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

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Simeon Hubrich

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

Series: Mechanik/Bruchmechanik

Volume 355 2021

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Introduction S. 1-5

„… discretization methods based on the fictitious domain approach can be applied instead of the standard FEM. To the …” „… best knowledge of the author, the fictitious domain approach was first introduced by Saulev [7, 8 …” „… introduced in [19–22]. The FCM combines the fictitious domain approach with finite elements using shape …”

Summary and outlook S. 150-153

„… methods based on the fictitious domain approach. In the following, these three important problematic …” „… could be carried out easily thanks to the fictitious domain approach. To this end, the deformed shape of …” „… moment fitting points that are located within the fictitious domain regarding FCM applications in …”

The finite cell method S. 23-35

„… method (FCM) that is based on a combination of the fictitious domain approach and shape functions of …” „… Fictitious domain approach In the last decade, the interest in fictitious domain methods – such as the finite …” „… briefly describe the essential idea of the fictitious domain approach and its implementation within the …”

Basis function removal for the FCM S. 79-123

„… 5 Basis function removal for the FCM Nonstandard discretization methods such as fictitious domain …” „… domain technique with high order shape functions – a simple approach has been suggested that is based on …” „… a modification of the weak form. In this approach, the authors assigned a fictitious material model …”

Titelei/Inhaltsverzeichnis

„… € 55,80. Keywords: Finite cell method – Fictitious domain approach – High-order finite element methods …” „… current configuration . . . . . . . . . . 22 3 The finite cell method 23 3.1 Fictitious domain approach …” „… ), which combines the fictitious domain approach with high order finite elements. In the FCM, these …”

Moment fitting quadratures S. 36-78

„… physical as well as in the fictitious domain, we can show that this approach is well suited considering …” „… extended finite element method (GFEM/XFEM) [90–94], or fictitious domain methods [8, 11, 13, 14] like the …” „… moment fitting based on the GLP for the special case where the fictitious domain vanishes. Consequently …”

Bibliography S. 154-169

„… . Ramière, P. Angot, and M. Belliard. A fictitious domain approach with spread interface for elliptic …” „… performance computers by fictitious domain method. Siberian Mathematical Journal, 4:912–925, 1963. [9] P …” „… . Neittaanmäki and D. Tiba. An embedding of domains approach in free boundary problems and optimal design. SIAM …”

A remeshing strategy for the FCM S. 124-149

„… meshes, thanks to the fictitious domain approach. This is a main advantage compared to the standard FEM …” „… process that is inherent to discretization methods based on the fictitious domain approach. The basic …” „… the fictitious domain approach. Next, the essential field variables are transferred from the old mesh …”

doi.org/10.51202/9783186355188

Meysam Joulaian - The hierarchical finite cell method for problems in structural mechanics

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Meysam Joulaian

The hierarchical finite cell method for problems in structural mechanics

Series: Mechanik/Bruchmechanik

Volume 348 2017

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Finite cell method for problems in solid mechanics S. 5-26

„… [63, 65]. When the fictitious domain approach is applied in the context of the FEM, the next task is …” „… the approach the finite cell method (FCM) that combines the fictitious domain method together with …” „… conditions is an essential problem of any fictitious domain approach, including the FCM. This is due to the …”

Titelei/Inhaltsverzeichnis

„… ¤ 55,80. Keywords: Finite cell method – Fictitious domain approach – High-order finite element methods …” „… finite cell method (FCM) is a combination of the fictitious domain approach and high-order finite …” „… elements. Thanks to the fictitious domain approach, the task of the mesh generation in the FCM is …”

Introduction S. 1-4

„… successful methods based on the fictitious domain approach is the finite cell method (FCM) which employs …” „… mesh generation of the FCM due to applying the fictitious domain approach and its high convergence rate …” „… difficulties of the standard FEM is to employ the fictitious domain method – also referred to as the immersed …”

Bibliography S. 140-154

„… fictitious domain approach with spread interface for elliptic problems with general boundary conditions …” „… Fictitious Domain Approach for Thin-Walled Structures. Computer Methods in Applied Mechanics and Engineering …” „… , 190:1925–1935, 2001. [65] A. Düster and E. Rank. Die Finite Cell Methode - Eine Fictitious Domain Methode mit …”

Local enrichment of the FCM S. 72-110

„… . smaller cells in the applied Cartesian mesh. In a second approach, the entire domain of interpolation is …” „… examples 101 4.7.3 Interplay between the fictitious domain and the enrichment zone Since there is no …” „… restriction in the mesh generation of the FCM, there can be situations where the fictitious domain and the …”

Numerical integration algorithms for the FCM S. 27-71

„… FCM very efficiently thanks to the application of the fictitious domain property of the method. Each …” „… Ωc (a) ΩB ΩA (b) Figure 3.1: (a) A cut cell and (b) the corresponding sub-domains. 28 3 Numerical …” „… and subdivides the cell into two sub-domains ΩA and ΩB. This function, which – in itself – is smooth …”

doi.org/10.51202/9783186348180

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

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Wadhah Garhuom

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

Series: Mechanik/Bruchmechanik

Volume 359 2024

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Introduction S. 1-5

„… discretization technique, which11 Introductionis based on the fictitious domain approach, in combination with …” „… fictitious domain approaches where themesh does not conform to the domain of interest. In such situations …” „… , which can furthercomplicate the meshing procedure.Fictitious or immersed boundary domain methods, such …”

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

„… allowing the points to be located as wellin the fictitious domain. This leads to a better-conditioned …” „… of the integration pointsare also located in the fictitious domain; see Figure 4.1 (b) for a cell cut …” „… fictitious domainThe resulting global system of equations in the FCM usually has large condition …”

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

„… based on the fictitious domain or immersed boundary domain con-cept, such as the FCM [47, 126] or CutFEM …” „… cut elements.Due to its connection to the fictitious domain, the penalty term is referred to as …” „… much stiffnessto the fictitious domain, which would decrease the condition number but significantly …”

Titelei/Inhaltsverzeichnis

„… overhead, combining the fictitious domain approach with high-order basis functions. Special quadrature …” „… the finite cell method (FCM),which combines the fictitious domain approach with hierarchic high-order …” „… solution in the fictitious domain . . . . . . . . . . . . . 434.8 Application to problems in …”

Bibliography S. 135-152

„… , 2015.[23] E. Burman and P. Hansbo. Fictitious domain finite element methods using cut ele-ments: II. A …” „… quadrature rules for fictitious domain meth-ods. Computers & Mathematics with Applications, 99:270–291 …” „… value problems on high performancecomputers by fictitious domain method. Siberian Mathematical Journal …”

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

„… points, while the points in the fictitious domain aredisregarded since they typically exhibit the worst …” „… gradually in the fictitious domain asthe distance from the domain boundary increases.0 0.2 0.4 0.6 0.8 …” „… stabilize the fictitious domain. The adaptive octree is employed with atree-depth of kAOT = 3 for the …”

doi.org/10.51202/9783186359186

VDI Wissensforum GmbH - Technische Zuverlässigkeit 2021

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VDI Wissensforum GmbH (ed.)

Technische Zuverlässigkeit 2021

Series: VDI-Berichte

Volume 2377 2021

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S. Kupjetz, T. Pfeiffer, J. Holz Entwicklungsbegleitende domänenübergreifende Zuverlässigkeitsanalyse von Einzelkomponenten bis hin zum Gesamtsystem am Beispiel einer Lithium-Ionen-Batteriezelle S. 185-196

„… sub-domains for the individual components of a lithium-ion cell. This makes it possible to keep the focus on …” „… safety. This is especially more likely when fundamental changes are made in different domains. It …” „… between different domains with significant effects on reliability. Keeping track of these different …”

doi.org/10.51202/9783181023778

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VDI Wissensforum GmbH (ed.)

Autoreg 2019

Series: VDI-Berichte

Volume 2349 2019

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N. Althar Udupa, E. Schulz, M. Schultalbers Polytopic LPV Controller Design to Control the Boost Manifold Pressure in an Internal Combustion Engine S. 377-388

„… parameter varying (LPV) approach. This research work throws light on a polytopic LPV controller …” „… made introduces significant conservatism in this approach. However, a trade-off between simplicity and …” „… . The fictitious output signals and are generated by weighting functions and , respectively …”

doi.org/10.51202/9783181023495

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