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 in the regions of interest. More precisely, we consider an isogeometric discretisation of an elliptic model problem defined on a two-dimensional simply connected hierarchical B-spline physical 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.

Unrefinement is a tool that allows to perform faster numerical simulations by controlling the level of precision in the specified area. We introduce an algorithm that creates a coarser geometry from an initial regular geometry, which is represented with respect to THB-splines, so that the coarser geometry approximates the initial geometry with a given level of the precision and is regular. The algorithm is based on the unrefinement of cells of the parameter domain, on which the geometry is defined, thus obtaining the new subdivision of the domain (the new subdomain hierarchy). The algorithm uses local linear projectors and optimization techniques in order to ensure the regularity and the approximation properties.