Solving Helmholtz equation by least-square collocation method based on reproducing kernel particle method

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	Solving Helmholtz equation by least-square collocation method based on reproducing kernel particle method
	Shi, Baojun ; Yuan, Mingwu ; Shu, Dongwei
刊名	lixue xuebaochinese journal of theoretical and applied mechanics
	2006
英文摘要	Helmholtz equation often arises while solving boundary value problems of partial differential equation by eigenfunction method. In physics, Helmholtz equation represents a stationary state of vibration in the fields of mechanics, acoustics and electromagnetics. A least-square collocation formulation for solving Helmholtz equation with Dirichlet and Neumann boundary conditions was established. The unknown interpolated functions were first constructed based on reproducing kernel particle method and Helmholtz equation was then discretized by point collocation method. The variance errors of unknown function in each discrete point are minimized by a least-square scheme to arrive at the final solution. To verify the proposed method, a wave propagation problem and a boundary layer problem of Helmholtz equation were solved. Numerical results by the present approach are compared with exact solutions and those by smooth particle hydrodynamics (SPH) method. Numerical examples show that the present method displays better accuracy and convergence than the classical SPH method for the same density of discrete points.; EI; 0; 1; 125-129; 38
语种	英语
内容类型	期刊论文
源URL	[http://ir.pku.edu.cn/handle/20.500.11897/410186]
专题	工学院
推荐引用方式 GB/T 7714	Shi, Baojun,Yuan, Mingwu,Shu, Dongwei. Solving Helmholtz equation by least-square collocation method based on reproducing kernel particle method[J]. lixue xuebaochinese journal of theoretical and applied mechanics,2006.
APA	Shi, Baojun,Yuan, Mingwu,&Shu, Dongwei.(2006).Solving Helmholtz equation by least-square collocation method based on reproducing kernel particle method.lixue xuebaochinese journal of theoretical and applied mechanics.
MLA	Shi, Baojun,et al."Solving Helmholtz equation by least-square collocation method based on reproducing kernel particle method".lixue xuebaochinese journal of theoretical and applied mechanics (2006).