Abstract
In this paper, radial point collocation method (RPCM) is introduced to solve the acoustic scattering problem. This is a mathematically simple, easy-to-program and truly meshless method, which has been successfully applied to solve the solid mechanics and convection diffusion problems. However, application of this method to investigate acoustic problems, in particle the acoustic scattering problem is relatively new. The main advantage of this method is its mathematically simple, easy to program, and truly meshless. A Hermite-type interpolation method is employed to improve the solution accuracy while the Neumann boundary conditions exist. In addition, acoustic scattering problem is a typical unbounded domain problem, in order to solve it with RPCM, the domain is truncated to a finite region and an artificial boundary condition (ABC) is imposed. Finally, numerical example is presented to validate the accuracy and effectiveness of RPCM. In the future, the extension of RPCM to more complex and practical problems, especially the three-dimensional situations need to be investigated in more detail.
Highlights
The acoustic scattering problem has been investigated quite extensively since the works of Lamb and Rayleigh[1]
Meshless methods can be divided into three categories according the formulation procedures of the governing equations: meshless methods based on weak-forms, meshless methods based on strong-forms, meshless methods based on the combination of the weak-form and the strong form
It should be notied that, when the proper artificial boundary condition is chosen, the solution obtained with radial point collocation method (RPCM) agrees very well with the exact solution
Summary
The acoustic scattering problem has been investigated quite extensively since the works of Lamb and Rayleigh[1] This kind of problem can be described as the solution of the Helmholtz equation in an unbounded domain. A profusion of numerical approaches have been developed to solve this problem Among these methods, finite element method (FEM) and boundary element method (BEM) are widely used. It is proved that for high wave numbers, the FEM has the pollution effect which leads to inaccurate results To avert these difficulties, meshless methods, as relatively new methods, have attracted researchers’ attention[2,3,4,5,6].
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