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ARTICLE

MLPG Method for Transient Heat Conduction Problem with MLS as Trial Approximation in Both Time and Space Domains

D. Mirzaei¹, M. Dehghan¹

1 Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave.,15914, Tehran, Iran.
Email addresses: d_mirzaei@aut.ac.ir (D. Mirzaei), mdehghan@aut.ac.ir (M. Dehghan).

Computer Modeling in Engineering & Sciences 2011, 72(3), 185-210. https://doi.org/10.3970/cmes.2011.072.185

Abstract

The meshless local Petrov-Galerkin (MLPG) method with an efficient technique to deal with the time variable are used to solve the heat conduction problem in this paper. The MLPG is a meshless method which is (mostly) based on the moving least squares (MLS) scheme to approximate the trial space. In this paper the MLS is used for approximation in both time and space domains, and we avoid using the time difference discretization or Laplace transform method to overcome the time variable. The technique is applied for continuously nonhomogeneous functionally graded materials (FGM) in a finite strip and a hallow cylinder. This idea can be easily extended to all MLS based methods such as the element free Galerkin (EFG), the local boundary integral equation (LBIE) and etc.

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Keywords

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