Modification on a fast meshless method for electromagnetic field computations

Abstract

This study modifies and discusses the application of a complete meshless method based on Shepard approximation with an emphasis on the detailed description of this computational technique and its numerical implementations. A new weighting function would be suggested. The global shape function and its derivatives are built based only on the discretisation of the domain in nodes. To deal with the essential boundary condition problem, an alternative method has been proposed. The method is also capable of treating physical discontinuities present at interfaces between different matters. Application of proposed method for the electromagnetic field computation and verification of the obtained results using finite difference method and radial point interpolation method is also presented. The results demonstrate a good agreement between the proposed meshless method and other numerical techniques. So, an adequacy accuracy of this methodology can be concluded whereas the approximation functions have lower computational costs.

Unconditionally stable improved meshless methods for electromagnetic time-domain modeling

“…In proposed procedure which has been introduced in Razmjoo et al (2010aRazmjoo et al ( , b, 2011b, there is no need to do that; therefore, shape functions can be constructed faster. As mentioned, according to the data-fitting algorithm and PUM, a complete approach for constructing shape function of the meshless methods has been proposed, recently (Razmjoo et al, 2010a(Razmjoo et al, , 2011b. A new weighting function is suggested so that shape function derivatives can be obtained easily in analytical forms (not numerical).…”

“…However, its accuracy can be at the same level. This shape Improved meshless methods function would be used in this paper and for more details we refer readers to Razmjoo et al (2011b).…”

“…For this purpose, a recently proposed direct meshless method (Razmjoo et al, 2011b), which is based on a new shape function, was adopted to discretize the space and a forward difference method for time discretization was used. In this paper, we focus on the time discretization of the wave equation.…”

Review on Computational Electromagnetics

“…Point interpolation method, radial point interpolation method and Shepard approximat ion are few natural neighboring methods used to define shape function. The Shepard approximation help in achieving good accuracy and considerable computing time [54]. These problems are solved by expanding unknown field variab le over such shape function and also reduce number of unknowns.…”

Proposing a Wavelet Based Meshless Method for Simulation of Conducting Materials

“…Putting the properties of both scaling and shape functions together, it sounds possible to work on an idea that proposes the shape functions, directly. In fact, eliminating the MMIS is the target of above idea for direct meshless method [14]. Let propose the following class of functions as candidates for the aim which satisfy above scaling function and also shape function properties; this class is different than that of [15].…”