基于径向基函数的无单元法的改进

基于径向基函数强形式的无单元(RBFS)法是真正意义上的无单元方法,但为了追求精度要求却未达到稀疏化。本文对RBFS进行了改进,通过构造具有δ函数性质的形函数,得到了具有稀疏带状性的系数矩阵,提高了计算效率,同时具有RBFS方法的优点。通过求解微分方程,得到节点均布时影响域半径与求解精度的关系曲线,验证了基函数中自由参数最佳取值的计算公式的适用性;并把节点均布下得到的影响域半径和自由参数的规律应用到节点任意排列的情况下,求解结果变化不大,均满足精度要求,由此得出这些规律仍然适用,这种无单元法对节点位置不敏感。

An Improvement Meshless Method Based on Radial Basis Functions

Radiai basis function strong form(RBFS) meshless method is a truly meshless method.The coefficient matrix is not sparse for satisfying accuracy by this method. An improved radial basis function strong form(IRBFS) meshless method was presented,by which the shape function possessing delta property was constructed,the sparse,and banded coefficient matrix was acquired,and the computation efficiency was improved.IRBFS has still the merits of RBFS.By solving differential equations,the relationship curves between influence domain radius and accuracy were obtained,and the appliance of free parameters optimal value formula in the radial basis functions was proved.The conclusions was applied to the condition of random nodes,and found that the results dont change obviously.The conclusions are valuable and this method isnt sensitive to the positions of nodes.