Adaptive isogeometric analysis on two-dimensional trimmed domains based on a hierarchical approach

Abstract

The focus of this work is on the development of an error-driven isogeometric framework, capable of automatically performing an adaptive simulation in the context of second- and fourth-order, elliptic partial differential equations defined on two-dimensional trimmed domains. The method is steered by an a posteriori error estimator, which is computed with the aid of an auxiliary residual-like problem formulated onto a space spanned by splines with single element support. The local refinement of the basis is achieved thanks to the use of truncated hierarchical B-splines. We prove numerically the applicability of the proposed estimator to various engineering-relevant problems, namely the Poisson problem, linear elasticity and Kirchhoff-Love shells, formulated on trimmed geometries. In particular, we study several benchmark problems which exhibit both smooth and singular solutions, where we recover optimal asymptotic rates of convergence for the error measured in the energy norm and we observe a substantial increase in accuracy per-degree-of-freedom compared to uniform refinement. Lastly, we show the applicability of our framework to the adaptive shell analysis of an industrial-like trimmed geometry modeled in the commercial software Rhinoceros, which represents the B-pillar of a car.

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Cited by in corpus (8)

• Mathematical foundations of adaptive isogeometric analysis
• Coupling of non-conforming trimmed isogeometric Kirchhoff-Love shells via a projected super-penalty approach
• A comparison of smooth basis constructions for isogeometric analysis
• Residual-based error estimation and adaptivity for stabilized immersed isogeometric analysis using truncated hierarchical B-splines
• A localized reduced basis approach for unfitted domain methods on parameterized geometries
• Patch-wise Quadrature of Trimmed Surfaces in Isogeometric Analysis
• A Consistent Higher-Order Isogeometric Shell Formulation
• Analysis-aware defeaturing: problem setting and a posteriori estimation