论文标题
具有$ C^1 $（截短的）层次花键的自适应等几何方法在平面多块域上
Adaptive isogeometric methods with $C^1$ (truncated) hierarchical splines on planar multi-patch domains
论文作者
论文摘要
等几年分析是一种强大的范式，它利用了花键的高光滑度来用于高阶偏微分方程的数值解。但是，标准多元B-Spline模型的张量产品结构不太适合代表复杂的几何形状，并且必须使用对多块几何形状的一般域上的高连续性。在本文中，我们专注于带有层次花键的自适应等几年方法，并将$ c^1 $ iSOGEOMETRIC条子条的构造扩展到多块平面域上的$ iSOGEOMETRIC条形图。我们引入了一个新的抽象框架，用于定义分层花样条，该框架用较弱的假设代替了每个级别的局部线性独立性的假设。我们还开发了一种简化算法，该算法可以保证该假设通过某些适当分级的层次分级多点网格配置来实现$ c^1 $ spline，并证明其具有线性复杂性。通过解决泊松和双旋次问题来测试自适应方法的性能。
Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline models is not well suited for the representation of complex geometries, and to maintain high continuity on general domains special constructions on multi-patch geometries must be used. In this paper we focus on adaptive isogeometric methods with hierarchical splines, and extend the construction of $C^1$ isogeometric spline spaces on multi-patch planar domains to the hierarchical setting. We introduce a new abstract framework for the definition of hierarchical splines, which replaces the hypothesis of local linear independence for the basis of each level by a weaker assumption. We also develop a refinement algorithm that guarantees that the assumption is fulfilled by $C^1$ splines on certain suitably graded hierarchical multi-patch mesh configurations, and prove that it has linear complexity. The performance of the adaptive method is tested by solving the Poisson and the biharmonic problems.
