Unconditionally stable improved meshless methods for electromagnetic time-domain modeling

Abstract

Purpose– In this paper, a modified meshless method, as one of the numerical techniques that has recently emerged in the area of computational electromagnetics, is extended to solving time-domain wave equation. The paper aims to discuss these issues.Design/methodology/approach– In space domain, the fields at the collocation points are expanded into a series of new Shepard's functions which have been suggested recently and are treated with a meshless method procedure. For time discretization of the second-order time-derivative, two finite-difference schemes, i.e. backward difference and Newmark-βtechniques, are proposed.Findings– Both schemes are implicit and always stable and have unconditional stability with different orders of accuracy and numerical dispersion. The unconditional stability of the proposed methods is analytically proven and numerically verified. Moreover, two numerical examples for electromagnetic field computation are also presented to investigate characteristics of the proposed methods.Originality/value– The paper presents two unconditionally stable schemes for meshless methods in time-domain electromagnetic problems.