We introduce an adaptive isogeometric method for multi-patch surfaces and Kirchhoff–Love shell structures with hierarchical splines characterized by continuity across patches. We extend the construction of smooth hierarchical splines from the multi-patch planar setting to analysis suitable surfaces. The adaptive scheme to solve fourth order partial differential equations is presented in a general framework before showing its application for the numerical solution of the bilaplacian and the Kirchhoff–Love model problems. A selection of numerical examples illustrates the performance of hierarchical adaptivity on different multi-patch surface configurations.

中文翻译：

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用于多面片曲面和壳的[公式省略]样条的自适应方法


我们引入了一种适用于多面片曲面和基尔霍夫-洛夫壳结构的自适应等几何方法，其具有以面片间连续性为特征的分层样条线。我们将平滑分层样条的构造从多面片平面设置扩展到分析合适的表面。在展示其在 bilaplacian 和 Kirchhoff-Love 模型问题数值求解中的应用之前，先在一般框架中介绍求解四阶偏微分方程的自适应方案。一系列数值示例说明了不同多面片表面配置上分层自适应的性能。