Acoustic Response in Multi-Domain Based on Least-Square Point Collocation Method and  Reproducing Kernel Particle Method

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Journal of Vibration and Shock ›› 2012, Vol. 31 ›› Issue (8) : 148-152,.

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Acoustic Response in Multi-Domain Based on Least-Square Point Collocation Method and Reproducing Kernel Particle Method

Li Hong-qiu1; Chen Guo-ping 1; Shi Bao-jun 2

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Abstract

Meshless method faces several challenges such as boundary problems and stability of the results. In this paper, approximated functions were constructed based on the principle of reproducing kernel particle method and least-square collocation method was used to solve boundary problems. The system coefficient matrix generated by this method is symmetric, which make sure the results stable. A least-square collocation formulation based on kernel reproducing particle method was established for solving multi-domain acoustic response. Helmholtz equation was then discretized. To verify the proposed method, several numerical examples of two-dimensional problems were analyzed. Compared to analytic solutions of two examples, the numerical solutions computed by this meshless method are valid. This method needn’t any initial mesh generation and mesh regeneration. Examples show whenever the points were distributed uniformly or randomly the results have good accuracy and convergence.

Key words

Acoustic response / multi-domain / Helmholtz equation / reproducing kernel particle method / least-square principle

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Li Hong-qiu;Chen Guo-ping;Shi Bao-jun . Acoustic Response in Multi-Domain Based on Least-Square Point Collocation Method and Reproducing Kernel Particle Method[J]. Journal of Vibration and Shock, 2012, 31(8): 148-152,