摘要
边界节点法(BNM)将边界积分方程和移动最小二乘近似方案相结合,同时具有边界元法降维和无网格法不需要划分网格的优势。BNM中的形函数不具有Delta函数性质,在BNM中边界条件不容易施加。将BNM中的移动最小二乘近似方案用一致紧支径向基函数代替,得到一种新的边界型无网格法——一致径向边界节点法。这种方法的形函数矩阵具有稀疏性和Delta函数性质,边界条件可以像传统的边界元方法一样很容易施加。最后以双调和方程边值问题为例,导出了相应的离散方程,并通过数值分析验证了该无网格法的可行性和有效性。
The boundary node method （BNM） is a meshless method which combines the moving least-squares （MLS） interpolation scheme with the standard boundary integral equations （BIEs）. It retains the meshless of the MLS interpolants and the dimensionality advantage of the BIEs. Since MLS shape functions lack the delta function property, it is difficult to impose boundary conditions in BNM. In order to overcome this problem, a consistent radial boundary node method （CRBNM） was presented. The CRBNM uses consistent compactly supported radial basis functions instead of the MLS to construct its interpolation. Thus the shape function matrices are sparse and have the property of delta function, and the boundary conditions can be applied as easy as in conventional boundary element method. The new boundary-type meshless method is applied to biharmonic problems. Numerical results for some 2D problems were presented, which demonstrate that the proposed meshless method is very effective for biharmonic problems.
出处
《重庆大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2007年第12期80-83,共4页
Journal of Chongqing University
基金
国家杰出青年科学基金资助项目(50625824)
关键词
双调和方程
边界节点法
径向基函数
一致紧支径向基函数
无网格法
biharmonic equations
boundary node method
radial basis function
consistent compactly supported radial basis functions
meshless method
