Immersed finite element methods provide a convenient analysis framework for problems involving geometrically complex domains, such as those found in topology optimization and microstructures for engineered materials. However, their implementation remains a major challenge due to, among other things, the need to apply nontrivial stabilization schemes and generate custom quadrature rules. This article introduces the robust and computationally efficient algorithms and data structures comprising an immersed finite element preprocessing framework. The input to the preprocessor consists of a background mesh and one or more geometries defined on its domain. The output is structured into groups of elements with custom quadrature rules formatted such that common finite element assembly routines may be used without or with only minimal modifications. The key to the preprocessing framework is the construction of material topology information, concurrently with the generation of a quadrature rule, which is then used to perform enrichment and generate stabilization rules. While the algorithmic framework applies to a wide range of immersed finite element methods using different types of meshes, integration, and stabilization schemes, the preprocessor is presented within the context of the extended isogeometric analysis. This method utilizes a structured B-spline mesh, a generalized Heaviside enrichment strategy considering the material layout within individual basis functions’ supports, and face-oriented ghost stabilization. Using a set of examples, the effectiveness of the enrichment and stabilization strategies is demonstrated alongside the preprocessor’s robustness in geometric edge cases. Additionally, the performance and parallel scalability of the implementation are evaluated.
Wunsch, Nils, et al. "Enriched immersed finite element and isogeometric analysis: algorithms and data structures." Engineering with Computers, Aug. 2025. https://doi.org/10.1007/s00366-025-02163-7
Wunsch, Nils, Doble, Keenan, Schmidt, Mathias R., Noël, Lise, Evans, John A., & Maute, Kurt (2025). Enriched immersed finite element and isogeometric analysis: algorithms and data structures. Engineering with Computers. https://doi.org/10.1007/s00366-025-02163-7
Wunsch, Nils, Doble, Keenan, Schmidt, Mathias R., et al., "Enriched immersed finite element and isogeometric analysis: algorithms and data structures," Engineering with Computers (2025), https://doi.org/10.1007/s00366-025-02163-7
@article{osti_2587400,
author = {Wunsch, Nils and Doble, Keenan and Schmidt, Mathias R. and Noël, Lise and Evans, John A. and Maute, Kurt},
title = {Enriched immersed finite element and isogeometric analysis: algorithms and data structures},
annote = {Immersed finite element methods provide a convenient analysis framework for problems involving geometrically complex domains, such as those found in topology optimization and microstructures for engineered materials. However, their implementation remains a major challenge due to, among other things, the need to apply nontrivial stabilization schemes and generate custom quadrature rules. This article introduces the robust and computationally efficient algorithms and data structures comprising an immersed finite element preprocessing framework. The input to the preprocessor consists of a background mesh and one or more geometries defined on its domain. The output is structured into groups of elements with custom quadrature rules formatted such that common finite element assembly routines may be used without or with only minimal modifications. The key to the preprocessing framework is the construction of material topology information, concurrently with the generation of a quadrature rule, which is then used to perform enrichment and generate stabilization rules. While the algorithmic framework applies to a wide range of immersed finite element methods using different types of meshes, integration, and stabilization schemes, the preprocessor is presented within the context of the extended isogeometric analysis. This method utilizes a structured B-spline mesh, a generalized Heaviside enrichment strategy considering the material layout within individual basis functions’ supports, and face-oriented ghost stabilization. Using a set of examples, the effectiveness of the enrichment and stabilization strategies is demonstrated alongside the preprocessor’s robustness in geometric edge cases. Additionally, the performance and parallel scalability of the implementation are evaluated.},
doi = {10.1007/s00366-025-02163-7},
url = {https://www.osti.gov/biblio/2587400},
journal = {Engineering with Computers},
issn = {ISSN 1435-5663},
place = {United States},
publisher = {Springer Science and Business Media LLC},
year = {2025},
month = {08}}
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA); US Air Force Office of Scientific Research (AFOSR); Defense Advanced Research Projects Agency (DARPA); National Science Foundation (NSF)
Grant/Contract Number:
AC52-07NA27344
OSTI ID:
2587400
Report Number(s):
LLNL--JRNL-871539
Journal Information:
Engineering with Computers, Journal Name: Engineering with Computers; ISSN 0177-0667; ISSN 1435-5663
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 378, Issue 2166https://doi.org/10.1098/rsta.2019.0061