gsUnstructuredSplines: Unstructured spline constructions for G+Smo

CMake flags	-DGISMO_OPTIONAL="<other submodules>;gsUnstructuredSplines"
License	MPL 2.0
OS support	Linux, Windows, macOS
Repository	gismo/gismo/gsUnstructuredSplines
Status	completed
Dependencies	gismo/gismo
Developer	Pascal Weinmueller,Hugo Verhelst,Andrea Farahat
Maintainers	pascal.weinmueller@mtu.de,h.m.verhelst@tudelft.nl
Last checked	21-10-2022

Installation

cd path/to/build/dir
cmake . -DGISMO_OPTIONAL="<other submodules>;gsUnstructuredSplines"
make

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Module overview

The gsUnstructuredSplines module provides ready-to-use unstructured spline constructions for smooth multi-patch modelling. The module provides the following unstructured spline constructions:

• Approximate $C^1$ (gsApproxC1Spline)

  Weinmüller, P. (2022). Weak and approximate C1 smoothness over multi-patch domains in isogeometric analysis, PhD Thesis

  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.

  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.

• Analysis-Suitable $G^1$ (gsC1SurfSpline)

  Farahat, A. (2023). Isogeometric Analysis with $C^1$-smooth functions over multi-patch surfaces, PhD Thesis

  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.

  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.

• Almost - $C^1$ (gsAlmostC1)

  Takacs, T. & Toshniwal, D. (2023). Almost-$C^1$ splines: Biquadratic splines on unstructured quadrilateral meshes and their application to fourth order problems. Computer Methods in Applied Mechanics and Engineering, 403, 115640.

• Degenerate patches (D-Patches) (gsDPatch)

  Toshniwal, D., Speleers, H. & Hughes, T. J. (2017). Smooth cubic spline spaces on unstructured quadrilateral meshes with particular emphasis on extraordinary points: Geometric design and isogeometric analysis considerations. Computer Methods in Applied Mechanics and Engineering, 327, 411-458.

• Multi-Patch B-Splines with Enhanced Smoothness (gsMPBESSpline)

  Buchegger, F., Jüttler, B., & Mantzaflaris, A. (2016). Adaptively refined multi-patch B-splines with enhanced smoothness. Applied Mathematics and Computation, 272, 159-172.

• Compairison of the first four methods

  Verhelst, H. M. and Weinmüller, P. and Mantzaflaris, A. and Takacs, T. and Toshniwal, D. (2024). A comparison of smooth basis constructions for isogeometric analysis. Computer Methods in Applied Mechanics and Engineering

Implementation aspects

The general implementation of unstructured spline constructions is provided by the gsMappedSpline and gsMappedBasis classes. These classes define a global basis construction through a linear combination of local basis functions. The linear combination is stored in the gsWeightMapper. In general, a mapped basis is configured as follows:

Examples

Biharmonic equation

For more information, see the (Doxygen page)[url] corresponding to this file

Kirchhoff-Love shell model

For more information, see the (Doxygen page)[url] corresponding to this file

Contributing to this module

Publications based on this module

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

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Changelog

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Geometries