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.

SUMMARYAlthough, the finite element method numerically is efficient it exhibits difficulties whenever the remeshing of the analysis domain must be performed. For such problems, utilizing meshless computation methods is very promising. But, their large computational cost, which arises from following a time-consuming process to find shape functions, is one of the most important factors limiting the use of these methods. In this paper, we introduce a direct approach, based on properties required for any shape function, to prepare the shape function and propose a new meshless method. The proposed method does not need any predetermined basis or weighting functions and can be performed faster and more efficiently. Another advantage of the introduced method is its capability to apply desirable changes to the shape function. Application of the proposed approach for electrostatic field computation and verification of the obtained results using theoretically known solution is also presented.

In this paper, a modified meshless method, one of the meshless numerical techniques that has recently emerged in the area of computational electromagnetics, is extended to time-domain electromagnetic modeling. In the space domain, the fields at the collocation points are expanded into a series of new Shepard functions which are suggested recently and are treated with a meshless method procedure. In comparison with the most traditional schemes of the meshless methods this approximation function has lower computational cost with same level of accuracy. Application of the method for electromagnetic field computation and verification of the obtained results using theoretically known solution is also presented.978-1-61284-757-3/11/$26.00 C2011 IEEE

SUMMARYAn improved truly meshless method is presented for three-dimensional (3D) electromagnetic problems. In the proposed method, the computational time for the construction of the introduced shape function is lower than the other meshless methods considerably. An efficient and stable nodal integration technique based on the Taylor series extension is also used in the proposed meshless method. Weak-form formulations adopted for creating discretized system equations of electrostatic and electromagnetic 3D problems are also presented. In the proposed fast truly meshless method, unlike in traditional meshless schemes where background mesh is utilized to compute integrals, nodal integration is used to avoid meshing. The numerical solutions for electrostatic and electromagnetic problems show that the presented method is a robust meshfree method and possesses better computational properties compared with traditional meshless methods.

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