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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.

A compact substrate integrated waveguide (SIW) with open complementary split‐ring resonators (OCSRRs) loaded on the waveguide surface is proposed. The OCSRRs can be interpreted in terms of electric dipoles and they are good candidates to behave as electric scatterers. By loading OCSRRs on the waveguide surface, a forward‐wave pass‐band propagating below the waveguide cutoff frequency is generated. The resonance frequency of the OCSRRs is approximately half of the resonance frequency of the complementary split ring resonator (CSRR). Therefore, the electrical size of this particle is larger than the CSRRs and the OCSRRs are more appropriate for the SIW miniaturization. A bandpass response with a sharp rejection frequency band is obtained by properly manipulating the structure of the elements. By changing the orientation of the OCSRRs, two types of unit cell are proposed. Moreover, by resizing the OCSRRs, resonance frequency can be easily moved and the bandwidth can be tuned by the coupling between two OCSRRs. Compared with some other reported bandpass filters (BPFs) with SIW technique, the presented BPF has great improvements on size reduction and selectivity. To verify the methodology, two filters with center frequency of 5.5 GHz are designed and measured. The measured results are in good agreement with the simulated ones. © 2016 Wiley Periodicals, Inc. Int J RF and Microwave CAE 26:674–682, 2016.

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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.