| 姜欣荣,陈文.基本解方法与边界节点法求解Helmholtz方程的比较研究[J].计算力学学报,2011,28(3):338~344 |
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| 基本解方法与边界节点法求解Helmholtz方程的比较研究 |
| Method of fundamental solution and boundary knot method for helmholtz equations: a comparative study |
| 投稿时间：2009-11-13 修订日期：2010-09-02 |
| DOI：10.7511/jslx201103006 |
| 中文关键词: 基本解方法 边界节点法 径向基函数 Helmholtz方程 |
| 英文关键词:method of fundamental solution boundary knot method radial basis function Helmholtz equation |
| 基金项目:国家自然科学基金(10672051)资助项目. |
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| 中文摘要: |
| 基本解方法和边界节点法是基于径向基函数的两种重要无网格边界离散数值技术。针对Helmholtz方程,本文比较研究这两种数值方法在不同计算区域问题上的计算精度、插值矩阵对称性、病态性及计算成本。数值试验结果表明,两种方法都可以有效求解边界数据准确的Helmholtz问题。在数值离散过程中,两种方法都可以通过调整配置点的位置减少插值矩阵的条件数;用边界节点法求解产生的插值矩阵是对称的,而基本解方法的插值矩阵不对称;边界节点法所需的计算时间比基本解方法略小,同时只需要后者一半的内存空间。 |
| 英文摘要: |
| Both the method of fundamental solution (MFS) and the boundary knot method (BKM) are RBF-based boundary-type meshless methods. This paper makes a comparative study of these two numerical methods in solving the Helmholtz equation under various regions, in terms of accuracy, symmetry, ill-conditioned interpolation matrix, and computational cost. Numerical results show that both methods can effectively solve the Helmholtz problems. In the discretization process, both methods can reduce the condition numbers by adjusting the location of the source points and collocation points. It is noted that the BKM interpolation matrix is symmetric while the MFS one is not. In addition, the BKM demands less CPU time than the MFS and requires a half memory of the MFS. |
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