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Acceleration Strategies Based on an Improved Bubble Packing Method

Published online by Cambridge University Press:  03 June 2015

Nan Qi ,
Yufeng Nie  and
Weiwei Zhang
Nan Qi*
Affiliation:
Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, 127 Youyi West Road, Xi’an 710129, China
Yufeng Nie*
Affiliation:
Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, 127 Youyi West Road, Xi’an 710129, China
Weiwei Zhang*
Affiliation:
Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, 127 Youyi West Road, Xi’an 710129, China
*
Email:appleflowerqn@163.com
Corresponding author.Email:yfnie@nwpu.edu.cn
Email:zhangweiwei@mail.nwpu.edu.cn
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Abstract

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 w1 and w2 are introduced to modify the insertion criterion. The range of those two coefficients are discussed to be w1 = 1, w2 ∈ [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.

Keywords

65L5065B99Bubble packing methodalgorithm efficiencyviscosity coefficientmesh generationDelaunay triangulation.
Type
Research Article
Information
Communications in Computational Physics , Volume 16 , Issue 1 , July 2014 , pp. 115 - 135
Copyright
Copyright © Global Science Press Limited 2014

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References

[1]Shimada, K., Physically-Based Mesh Generation: Automated Triangulation of Surfaces and Volumes via Bubble Packing, PhD Thesis, Massachusetts Institute of Technology, 1993.Google Scholar
[2]Nie, Y., Zhang, W., Liu, Y. and Wang, L., A node placement method with high quality for mesh generation, IOP Conference Series: Materials Science and Engineering, IOP Publishing, 10 (2010), 012–218.Google Scholar
[3]Shimada, K. and Gossard, D., Bubble mesh: automated triangular meshing of non-manifold geometry by packing, sphere, Proceedings of the Third ACM Symposium on Solid Modeling and Applications, ACM, (1995), 409–419.CrossRefGoogle Scholar
[4]Shimada, K. and Gossard, D., Automatic triangular mesh generation of trimmed parametric surfaces for finite element analysis, Comput. Aid. Geometric Design, 15(3) (1998), 199–222.CrossRefGoogle Scholar
[5]Shimada, K., Yamada, A. and Itoh, T., Anisotropic triangulation of parametric surfaces via close packing of ellipsoids, Int. J. Comput. Geometry Appl., 10(04) (2000), 417–440.Google Scholar
[6]Shimada, K., Liao, J. and Itoh, T. et al., Quadrilateral meshing with directionality control through the packing of square cells, Proceedings of 7th International Meshing Roundtable, (1998), 61–75.Google Scholar
[7]Yamakawa, S. and Shimada, K., Quad-layer: layered quadrilateral meshing of narrow two-dimensional domains by bubble packing and chordal axis transformation, Transactions- American Society of Mechanical Engineers Journal of Mechanical Design, 124(3) (2002), 564–573.Google Scholar
[8]Yamakawa, S. and Shimada, K., Triangular/quadrilateral remeshing of an arbitrary polygonal surface via packing bubbles, Proc. Geometric Model. Process., 2004 (2004), 153–162.Google Scholar
[9]Itoh, T. and Shimada, K., Automatic conversion of triangular meshes into quadrilateral meshes with directionality, Int. J. CAD/CAM, 1(2) (2001), 20–38.Google Scholar
[10]Yamakawa, S. and Shimada, K., Anisotropic tetrahedral meshing via bubble packing and advancing front, Int. J. Numer. Methods Eng., 57(13) (2003), 1923–1942.CrossRefGoogle Scholar
[11]Kim, J., Kim, H., Lee, B. and Im, S., Adaptive mesh generation by bubble packing method, Struct. Eng. Mech., 15(1) (2003), 135–150.Google Scholar
[12]Zienkiewicz, O. and Zhu, J., Error estimates and adaptive refinement for plate bending problems, Int. J. Numer. Methods Eng., 28(12) (1989), 2839–2853.Google Scholar
[13]Zienkiewicz, O. and Zhu, J., Adaptivity and mesh generation, Int. J. Numer. Methods Eng., 32(4) (1991), 783–810.Google Scholar
[14]Chung, S. and Kim, S., A remeshing algorithm based on bubble packing method and its application to large deformation problems, Finite Elements Anal. Design, 39(4) (2003), 301–324.Google Scholar
[15]Chung, S., Choi, Y. and Kim, S., Computational simulation of localized damage by finite element remeshing based on bubble packing method, Comput. Model. Eng. Sci., 4(6) (2003), 707–718.Google Scholar
[16]Liu, Y. and Nie, Y., Node placement method with bubble simulation and parallelism, Chinese J. Comput. Phys., 6 (2009), 813–820.Google Scholar
[17]Rossi, M., Tanaka, D., Shimada, K. and Rabin, Y., Computerized planning of cryosurgery using bubble packing: an experimental validation on a phantom material, Int. J. Heat Mass Transfer, 51(23) (2008), 5671–5678.Google Scholar
[18]Tanaka, D., Shimada, K., Rossi, M. and Rabin, Y., Cryosurgery planning using bubble packing in 3d, Comput. Methods Biomech. Biomed. Eng., 11(2) (2008), 113–121.Google Scholar
[19]Rossi, M., Tanaka, D., Shimada, K. and Rabin, Y., Computerized planning of prostate cryosurgery using variable cryoprobe insertion depth, Cryobiology, 60(1) (2010), 71–79.Google Scholar
[20]Wu, L., Chen, B. and Zhou, G., An improved bubble packing method for unstructured grid generation with application to computational fluid dynamics, Numer. Heat Trans. Part B Fundamentals, 58(5) (2010), 343–369.Google Scholar
[21]Cai, L., Nie, Y., Xie, W. and Zhang, W., Numerical path integration method based on bubble grids for nonlinear dynamical systems, Appl. Math. Model., (2013), 1490–1501.CrossRefGoogle Scholar
[22]Liu, Y., Nie, Y., Zhang, W. and Wang, L., Node placement method by bubble simulation and its application, Comput. Model. Eng. Sci., 55(1) (2010), 89–110.Google Scholar
[23]Qi, N., Nie, Y. and Zhang, W., Afast node placement method with bubble simulation, Chinese J. Comput. Phys., 29(3) (2012), 333–339.Google Scholar
[24]Persson, P. and Strang, G., A simple mesh generator in matlab, SIAM Review, 46(2) (2004), 329–345.Google Scholar
[25]Yokoyama, T., Cingoski, V., Kaneda, K. and Yamashita, H., 3-d automatic mesh generation for fea using dynamic bubble system, Magn. IEEE Transact., 35(3) (1999), 1318–1321.Google Scholar
[26]Dibben, D., 3d mesh generation using bubble meshing for microwave applicators, Magn. IEEE Transact., 36(4) (2000), 1514–1518.Google Scholar