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Implementation of an efficient element-free Galerkin method for electromagnetic computation. (English) Zbl 1195.78080

Summary: The element-free Galerkin method (EFGM) is based, as the finite-element method, on an integral formulation. This method, requiring only a set of nodes distributed on the analysis area, employs the moving least squares (MLS) approximation for the construction of the shape functions. The main objective of this work is to determine the effects of some parameters such as the width of influence domain, the number of integration points and the weight function, on the approximated solution obtained by the EFGM. For this study, Poisson’s equation is considered. The weight function parameters are chosen so that the error falls down leading to a more accurate result.

MSC:

78M25 Numerical methods in optics (MSC2010)
78A55 Technical applications of optics and electromagnetic theory
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References:

[1] Nayroles, B.; Touzot, G.; Villon, P., Generalizing the finite element method: diffuse approximation and diffuse elements, Comput Mech, 10, 307-318 (1992) · Zbl 0764.65068
[2] Belytschko, T.; Lu, Y. Y.; Gu, L., Element-free Galerkin methods, Int J Numer Methods Eng, 37, 229-256 (1994) · Zbl 0796.73077
[3] Cingoski, V.; Miyamoto, N.; Yamashita, H., Element-free Galerkin method for electromagnetic field computations, IEEE Trans Magn, 34, 5, 3236-3239 (1998)
[4] Ho, S. L.; Yang, S.; Machado, J. M.; Wong, H. C., Appplication of meshless method in electromagnetics, IEEE Trans Magn, 37, 5, 3198-3202 (2001)
[5] Xuan, L.; Zeng, Z.; Shanker, B.; Udpa, L., Element-free Galerkin method for static and quasi-static electromagnetic field computation, IEEE Trans Magn, 40, 1, 12-20 (2004)
[6] Lu, Y. Y.; Belytschko, T.; Gu, L., A new implementation of the element free Galerkin method, Comput Methods Appl Mech Eng, 113, 397-414 (1994) · Zbl 0847.73064
[7] Lancaster, P.; Salkauskas, K., Surfaces generated by moving least squares methods, Math Comput, 37, 155, 141-158 (1981) · Zbl 0469.41005
[8] Dolbow, J.; Belytshko, T., An introduction to programming the meshless element free Galerkin method, Arch Comput Methods Eng, 5, 3, 207-241 (1998)
[9] Reddy, J. N., An introduction to finite element method (1993), McGraw-Hill, Inc: McGraw-Hill, Inc NewYork
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