, the onerous mesh generation or adaptive updating process. Accordingly, many meshless methods, all of which originate from computational mechanics, have been proposed and proved to be very promising in the study of electromagnetic field problems [2]- [5]. Since the interpolation of meshless methods is based on a set of nodes, and a connectivity of elements is not required, they offer the flexibility of additions and deletions of a set of nodes, which may be distributed in the solution domain irregularly, with relative ease.…”