Abstract
An interpolating element-free Galerkin (IEFG) method is presented for transient heat conduction problems. The shape function in the moving least-squares (MLS) approximation does not satisfy the property of Kronecker delta function, so an interpolating moving least-squares (IMLS) method is discussed; then combining the shape function constructed by the IMLS method and Galerkin weak form of the 2D transient heat conduction problems, the interpolating element-free Galerkin (IEFG) method for transient heat conduction problems is presented, and the corresponding formulae are obtained. The main advantage of this approach over the conventional meshless method is that essential boundary conditions can be applied directly. Numerical results show that the IEFG method has high computational accuracy.
Highlights
In recent years, meshless methods have been successfully developed and applied to solve a variety of science and engineering problems [1,2,3,4,5,6,7,8]
The shape function in the moving least-squares (MLS) approximation does not satisfy the property of Kronecker delta function, so an interpolating moving least-squares (IMLS) method is discussed; combining the shape function constructed by the IMLS method and Galerkin weak form of the 2D transient heat conduction problems, the interpolating element-free Galerkin (IEFG) method for transient heat conduction problems is presented, and the corresponding formulae are obtained
The element-free Galerkin (EFG) method is the most important meshless method, the shape function in the EFG method is formed with moving least-squares (MLS) approximation, a disadvantage of the MLS approximation is that the final algebraic equations system is sometimes illconditioned, and we cannot obtain a good solution, or even correctly obtain a numerical solution; Cheng and Peng proposed an improved moving least-squares approximation by orthogonalizing the basis functions in the MLS approximation, and based on it Cheng and Peng put forward a boundary element-free method [23]
Summary
Meshless methods have been successfully developed and applied to solve a variety of science and engineering problems [1,2,3,4,5,6,7,8]. An interpolating element-free Galerkin (IEFG) method is presented for transient heat conduction problems. Chen and Cheng used complex variable reproducing kernel particle method to solve transient heat conduction problems [32]; its advantage is that 2D problem is solved with 1D basis function.
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