The study of quantum three-body problems has been centered on low-energy states that rely on accurate numerical approximation. Recently, isogeometric analysis (IGA) has been adopted to solve the problem as an alternative but more robust (with respect to atom mass ratios) method that outperforms the classical Born-Oppenheimer (BO) approximation. In this paper, we focus on the performance of IGA and apply the recently-developed softIGA to reduce the spectral errors of the low-energy bound states. The main idea is to add high-order derivative-jump terms with a penalty parameter to the IGA bilinear forms. With an optimal choice of the penalty parameter, we observe eigenvalue error superconvergence. We focus on linear (finite elements) and quadratic elements and demonstrate the outperformance of softIGA over IGA through a variety of examples including both two- and three-body problems in 1D.
翻译:量子三体问题研究集中在依靠精确数字近似值的低能国家。 最近,对等测量分析(IGA)作为替代但更稳健(原子质量比率)的方法,超过了古典的Born-Oppenheimer近似值。在本文中,我们侧重于IGA的性能,运用最近开发的软IGA来减少低能约束国家的光谱错误。主要想法是在IGA双线形式中添加高阶衍生物倾斜条件和惩罚参数。在最佳选择惩罚参数时,我们观察了超趋值误差超趋同性。我们侧重于线性(定点元素)和四面元素,并通过多种例子,包括1D的二体和三体问题,来展示软IGA在IGA上的超值。