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This communication presents a novel transient meshless formulation for analyzing wave propagation through linear dispersive materials. Many real materials are linear dispersive; thus, their constitutive parameters are not constant and change with frequency. However, the conventional numerical techniques are not proper tools for numerical analysis of dispersive materials, considering that they are formulated based on the assuming constant constitutive parameters for the materials. Therefore, until now, a number of numerical techniques have been proposed for modeling frequency behavior of dispersive materials. On the other hand, meshless methods are new and powerful numerical techniques which their capability in simulating the problem domain without using connection information among nodes makes them efficient techniques for modeling problems with complex geometries. In this communication, we have demonstrated that by incorporating some approaches into the meshless methods, we can turn them into suitable tools for modeling dispersive media. In order to obtain a meshless analysis of a dispersive medium, we have considered the scalar radial basis function meshless method, and for taking the frequency behavior of the medium into account, the auxiliary differential equations method has been used. Hence, the proposed dispersive meshless method not only models the frequency behavior of the dispersive materials but also provides more flexibility in simulating problems with complex geometries. In addition, the efficiency and accuracy of our proposed method are investigated by two numerical examples. [ABSTRACT FROM PUBLISHER]

This paper is going to handle an adaptive meshless method by which a wide range of microwave problems in terms of frequency are numerically solved whose accuracy and computational time are acceptable with respect to some other numerical schemes. As the origin, in the process of imposing the conventional radial point interpolation method (CRPIM) to laser problems, a special function was found, which results in a well-behaved basis function for CRPIM. This basis function possesses two fundamental advantages in view of meshless methods. At first, and in contradiction with conventional basis functions, the shape parameters are deterministic, which results in a higher accuracy than conventional basis functions. Second, it will construct the shape functions without any need for the middle matrix inversion step. Also, the adaptive basis function inherits the fundamental properties of fields. Hence, the computational time is reduced, approximately by half, comparing with the conventional basis functions. To investigate the proposed adaptive method named quantum radial point interpolation method in different areas of interest, it has been employed to solve three classes of partial differential equations in computational electromagnetics, i.e., Schrodinger’s equation in a quantum wave laser, Laplace and electromagnetic wave equations. The results are more accurate and faster than the CRPIM and the finite-element method. [ABSTRACT FROM PUBLISHER]

Although, 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. Copyright © 2010 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: We present a new formulation to implement the complex frequency shifted-perfectly matched layer (CFS-PML) for boundary truncation in three-dimensional vector finite-element time-domain method applied to the vector wave equation. It is shown that the proposed method is highly absorptive to evanescent modes, when computing the wave interaction of elongated structures or sharp corners, and can improve the performance of the boundary truncation, significantly. The impact of the CFS-PML parameters on the reflection error is investigated and optimal choices of these parameters are derived. [Copyright &y& Elsevier]

In this paper, two implicit finite-element time-domain (FETD) solutions of the Maxwell equations are presented. The first time-dependent formulation employs a time-integration method based on the alternating-direction implicit (ADI) method. The ADI method is directly applied to the time-dependent Maxwell curl equations in order to obtain an unconditionally stable FETD approach, unlike the conventional FETD method, which is conditionally stable. A numerical formulation for the 3-D ADI-FETD method is presented. For stability analysis of the proposed method, the amplification matrix is derived. Investigation of the proposed method formulation shows that it does not generally lead to a tri-diagonal system of equations. Therefore, the Crank—Nicolson FETD method is introduced as another alternative in order to obtain an unconditionally stable method. Numerical results are presented to demonstrate the effectiveness of the proposed methods and are compared to those obtained using the conventional FETD method. [ABSTRACT FROM AUTHOR]