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Isogeometric collocation using analysis-suitable T-splines of arbitrary degree

机译：使用任意度数的适合于分析的T样条进行等几何搭配

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摘要

This paper deals with the use of analysis-suitable T-splines of arbitrary degree in combination with isogeometric collocation methods for the solution of second-and fourth-order boundary-value problems. In fact, analysis-suitable T-splines appear to be a particularly efficient locally refinable basis for isogeometric collocation, able to conserve the cost of only one point evaluation per degree of freedom typical of standard NURBS-based isogeometric collocation. Furthermore, T-splines allow to easily create highly non-uniform meshes without introducing elements with high aspect ratios; this makes it possible to avoid the numerical instabilities that may arise in the case of problems characterized by reduced regularity when Neumann boundary conditions are imposed in strong form and elements with high aspect ratio are used. The local refinement properties of T-splines can be also successfully exploited to approximate problems where point loads are applied. Finally, several numerical tests are herein presented in order to confirm all the above-mentioned features, as well as the good overall convergence properties of the combination of isogeometric collocation and analysis-suitable T-splines. (C) 2015 Elsevier B.V. All rights reserved.
机译：本文研究了适合分析的任意程度的T样条与等几何配点方法的结合，用于解决二阶和四阶边值问题。实际上，适合分析的T样条曲线似乎是等几何配点的一种特别有效的本地精炼基础，能够节省基于标准NURBS的典型等几何配点的每个自由度仅需进行一点评估的成本。此外，T样条可以轻松创建高度不均匀的网格，而无需引入具有高长宽比的元素。这样就可以避免在以强形式施加诺伊曼边界条件并使用高纵横比的元素时，规则性降低的问题，可能会出现数值不稳定性。 T样条曲线的局部细化特性也可以成功地用于近似应用点载荷的问题。最后，本文提供了一些数值测试，以确认所有上述特征以及等几何搭配和适合分析的T样条曲线组合的良好总体收敛性。 （C）2015 Elsevier B.V.保留所有权利。

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