Commun. Comput. Phys., 16 (2014), pp. 115-135.

Acceleration Strategies Based on an Improved Bubble Packing Method

Nan Qi 1, Yufeng Nie 1*, Weiwei Zhang 1

1 Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, 127 Youyi West Road, Xi'an 710129, China.

Received 8 February 2013; Accepted (in revised version) 15 November 2013
Available online 10 April 2014


The bubble packing method can generate high-quality node sets in simple and complex domains. However, its efficiency remains to be improved. This study is a part of an ongoing effort to introduce several acceleration schemes to reduce the cost of simulation. Firstly, allow the viscosity coefficient c in the bubble governing equations to change according the coordinate of the bubble which are defined separately as odd and normal bubbles,and meanwhile with the saw-shape relationship with time or iterations. Then, in order to relieve the over crowded initial bubble placement, two coefficients w_1 and w_2 are introduced to modify the insertion criterion. The range of those two coefficients are discussed to be w_1=1, w_2\in[0.5,0.8]. Finally, a self-adaptive termination condition is logically set when the stable system equilibrium is achieved. Numerical examples illustrate that the computing cost can significantly decrease by roughly 80% via adopting various combination of proper schemes (except the uniform placement example), and the average qualities of corresponding Delaunay triangulation substantially exceed 0.9. It shows that those strategies are efficient and can generate a node set with high quality.

AMS subject classifications: 65L50, 65B99

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Key words: Bubble packing method, algorithm efficiency, viscosity coefficient, mesh generation, Delaunay triangulation.

*Corresponding author.
Email: (N. Qi), (Y. Nie), (W. Zhang)

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