论文标题
分析意识到具有诺伊曼特征的复杂几何形状的击败
Analysis-aware defeaturing of complex geometries with Neumann features
论文作者
论文摘要
通常进行计算域的局部修改，以简化网格序列的过程并减少计算成本和内存要求。但是，删除域的几何特征通常会在定义其定义的差分问题的解决方案中引入不可忽略的误差。在这项工作中，我们通过研究包含任意数量的不同Neumann特征的域的情况，并对泊松，线性弹性和Stokes的方程进行分析，从[1]扩展了结果。我们引入了一个简单，计算上的便宜，可靠和有效的几何失败误差的后验估计器。此外，我们还引入了一种几何改进策略，该策略解释了失败的错误：从完全失败的几何形状开始，算法在每个迭代步骤中都确定需要将功能添加到几何模型中，以减少失败错误。然后在下一次迭代中添加这些重要特征（部分）失败的几何模型，直到解决方案达到规定的准确性为止。最终报告了广泛的二维数值实验，以说明这项工作。
Local modifications of a computational domain are often performed in order to simplify the meshing process and to reduce computational costs and memory requirements. However, removing geometrical features of a domain often introduces a non-negligible error in the solution of a differential problem in which it is defined. In this work, we extend the results from [1] by studying the case of domains containing an arbitrary number of distinct Neumann features, and by performing an analysis on Poisson's, linear elasticity, and Stokes' equations. We introduce a simple, computationally cheap, reliable, and efficient a posteriori estimator of the geometrical defeaturing error. Moreover, we also introduce a geometric refinement strategy that accounts for the defeaturing error: Starting from a fully defeatured geometry, the algorithm determines at each iteration step which features need to be added to the geometrical model to reduce the defeaturing error. These important features are then added to the (partially) defeatured geometrical model at the next iteration, until the solution attains a prescribed accuracy. A wide range of two- and three-dimensional numerical experiments are finally reported to illustrate this work.
