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In this study, one of the most important destructive effects in end-pumped Nd:YAG laser, that is, thermal lensing is analyzed. Different partial differential equations, supplemented by suitable boundary conditions, are solved and joined to illustrate the fluctuations in laser Transverse Electromagnetic (TEM) mode. Because of no analytic demonstration of this effect, an efficient meshless method known as radial point interpolation meshless method (RPIM) is used to simulate the problem divided into two two-dimensional cases, that is, xz and yz planes so as to be graphically understandable. The results are in good agreement with measurement reports, and the RPIM shows better accuracy than FEM. [ABSTRACT FROM AUTHOR]

SUMMARY In this work, the application of Daubechies' scaling functions (DSFs) in computational engineering, particulary radial point interpolation meshless method (RPIM) in electromagnetic engineering, is studied. This analysis indicates some shortcomings of DSFs in computational engineering. In fact, the DSFs take the role of shape functions in RPIM, but they do not hold some general properties of shape functions. Modifying these shortcomings according to engineering requirements as time consumption rate, new scaling (shape) functions are derived, and testing them into two important classes of electromagnetic problems, that is, incident wave on dielectrics and scatterers, gives good agreement with exact solutions. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY An 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. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

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]