
Isogeometric and Immersogeometric Analysis with FEniCSx: A Python Library Framework
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In this work, we introduce a suite of Python libraries designed to solve (immersed) isogeometric analysis (IGA) problems using the FEniCSx computing platform [1]. Firstly, we present tIGArx [2], a Python library for isogeometric analysis (IGA) using FEn- iCSx, which builds upon the existing tIGAr library [3], adapting it for compatibility with the new FEniCSx platform, and improving its computational performance. Secondly, we introduce QUGaR [4], a C++/Python library for generating high-order efficient quadrature rules for unfitted geometries. By leveraging the high-performance finite element capabilities of FEniCSx, these libraries support spline discretization spaces, enabling high-order computations in a scalable and efficient manner. Additionally, our framework extends to immersed discretizations, both for IGA and classical finite elements, allowing for simulations on complex geometries without the need for body-fitted meshes, thus enhancing flexibility in computational modeling. tIGArx and QUGaR provide a modular and user-friendly interface, making it easier for researchers and engineers to implement (immersed) isogeometric methods in a broad range of applications. We discuss the design choices behind the implementation, key features, and performance considerations. Through a series of numerical examples, we demonstrate the accuracy and efficiency of the framework, showcasing its potential for advancing isogeometric methods within the FEniCSx ecosystem. By providing an open-source and adaptable toolset, this work aims to further bridge the gap between classical finite element and isogeometric discretizations, making them more accessible and practical for a wider audience. REFERENCES [1] I. A. Baratta, J. P. Dean, J. S. Dokken, M. Habera, J. S. Hale, C. N. Richardson, M. E. Rognes, M. W. Scroggs, N. Sime, and G. N. Wells. DOLFINx: The next genera- tion FEniCS problem solving environment, preprint (2023). doi.org/10.5281/zenodo. 10447666 [2] P. Antolin and D. Dobrota. tIGArx: A Python library for isogeometric analysis (IGA) using FEniCSx (2025). https://github.com/pantolin/tigarx [3] D. Kamesky and Y. Bazilevs, tIGAr: Automating isogeometric analysis with FEniCS. Computer Methods in Applied Mechanics and Engineering. (2019) 344: 477–498. [4] P. Antolin. QUGaR: Quadratures for Unfitted GeometRies (2025). https://github. com/pantolin/qugar