QuESo - Quadrature for Embedded Solids

QuESo (formerly TIBRA) is a preprocessor to generate analysis-ready embedded finite element models from arbitrarily complex solids described in boundary representation (B-Rep). The geometry is processed as a standard STL file. QuESo is designed to provide highly efficient quadrature rules that can be used in any embedded or immersed boundary method. To this end, the STL model is embedded into a background mesh defined by a regular grid, i.e., with hexahedral integration domains (finite elements). The user can specify the polynomial degree and the number of elements in each spatial direction. QuESo reads the STL file and computes the integration points required for a subsequent FE analysis. Both classical $C^0$ finite elements and isogeometric elements defined on trivariate B-Spline domains are supported. An interface to the FE framework Kratos Multiphysics is provided. The integration points have the following characteristics:

• All integration weights are positive.
• Point locations are restricted to the material domain.
• The number of points per cut element is always $n \leq (p+1)^3$.

QuESo is written in C++ and has a user-friendly Python interface. If you want to learn how to use QuESo, check out the Wiki. Additionally, there are several examples in Examples. Please do not hesitate to contact me with questions about QuESo.

Special Thanks To

• Lester Hedges for the AABB tree
• Mike Lapshin for the NNLS solver
• pybind11 for exposing C++ to python
• Boost for the C++ unit test framework

How to cite QuESo?

Please use the following references when citing QuESo in your work.

• Manuel Meßmer, Tobias Teschemacher, Lukas F. Leidinger, Roland Wüchner, Kai-Uwe Bletzinger, Efficient CAD-integrated isogeometric analysis of trimmed solids, Comput. Methods Appl. Mech. Engrg. 400 (2022) 115584, https://doi.org/10.1016/j.cma.2022.115584.

• Manuel Meßmer, Stefan Kollmannsberger, Roland Wüchner, Kai-Uwe Bletzinger, Robust numerical integration of embedded solids described in boundary representation, Comput. Methods Appl. Mech. Engrg. 419 (2024) 116670, https://doi.org/10.1016/j.cma.2022.115584.

• Manuel Meßmer, Lukas F. Leidiner, Stefan Hartmann, ..., Kai-Uwe Bletzinger, Isogeometric Analysis on Trimmed Solids: A B-Spline-Based Approach Focusing on Explicit Dynamics, 13th European LS-DYNA Conference, Ulm, Germany, 2021. Meßmer et al. 2022.

• Manuel Meßmer, QuESo, https://github.com/manuelmessmer/QuESo.

It would be great to hear from you if QuESo was of use in your project.