The objective of this study is to address the difficulty of simplifying the geometric model in which a differential problem is formulated, also called defeaturing, while simultaneously ensuring that the accuracy of the solution is maintained under control. This enables faster and more efficient simulations, without sacrificing accuracy. More precisely, we consider an isogeometric discretisation of an elliptic model problem defined on a two-dimensional hierarchical B-spline computational domain with a complex boundary. Starting with an oversimplification of the geometry, we build a goal-oriented adaptive strategy that adaptively reintroduces continuous geometrical features in regions where the analysis suggests a large impact on the quantity of interest. This strategy is driven by an a posteriori estimator of the defeaturing error based on first-order shape sensitivity analysis, and it profits from the local refinement properties of hierarchical B-splines. The adaptive algorithm is described together with a procedure to generate (partially) simplified hierarchical B-spline geometrical domains. Numerical experiments are presented to illustrate the proposed strategy and its limitations.

翻译：本研究旨在解决微分问题所基于的几何模型简化（也称为去特征化）的难题，同时确保解的精度可控。这使得在不牺牲精度的情况下，能够实现更快速、更高效的模拟。更具体地说，我们考虑一个定义在具有复杂边界的二维层次B样条计算域上的椭圆模型问题的等几何离散化。从几何的过度简化出发，我们构建了一种面向目标的自适应策略，该策略在分析表明对关注量影响较大的区域中自适应地重新引入连续几何特征。该策略由基于一阶形状灵敏度分析的后验去特征化误差估计器驱动，并利用了层次B样条的局部细化特性。本文描述了自适应算法以及生成（部分）简化的层次B样条几何域的过程。通过数值实验展示了所提出策略及其局限性。