论文标题
杂交等几何方法，用于椭圆形问题的CAD表面有间隙
Hybridized Isogeometric Method for Elliptic Problems on CAD Surfaces with Gaps
论文作者
论文摘要
我们开发了一种解决可能具有差距/重叠的CAD贴片所描述的表面上求椭圆形偏微分方程的方法。该方法基于杂交，使用三维网格，该网格涵盖了斑块之间的间隙/重叠。因此，在三维网格上定义了混合变量，我们需要添加适当的正常稳定化以获得准确的溶液，我们可以通过将合适的项添加到弱形式中来完成。在实际应用中，可以使用OCTREE来方便地构建混合网格，以有效计算必要的几何信息。我们证明了错误估计，并提供了几个数值示例，说明了该方法在不同问题中的应用，包括现实的CAD模型。
We develop a method for solving elliptic partial differential equations on surfaces described by CAD patches that may have gaps/overlaps. The method is based on hybridization using a three-dimensional mesh that covers the gap/overlap between patches. Thus, the hybrid variable is defined on a three-dimensional mesh, and we need to add appropriate normal stabilization to obtain an accurate solution, which we show can be done by adding a suitable term to the weak form. In practical applications, the hybrid mesh may be conveniently constructed using an octree to efficiently compute the necessary geometric information. We prove error estimates and present several numerical examples illustrating the application of the method to different problems, including a realistic CAD model.
