TY - JOUR
T1 - Analyzing three-dimensional potential problems with the improved element-free Galerkin method
AU - Zhang, Zan
AU - Zhao, Peng
AU - Liew, K. M.
PY - 2009/7
Y1 - 2009/7
N2 - The potential problem is one of the most important partial differential equations in engineering mathematics. A potential problem is a function that satisfies a given partial differential equation and particular boundary conditions. It is independent of time and involves only space coordinates, as in Poisson's equation or the Laplace equation with Dirichlet, Neumann, or mixed conditions. When potential problems are very complex, both in their field variable variation and boundary conditions, they usually cannot be solved by analytical solutions. The element-free Galerkin (EFG) method is a promising 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 employing improved moving least-squares (IMLS) approximation, we derive the formulas for an improved element-free Galerkin (IEFG) method for three-dimensional potential problems. Because there are fewer coefficients in the 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, the IEFG method should result in a higher computing speed. © 2009 Springer-Verlag.
AB - The potential problem is one of the most important partial differential equations in engineering mathematics. A potential problem is a function that satisfies a given partial differential equation and particular boundary conditions. It is independent of time and involves only space coordinates, as in Poisson's equation or the Laplace equation with Dirichlet, Neumann, or mixed conditions. When potential problems are very complex, both in their field variable variation and boundary conditions, they usually cannot be solved by analytical solutions. The element-free Galerkin (EFG) method is a promising 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 employing improved moving least-squares (IMLS) approximation, we derive the formulas for an improved element-free Galerkin (IEFG) method for three-dimensional potential problems. Because there are fewer coefficients in the 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, the IEFG method should result in a higher computing speed. © 2009 Springer-Verlag.
KW - 3D Potential problem
KW - Improved element-free Galerkin (IEFG) method
KW - Improved moving least squares (IMLS) approximation
KW - Weighted orthogonal function
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U2 - 10.1007/s00466-009-0364-9
DO - 10.1007/s00466-009-0364-9
M3 - RGC 21 - Publication in refereed journal
VL - 44
SP - 273
EP - 284
JO - Computational Mechanics
JF - Computational Mechanics
SN - 0178-7675
IS - 2
ER -