Abstract
Potential difficulties appears with various physical and engineering problems where functions satisfy a given partial differential equations and particular boundary conditions. From problems which are time independent and involve only space coordinates, one- dimensional examples and bidimensional diffusion equations are studied using two meshless methods: Element Free Galerkin (EFG) and Improved Element free Galerkin(IEFG).These two methods give good results when compared with analytical solution, but IEFG method based on IMLS approximation is in a higher computing speed and precision.
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References
Belytschko, T., Krongauz, Y., Organ, D.: Meshless methods: An overview and recent developments. Computer Methods in Applied Mechanics and Engineering 139, 3–47 (1996)
Liew, K.M., Ng, T., Yand Wu, Y.C.: Meshfree method for large deformation analysis–a reproducing kernel particle approach. Engineering Structure 24, 543–551 (2002)
Atluri, S.N., Zhu, T.: A new meshless local Petrov–Galerkin (MLPG) approach in computational mechanics. Computational Mechanics 22, 117–127 (1998)
Belytschko, T., Lu, Y.Y., Gu, L.: Element-free Galerkin methods. International Journal for Numerical Methods in Engineering 37, 229–256 (1994)
Onarte, E.: A finite point method in computational mechanics. International Journal for Numerical Methods in Engineering 39, 3839–3866 (1996)
Liu, W.K., Chen, Y., Uras, R.A., Chang, C.T.: Generalized multiple scale reproducing kernel particle. Computer Methods in Applied Mechanics and Engineering 139, 91–158 (1996)
Zhang, Z.: Improved element-free Galerkin method for two-dimensional potential problems. Engineering Analysis with Boundary Elements 33, 547–554 (2009)
Liew, K.M., Yumin, C.: Boundary element-free method (BEFM) and its application to two-dimensional elasticity problems. International Journal for Numerical Methods in Engineering 65(8), 1310–1332 (2006)
Lancaster, P., Salkauskas, K.: Surface generated by moving least squares methods. Mathematics of Computation 37, 141–158 (1981)
Hongping Ren, Y.: Cheng The interpolating element-free Galerkin (IEFG) method for two-dimensional potential problems. Engineering Analysis with Boundary Elements 36, 873–880 (2012)
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Debbabi, I., sendi, Z., Salah, H.B. (2015). Element Free and Improved Element Free Galerkin Methods for One and Two-Dimensional Potential Problems. In: Chouchane, M., Fakhfakh, T., Daly, H., Aifaoui, N., Chaari, F. (eds) Design and Modeling of Mechanical Systems - II. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-17527-0_20
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DOI: https://doi.org/10.1007/978-3-319-17527-0_20
Publisher Name: Springer, Cham
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