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Improved element-free Galerkin method for two-dimensional potential problems
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DOI：10.1016/j.enganabound.2008.08.004.png)
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Potential difficulties arise in connection with various physical and engineering problems in which the functions satisfy a given partial differential equation and particular boundary conditions. These problems are independent of time and involve only space coordinates, as in Poisson's equation or the Laplace equation with Dirichlet, Neuman, or mixed conditions. When the problems are too complex, they usually cannot be solved with analytical solutions. The element-free Galerkin (EFG) method is a meshless method for solving partial differential equations on which the trial and test functions employed in the discretization process result from moving least-squares (MLS) interpolants. In this paper, by using the weighted orthogonal basis function to construct the MLS interpolants we derive the, formulae of an improved EFG (IEFG) method for two-dimensional potential problems. There are fewer coefficients in the improved MLS (IMLS) approximation than in the MLS approximation, and in the IEFG method fewer nodes are selected in the entire domain than in the conventional EFG method. Hence, the IEFG method should result in a higher computing speed. (C) 2008 Elsevier Ltd. All rights reserved
Keyword:
Weighted orthogonal function
Improved moving least-squares (IMLS) approximation
Meshless method
Element-free Galerkin (EFG) method
Improved element-free Galerkin (IEFG) method
Potential problem
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