# 边界节点法

2018-09-06 14:25:21     所属分类：数值分析

• 1 方法描述
• 2 公式
• 3 发展历史及研究现状
• 4 参阅
• 5 参考文献
• 6 相关链接

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• 基本解法
• 正则化无网格法
• 边界粒子法
• 奇异边界法

## 参考文献

1. ^ R. Mathon and R. L. Johnston, The approximate solution of elliptic boundary-value problems by fundamental solutions, SIAM Journal on Numerical Analysis, 638-650, 1977.
2. ^ W. Chen and M. Tanaka, A meshfree, exponential convergence, integration-free, and boundary-only RBF technique, Computers and Mathematics with Applications, 43, 379-391, 2002.
3. ^ W. Chen, Symmetric boundary knot method, Engineering Analysis with Boundary Elements, 26(6), 489-494, 2002.
4. ^ W. Chen and Y.C. Hon, Numerical convergence of boundary knot method in the analysis of Helmholtz, modified Helmholtz, and convection-diffusion problems, Computer Methods in Applied Mechanics and Engineering, 192, 1859-1875, 2003.
5. ^ Y.C. Hon and W. Chen, Boundary knot method for 2D and 3D Helmholtz and convection-diffusion problems with complicated geometry, International Journal for Numerical Methods in Engineering, 1931-1948, 56(13), 2003
6. ^ X.P. Chen, W.X. He and B.T. Jin, Symmetric boundary knot method for membrane vibrations under mixed-type boundary conditions, International Journal of Nonlinear Science and Numerical Simulation, 6, 421-424, 2005.
7. ^ B.T. Jing and Z. Yao, Boundary knot method for some inverse problems associated with the Helmholtz equation, International Journal for Numerical Methods in Engineering, 62, 1636-1651, 2005.
8. ^ W. Chen, L.J. Shen, Z.J. Shen, G.W. Yuan, Boundary knot method for Poisson equations, Engineering Analysis with Boundary Elements, 29(8), 756-760, 2005.
9. ^ B.T. Jin, Y. Zheng, Boundary knot method for the Cauchy problem associated with the inhomogeneous Helmholtz equation, Engineering Analysis with Boundary Elements, 29, 925-935, 2005.
10. ^ B.T. Jin and W. Chen, Boundary knot method based on geodesic distance for anisotropic problems, Journal of Computational Physics, 215(2), 614-629, 2006.
11. ^ F.Z. Wang, W. Chen, X.R. Jiang, Investigation of regularized techniques for boundary knot method. International Journal for Numerical Methods in Biomedical Engineering, 26(12), 1868-1877, 2010
12. ^ F.Z. Wang, Leevan L, W. Chen, Effective condition number for boundary knot method. CMC: Computers, Materials, & Continua, 12(1), 57-70, 2009
13. ^ Z.J. Fu; W. Chen, Q.H Qin, Boundary knot method for heat conduction in nonlinear functionally graded material, Engineering Analysis with Boundary Elements, 35(5), 729-734, 2011.
14. ^ D. Mehdi and S. Rezvan, A boundary-only meshfree method for numerical solution of the Eikonal equation, Computational Mechanics, 47, 283-294, 2011.

## 相关链接

• Boundary knot method
• Examplary Matlab codes and geometric configurations