Adaptive Fast Multipole Regularized Meshless Method for Large-Scale Three Dimensional Potential Problems

LIU Cong-jian; CHEN Wen; WANG Hai-tao; GU Yan

doi:10.3879/j.issn.1000-0887.2013.03.006

Volume 34 Issue 3

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LIU Cong-jian, CHEN Wen, WANG Hai-tao, GU Yan. Adaptive Fast Multipole Regularized Meshless Method for Large-Scale Three Dimensional Potential Problems[J]. Applied Mathematics and Mechanics, 2013, 34(3): 259-271. doi: 10.3879/j.issn.1000-0887.2013.03.006

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Adaptive Fast Multipole Regularized Meshless Method for Large-Scale Three Dimensional Potential Problems

doi: 10.3879/j.issn.1000-0887.2013.03.006

¹Department of Engineering Mechanics, College of Mechanics and Materials, Hohai University, Nanjing 210098, P.R.China;²Institute of Nuclear and New Energy Technology,Tsinghua University, Beijing 100084, P.R.China

Received Date: 2013-01-01
Rev Recd Date: 2013-02-01
Publish Date: 2013-03-15

Abstract

Abstract

The regularized meshless method (RMM) is a new meshless boundary collocation method. This method overcame the perplexing fictitious boundary associated in the method of fundamental solutions (MFS), while inherited all its merits being truly meshless, integration-free, and easy toprogram. Like the MFS, the RMM also produced dense and nonsymmetric coefficient interpolation matrix, which required O(N2) multiplication operations and memory requirements in an iterative solution procedure. Since the calculation operations would dramatically increase with the number of DOF, the RMM was computationally too expensive to solve largescale problems. In order to overcome this bottleneck, this study combined the RMM with the popular diagonal form fast multipole method (FMM) to develop the fast multipole regularized meshless method (FM-RMM). The proposed scheme was integrationfree and meshfree and significantly reduced
- fast multipole method,
- meshless,
- regularized meshless method,
- method of fundamental solution,
- threedimensional potential problems

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References(22)

References

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