December 2023 Release (v23.12)

What is new?

The first release of the gsUnstructuredSplines module of G+Smo! Please find the features of this release below.

The release accompanies the v23.12 releases of gsKLShell, gsStructuralAnalysis, the v23.12.0 release of gismo and the publication of the PhD thesis of @hverhelst.

5 constructions for unstructured splines

1. The Analysis-Suitable $G^1$ construction, see the gsC1SurfSpline class,
2. The Approximate $C^1$ construction, see the gsApproxC1Spline class,
3. The Almost-$C^1$ construction, see the gsAlmostC1 class,
4. The Degenerate-Patches approach, see the gsDPatch class,
5. The Multi-Patch B-Splines with Enhanced Smoothness construction, see the gsMPBESSpline class.

Biharmonic and shell examples

Several examples are included in examples, for validation on biharmonic equations, and for application using the Kirchhoff-Love shell model (see gsKLShell).

Reproduction of publications

The publications listed below are based on the results of this module. Most of the results can be reproduced with the current state of the module. A future release of more elaborate documentation will help to reproduce results.

Journal articles

1. Verhelst, H. M., Weinmüller, P., Mantzaflaris, A., Takacs, T., & Toshniwal, D. (2023). A comparison of smooth basis constructions for isogeometric analysis. Computer Methods in Applied Mechanics and Engineering, 419, 116659.
2. Farahat, A., Verhelst, H. M., Kiendl, J., & Kapl, M. (2023). Isogeometric analysis for multi-patch structured Kirchhoff–Love shells. Computer Methods in Applied Mechanics and Engineering, 411, 116060.
3. Farahat, A., Jüttler, B., Kapl, M., & Takacs, T. (2023). Isogeometric analysis with C1-smooth functions over multi-patch surfaces. Computer Methods in Applied Mechanics and Engineering, 403, 115706.
4. Weinmüller, P., & Takacs, T. (2022). An approximate C1 multi-patch space for isogeometric analysis with a comparison to Nitsche’s method. Computer Methods in Applied Mechanics and Engineering, 401, 115592.
5. Weinmüller, P., & Takacs, T. (2021). Construction of approximate $C^1$ bases for isogeometric analysis on two-patch domains. Computer Methods in Applied Mechanics and Engineering, 385, 114017.
6. Buchegger, F., Jüttler, B., & Mantzaflaris, A. (2016). Adaptively refined multi-patch B-splines with enhanced smoothness. Applied Mathematics and Computation, 272, 159-172.

PhD Theses

1. Verhelst, H.M. (2024). Isogeometric analysis of wrinkling, PhD Thesis
2. Farahat, A. (2023). Isogeometric Analysis with $C^1$-smooth functions over multi-patch surfaces, PhD Thesis
3. Weinmüller, P. (2022). Weak and approximate C1 smoothness over multi-patch domains in isogeometric analysis, PhD Thesis

What is left?

The next steps for the module are:

• To implement an example with a biharmonic equation for surfaces (see #17)
• To use the gsBiharmonicExprAssembler from gism/gsAssembler in the biharmonic_planar_eigenvalue_example and others (see #18 )
• To clean more what is left of the large amount of geometry files (see #16 )
• To write documentation for reproducibity, according to the PhD theses of P. Weinmüller and H.M.Verhelst (see #14 )