Analysis-suitable parameterization for isogeometric analysis

Photo 1, Photo 2, Photo 3

In isogeometric analysis (IGA), generating high-quality parameterizations from CAD boundary representations is crucial for accurate and efficient simulation. This talk presents a suite of analysis-suitable parameterization techniques developed to bridge the gap between CAD and CAE, enabling seamless simulation workflows in complex domains.

We recall optimization-based [1,2] and PDE-based [3] methods for generating bijective, low-distortion parameterizations, with particular emphasis on robust strategies for elongated and highly anisotropic domains. Key ingredients include barrier- and penalty-function-based formulations, Jacobian regularization, and adaptive techniques that respond to geometric and physical field features. In addition, we introduce a curvature-driven anisotropic parameterization strategy [4], which interprets IGA solutions as parametric surfaces and uses their principal curvatures to guide mesh density and directionality. This leads to improved accuracy in localized feature regions and greater efficiency in downstream simulations.

The proposed techniques have been successfully applied to challenging industrial geometries, such as twin-screw compressors [5], and validated using commercial CFD software. Core implementations are available as open-source code in the G+Smo library, supporting further research and practical deployment.

[1] Ji et al., J. Comput. Appl. Math., 396 (2021): 113615.
[2] Ji et al., Comput. Aided Geom. Des., 94 (2022): 102081.
[3] Ji et al., Comput. Aided Geom. Des., 102 (2023): 102191.
[4] Ji et al., Comput.-Aided Des., 150 (2022): 103305.
[5] Ji & Möller, IOP Conf. Ser.: Mater. Sci. Eng., 1322 (2024): 012014.

Keywords: Isogeometric Analysis, Analysis-Suitable Parameterization, Bijective Parameterization, Curvature-Based Adaptivity, Twin-Screw Compressors