The improved element-free Galerkin method for three-dimensional wave equation |
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Authors: | Zan Zhang Dong-Ming Li Yu-Min Cheng Kim Moew Liew |
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Institution: | Key Laboratory of Mechanics in Energy Engineering,Shanghai University,200072 Shanghai,China Department of Civil and Architectural Engineering,City University of Hong Kong,Tat Chee Avenue,Kowloon,Hong Kong SAR,China |
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Abstract: | The paper presents the improved element-freeGalerkin(IEFG) method for three-dimensional wave propagation.The improved moving least-squares(IMLS) approximation is employed to construct the shape function,whichuses an orthogonal function system with a weight function asthe basis function.Compared with the conventional movingleast-squares(MLS) approximation,the algebraic equationsystem in the IMLS approximation is not ill-conditioned,andcan be solved directly without deriving the inverse matrix.Because there are fewer coefficients in the IMLS than in theMLS approximation,fewer nodes are selected in the IEFGmethod than in the element-free Galerkin method.Thus,theIEFG method has a higher computing speed.In the IEFGmethod,the Galerkin weak form is employed to obtain a discretized system equation,and the penalty method is appliedto impose the essential boundary condition.The traditionaldifference method for two-point boundary value problems isselected for the time discretization.As the wave equationsand the boundary-initial conditions depend on time,the scaling parameter,number of nodes and the time step length areconsidered for the convergence study. |
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Keywords: | Weighted orthogonal function Improved moving least squares(IMLS) approximation Improved elementfree Galerkin(IEFG) method Penalty method Temporaldiscretization Wave equation |
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