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The hierarchical finite cell method for nonlinear problems: Moment fitting quadratures, basis function removel, and remeshing

Simeon Hubrich

Series: Mechanik/Bruchmechanik

Volume 355 2021

Results in this title

„… 4 Moment fitting quadratures In nonstandard discretization methods – such as the generalized or …” „… quadrature rules for arbitrary domains by solving the moment fitting equation system, which is generally a …” „… , thus resulting in more efficient moment fitting quadratures. Moreover, to increase the robustness for …”

Summary and outlook S. 150-153

„… the resulting quadrature rules, the moment fitting method using the Gauss-Legendre points turned out …” „… significantly. However, for nonlinear problems of the FCM, the moment fitting quadratures proved to be less …” „… the presented moment fitting quadratures improves the numerical integration of finite cells …”

Titelei/Inhaltsverzeichnis S. I-VII

„… nonlinear problems: Moment fitting quadratures, basis function removel, and remeshing H ub ri ch H …” „… : Moment fitting quadratures, basis function removal, and remeshing Vom Promotionsausschuss der Technischen …” „… : Moment fitting quadratures, basis function removel, and remeshing M.Sc. Simeon Hubrich, Hamburg …”

Introduction S. 1-5

„… quadrature methods based on the moment fitting approach in this thesis, in order to account for discontinuous …” „… robustness of the moment fitting quadratures for nonlinear problems of the FCM, an adaptive moment fitting …” „… that the presented moment fitting quadratures perform much more efficiently without loss in accuracy …”

Bibliography S. 154-169

„… problems: Moment fitting quadratures, basis function removel, and remeshing H ub ri ch H ie ra rc …” „… broken finite cells based on moment fitting applied to finite strain problems. Proceedings in Applied …” „… nonlinear problems of the finite cell method using an adaptive scheme based on moment fitting. Computers …”

Basis function removal for the FCM S. 79-123

„… to numerical integration, we employ the moment fitting method given in Sec. 4.2.1. For the …” „… computation of the moment fitting weights, we thereby apply an octree integration of tree depth level k = 10 …” „… moment fitting does not perform well for nonlinear problems of the FCM, we employ the adaptive moment …”

doi.org/10.51202/9783186355188

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Improving the robustness of the finite cell method for problems with large deformations

Wadhah Garhuom

Series: Mechanik/Bruchmechanik

Volume 359 2024

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Non-negative moment fitting quadrature for cut finite elements and cells S. 27-58

„… quadrature scheme can be applied to the cut cells since the274 Non-negative moment fitting quadrature for cut …” „… ] applied an artificialneural network (ANN) to speed up the construction of the moment fitting quadrature …” „… . Afterwards, the Gaussian quadrature scheme is applied tothe non-broken subcells while the moment fitting is …”

Titelei/Inhaltsverzeichnis S. I-VIII

„… EURFür die Dokumentation: Finite-Cell Methode, Moment-Fitting-Quadratur, Eigenwert-Stabilisierung …” „… , Remeshing, Große VerformungKeywords: Finite cell method, Moment fitting quadrature, Eigenvalue stabilization …” „… Ansatzfunktionen, um den Netzgene-rierungsaufwand zu reduzieren. Eine nicht-negative Moment-Fitting-Quadratur …”

Summary and outlook S. 130-133

„… non-negative moment fitting quadrature rule, described in Chapter 4. Here, each integra-tion point is created …” „… the adaptive moment fitting quadrature rule, in which the num-ber of quadrature points is decreased at …” „… the moment fitting equations while also incor-porating inequality constraints to guarantee that the …”

Introduction S. 1-5

„… simulations as follows: The moment fitting quadrature, in contrast to the often-used adaptive …” „… issue, we31 Introductionpropose in this thesis a non-negative moment fitting quadrature rule [59, 111 …” „… is introduced followed by a derivation of a non-negativeversion of the moment fitting quadrature rule …”

Bibliography S. 135-152

„… ,193(12-14):1257 – 1275, 2004.[59] W. Garhuom and A. Düster. Non-negative moment fitting quadrature for cut …” „… hierarchical finite cell method for nonlinear problems: moment fit-ting quadratures, basis function removel …” „… . Düster and O. Allix. Selective enrichment of moment fitting and application tocut finite elements and …”

Publications resulting from this project S. 134

„… , 2022. doi: 10.1007/s00466-022-02140-7[5] W. Garhuom and A. Düster. Non-negative moment fitting …” „… quadrature for cut finite elementsand cells undergoing large deformations. Computational Mechanics 70, pp …” „… chapters[1] W. Garhuom, S. Hubrich, L. Radtke, and A. Düster. Adaptive Quadrature and RemeshingStrategies …”

The finite cell method S. 17-26

„… which are based on moment fitting quadraturerules.26 …” „… body-confirming meshes such as FEM is the Gaussian quadrature rule whichcan integrate a polynomial of order pq …” „… )) detJcwi. (3.40)3.3.1 Gaussian quadratureThe Gaussian quadrature scheme performs well for integrating …”

Eigenvalue stabilization technique to increase the robustness of the FCM S. 59-88

„… into 129 cells (6×6×6 subdivisions). The non-negative moment fitting is usedto integrate the broken …” „… a shapefunction order of p = 2. The non-negative moment fitting is applied for the integration ofthe …” „… thesis, we follow the workproposed by Abedian et al. [5] where they apply the Gaussian quadrature in the …”

Remeshing strategy for large deformations in the FCM S. 89-129

„… integrating the physicaldomain of the cut cells, the non-negative moment fitting is utilized with a tree-depth …” „… moment fitting is used for the integration of the cells that are cut by thedomain. The goal here is to …” „… of p = 4. The non-negative moment fitting is applied to integrate the cutcells with an integration …”

doi.org/10.51202/9783186359186

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The hierarchical finite cell method for problems in structural mechanics

Meysam Joulaian

Series: Mechanik/Bruchmechanik

Volume 348 2017

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Numerical integration algorithms for the FCM S. 27-71

„… explain the procedure of setting up the quadrature based on the moment fitting method in order to compute …” „… the quadrature for further usage. Qc Figure 3.6: The moment fitting approach for integration …” „… quadrature rule and, in return, obtain a simple solution 3.4 Moment fitting method 41 procedure as suggested …”

Summary and Outlook S. 133-135

„… linear system in the moment fitting, which is easy to solve. As a result, the obtained quadrature rules …” „… instance in elastoplastic problems. The resulting quadrature rules based on the moment fitting method – in …” „… research • In order to construct quadrature rules on cut cells with the moment fitting method, we fixed the …”

Titelei/Inhaltsverzeichnis S. I-X

„… , wobei vor allem auf die adaptive Gauß- Quadratur und die Moment-Fitting-Methode eingegangen wird. Die …” „… – Heterogeneous materials – Adaptive integration – Moment fitting – Local enrichment – Partition of unity method …” „… the moment fitting approach. To improve the convergence behavior of the FCM for problems with …”

Bibliography S. 140-154

„… moment-fitting. In Proceedings of 3rd ECCOMAS Young Investigators Conference, 6th GACM Colloquium, pages 1–4 …” „… integration of discontinuities on arbitrary domains based on moment fitting. Computational Mechanics …” „… moment-fitting. International Journal for Numerical Methods in Engineering, 96:512–528, 2013. [130] B. Müller, F …”

doi.org/10.51202/9783186348180

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