Abstract

The piecewise polynomial functions constructed from the multivariate Hermitian interpolation polynomials that are continuous together with derivatives on the boundaries of finite elements are used in implementations of the high-accuracy finite element method (FEM). The efficiency of our finite element schemes, algorithms and program GCMFEM implemented in Maple and Mathematica are demonstrated by reference calculations of the boundary value problems (BVPs) for the Geometric Collective Model (GSM) of atomic nuclei. The BVP for GSM is reduced also to the BVP for a system of ordinary differential equations, which is solved by program KANTBP 5M implemented in Maple and compared with solution of algebraic eigenvalue problem in representation of the basis functions associated within irreducible representations of the \(U(5) \supset O(5) \supset O(3)\) chain of groups.

中文翻译：

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原子核几何集体模型：有限元方法实现

摘要

由与有限元边界上的导数连续的多元埃尔米特插值多项式构造的分段多项式函数用于高精度有限元法（FEM）的实现。我们在 Maple 和 Mathematica 中实现的有限元方案、算法和程序 GCMFEM 的效率通过原子核几何集体模型 (GSM) 边值问题 (BVP) 的参考计算得到证明。GSM 的 BVP 也简化为常微分方程组的 BVP，该方程由在 Maple 中实现的程序 KANTBP 5M 求解，并与表示不可约表示内关联的基函数的代数特征值问题的解决方案进行比较U(5) \supset O(5) \supset O(3)\)群链。