Analysis-suitable paramterization techniques for isogeometric analysis
Date:
Isogeometric analysis (IGA), as introduced by Hughes et al., proposes an integrated approach to seamlessly connect Computer-Aided Design (CAD) with Computer-Aided Engineering (CAE). This integration circumvents the need for converting spline-based CAD models to linear mesh models, thereby preserving geometric accuracy throughout the analysis phase. Nonetheless, the prevalent use of boundary representation (B-Rep) in CAD systems poses challenges for IGA workflows, necessitating the generation of high-quality, analysis-suitable parameterizations from input B-Reps.
The first part of this talk focuses on two advanced parameterization techniques: the Barrier-type Optimization-based and the PDE-based elliptic Grid Generation Method. These strategies have been successfully implemented in practical scenarios, notably in structured mesh generation for twin-screw compressors. We have incorporated these methods into the Geometry + Simulation Modules (G+Smo) library, an open-source C++ toolkit for geometric design and isogeometric simulations.
In the latter part of this talk, we introduce a bi-level, curvature-based $r$-adaptive parameterization approach designed to enhance numerical accuracy without increasing the degrees of freedom. The principal feature is utilizing the so-called absolute principal curvature of the IGA solution surfaces to characterize numerical errors. Numerical experiments demonstrate the effectiveness and efficiency of our method.
Keywords: Isogeometric analysis, Analysis-suitable parameterization, NURBS