基于余弦样条函数的有限点阵法

应用节点影响域的概念,提出了基于余弦样条函数的有限点阵方法.利用余弦样条函数的性质,通过张量积的形式构造余弦样条函数正则解空间,用于逼近场函数,余弦样条基的线性组合使得边界条件处理如同有限元法一样方便.余弦样条与边界型方法结合,可用于求解不规则域问题.数值实例的计算结果表明,文中方法避免了高阶多项式构造形函数所带来的数值振荡,解的连续性不受限制,为改进计算精度而加密点阵所导致的计算量增加量较少,计算收敛快.

Finite point matrix method based on cosine spline

A finite point matrix method based on the cosine splines is presented by utilizing the conception of the nodal influence domain in this paper.Some important properties of the cosine spline functions are identified for deriving the formulas and exhibiting the performances of the numerical method proposed here.With applications of the cosine spline bases as solution space,a normalized space is constructed for approximation of the field functions through tensor product method.Linear combination of the cosine spline bases results in the treatment of the boundary conditions prescribed as conveniently as traditional finite element method.Coupled with the boundary type numerical methods,cosine splines can be employed for solving problems in an irregular domain by node matrix distributed on the boundary.Several numerical examples are posed to identify the method and show the advantages while the method is adopted.Results demonstrate that numerical oscillation resulted from high degree polynomial shape functions is avoided and continuity rank is limited no more.Densifying point matrix required for improving accuracy brings a lightly enhancement on the quantity of calculation only.Rapid convergence is another identification mark of the method.