自适应快速多极正则化无网格法求解大规模三维位势问题

刘从建; 陈文; 王海涛; 谷岩

doi:10.3879/j.issn.1000-0887.2013.03.006

自适应快速多极正则化无网格法求解大规模三维位势问题

doi: 10.3879/j.issn.1000-0887.2013.03.006

¹河海大学力学与材料学院,工程力学系,南京 210098;²清华大学核能与新能源技术研究院,北京 100084

基金项目: 国家重点基础研究发展规划(973)资助项目(2010CB832702) ;国家杰出青年科学基金资助项目（11125208）

详细信息

作者简介:
刘从建(1988—),男,山东人,硕士生(E-mail:lcj198818@126.com);陈文(1967—),男,江苏人,教授,博士,博士生导师 (通讯作者.E-mail:chenwen@hhu.edu.cn).

中图分类号: O342;O242.1
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- 文章访问数: 1941
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- PDF下载量: 1491
- 被引次数: 0
出版历程
- 收稿日期: 2013-01-01
- 修回日期: 2013-02-01
- 刊出日期: 2013-03-15

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

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

摘要

摘要: 正则化无网格法（regularized meshless method, RMM）是一种新的边界型无网格数值离散方法．该方法克服了近年来引起广泛关注的基本解方法（method of fundamental solutions, MFS）的虚假边界缺陷，继承了其无网格、无数值积分、易实施等优点．另一方面，RMM方法同MFS方法的插值方程都涉及非对称稠密系数矩阵，运用常规代数方程的迭代法求解时都要求O(N2)量级的乘法计算量和存储量．随着问题自由度的增加，该方法的计算量增加极快，效率较低，一般难以计算大规模问题．为了克服这个缺点，利用对角形式的快速多级算法（fast multipole method, FMM）来加速RMM方法，发展了快速多级正则化无网格法（fast multipole regularized mesheless method, FM-RMM）．该方法无需数值积分并且具有O(N)量级的计算量和存储量，可有效地求解大规模工程问题．数值算例表明，FM-RMM算法可成功在内存为4GB的Core(TM)Ⅱ台式机上求解高达百万级自由度的三维位势问题．
- 快速多级算法 /
- 无网格 /
- 正则化无网格法 /
- 基本解方法 /
- 三维位势问题
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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参考文献(22)

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自适应快速多极正则化无网格法求解大规模三维位势问题

doi: 10.3879/j.issn.1000-0887.2013.03.006

作者简介:
刘从建(1988—),男,山东人,硕士生(E-mail:lcj198818@126.com);陈文(1967—),男,江苏人,教授,博士,博士生导师 (通讯作者.E-mail:chenwen@hhu.edu.cn).

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

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自适应快速多极正则化无网格法求解大规模三维位势问题

doi: 10.3879/j.issn.1000-0887.2013.03.006

作者简介: 刘从建(1988—),男,山东人,硕士生(E-mail:lcj198818@126.com);陈文(1967—),男,江苏人,教授,博士,博士生导师 (通讯作者.E-mail:chenwen@hhu.edu.cn).

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出版历程

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

计量

出版历程

目录

作者简介:
刘从建(1988—),男,山东人,硕士生(E-mail:lcj198818@126.com);陈文(1967—),男,江苏人,教授,博士,博士生导师 (通讯作者.E-mail:chenwen@hhu.edu.cn).