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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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Numerical integration algorithms for the FCM S. 27-71

„… 27 Chapter 3 Numerical integration algorithms for the FCM In this chapter, our aim is to study the …” „… numerical integration algorithms for the FCM. As the mesh does not necessarily conform geometrically to the …” „… interface within the cell. In view of the numerical integration, the underlying integrals of unbroken cells …”

Bibliography S. 140-154

„… propagation and nonstandard reduced integration. SIAM Journal on Numerical Analysis, 48:346–371, 2010. [20] S …” „… . [92] S. Hubrich, M. Joulaian, and A. Düster. Numerical integration in the finite cell method based on …” „… , 199(49–52):3237–3249, 2010. [127] S. E. Mousavi and N. Sukumar. Numerical integration of polynomials and discontinuous …”

Titelei/Inhaltsverzeichnis S. I-X

„… introduce and study different numerical integration schemes, such as the adaptive integration method and …” „… boundary conditions . . . . . . . . . . . . . . . . . . 15 2.4.3 Numerical integration of cut cells …” „… integration algorithms for the FCM 27 3.1 Numerical integration of unbroken cells …”

Summary and Outlook S. 133-135

„… work was to improve this method from the viewpoint of numerical integration and the local enrichment …” „… follows. • Numerical integration of the FCM: We discussed different numerical integration schemes in the …” „… FCMwith the moment fitting method only requires slightly more effort in terms of numerical integration in …”

Introduction S. 1-4

„… challenges – which are, for instance, the numerical integration of elements that are cut by the boundary [14 …” „… performing a simulation with the FCM. In Chapter 3, we will then focus on the issue of numerical integration …” „… propose a novel integration approach based on the moment fitting method [127, 129, 167]. Several numerical …”

The spectral cell method S. 111-132

„… mass matrix, we apply the GLL quadrature rule of order ng = p + 1 for the numerical integration of …” „… is resolved during the numerical integration of the cells, so we apply the adaptive quadtree …” „… 111 Chapter 5 The spectral cell method An intricate field of the numerical analysis is the dynamic …”

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

„… ⎤ ⎥⎦ . (2.24) One of the advantages of a simple mapping is that it allows an exact numerical integration of the …” „… captured during the numerical integration of the (discretized) weak form. To obtain an efficient …” „… the scope of the numerical integration, we need to find out whether an integration point happens to be …”

Local enrichment of the FCM S. 72-110

„… accurately. In this particular case, it is possible to perform the numerical integration exactly up to …” „… geometrical mesh and the discretization mesh, special care has to be taken during the numerical integration …” „… . That is, the numerical integration has to be carried out on the finer mesh – usually the geometrical …”

Polynomial integrands S. 138

„… investigate the accuracy of the discussed numerical integration algorithms. These polynomials are based on the …”

doi.org/10.51202/9783186348180

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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Bibliography S. 154-169

„… with Applications, 75:3298–3316, 2018. [31] S. Hubrich and A. Düster. Adaptive numerical integration of …” „… Mathematics and Mechanics, 18:e201800089, 2018. [32] S. Hubrich and A. Düster. Numerical integration for …” „… . Düster. Numerical integration for nonlinear problems of the finite cell method using an adaptive scheme …”

The finite cell method S. 23-35

„… well as the derivation of the discrete equation system. Sec. 3.3 focuses on the numerical integration …” „… Numerical integration When it comes to computing the local cell quantities, special care has to be taken …” „… during the numerical integration process. Thereby, we have to distinguish between cut and noncut finite …”

Introduction S. 1-5

„… bottleneck of the FCM is related to the numerical integration of finite cells. Integrals of cells that are …” „… subcells and, thus, in a large number of integration points. This in turn renders the numerical calculation …” „… numerical integration of finite cells. Within the context of the FCM, it is common to employ adaptive …”

Titelei/Inhaltsverzeichnis S. I-VII

„… – Numerical integration – Moment fitting quadratures – Basis function removal – Remeshing – Data transfer …” „… schemes are introduced that allow to reduce the effort of the numerical integration process significantly …” „… Discretization of the weak forms . . . . . . . . . . . . . . . . . . . . 27 3.3 Numerical integration …”

Summary and outlook S. 150-153

„… aspects are briefly summarized. • In the first topic this thesis, we discussed the numerical integration …” „… large number of quadrature points, thus leading to computationally expensive numerical integration …” „… processes. To perform the numerical integration more efficiently, we proposed novel quadrature methods based …”

Moment fitting quadratures S. 36-78

„… numerical integration process. This is due to the fact that the computational mesh is decoupled from the …” „… scope of this chapter, we focus on the numerical integration process of the finite cell method. As …” „… are discussed in the following. A rather simple commonly applied numerical integration approach is …”

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 …” „… fitting – presented in Sec. 4.2 – in order to reduce the error induced by the numerical integration. For …” „… reduced significantly, thus, reducing the effort of the numerical integration process. In this thesis, we …”

A remeshing strategy for the FCM S. 124-149

„… mesh builds the basis for the numerical integration of the cut cells. Here, it is used to check whether …” „… . Moreover, for the numerical integration, we employ the adaptive Gaussian scheme utilizing an octree based …” „… apply α = 10−q with q = 5 and an order of p = 2 for the ansatz. Furthermore, the numerical integration …”

Basic elements of continuum mechanics S. 6-22

„… } . (2.82) Now, applying integration by parts formula of the first term in Eq. (2.81) and making use of the …” „… approximate solution. Due to its nonlinear character numerical algorithms have to be utilized to solve the …”

doi.org/10.51202/9783186355188

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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Bibliography S. 135-152

„… . Kudela, S. Kollmannsberger, E. Rank, A. A Schröder,and A. Düster. Numerical integration of …” „… Bibliography[78] S. Hubrich and A. Düster. Adaptive numerical integration of broken finite cellsbased on …” „… 201800089, 2018.[79] S. Hubrich and A. Düster. Numerical integration for nonlinear problems of thefinite …”

Introduction S. 1-5

„… conventional Gaussian quadrature schemes. Tocarry out the numerical integration in the cut cells, it is …” „… spatial discretiza-tion of the weak form is performed. Finally, the numerical integration based on …” „… 1 Introduction1.1 MotivationThe finite element method (FEM) is a numerical approach used to solve …”

Titelei/Inhaltsverzeichnis S. I-VIII

„… . . . . . . . . . . . . . . . . . . . . . . . . . . 233.3 Numerical integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.3.1 Gaussian …” „… wird entwickelt, um die Integration von gebrochenen Zellen zu verbessern und die Newton-Raphson-Methode …” „… the FCM robustness for large deformation analysis. Different numerical examples showcase the …”

The finite cell method S. 17-26

„… .3.3 Numerical integrationThe integrals introduced in Sections 3.2.2 and 3.2.3 for the cell stiffness …” „… there-fore numerical integration schemes are utilized. A well-known integration method in thecontext of …” „… respect to a reference cellΩc□ by utilizing the mapping functions. Afterwards, the numerical integration …”

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

„… .(6.10)Second, the geometry is used during the numerical integration to perform inside-outsidetesting to …” „… strain problems in solid mechanics are still adifficult challenge using numerical techniques such as the …” „… at the integration pointsof the new mesh – which can be thought of as some kind of history data …”

Summary and outlook S. 130-133

„… inthis work. For the integration of broken cells using the finite cell method, we developed a …” „… non-negative moment fitting quadrature rule, described in Chapter 4. Here, each integra-tion point is created …” „… integration pointsgreater than the number of moments should be distributed in the physical domain.This choice …”

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

„… . Therefore, special integration schemes are requiredto perform the numerical integration in the cut cells.One …” „… moment fitting quadrature for cut finite elements and cellsFigure 4.1: Numerical integration of a broken …” „… distribute the points without any refinements (kNNMF = 0).Figure 4.3: Numerical integration of a broken cell …”

doi.org/10.51202/9783186359186

Patrick Erbts - Partitioned solution strategies for electro-thermo-mechanical problems applied to the field-assisted sintering technology

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Patrick Erbts

Partitioned solution strategies for electro-thermo-mechanical problems applied to the field-assisted sintering technology

Series: Mechanik/Bruchmechanik

Volume 345 2016

Results in this title

Numerical methods S. 45-78

„… reference is made to [19, 43]. 3.2.4 Numerical integration So far, the computation of the integrals arising …” „… 45 CHAPTER3 Numerical methods The third chapter is concerned with numerical methods to find an …” „… numerical solution procedures for the governing equations of the mechanical, thermal, electrical and …”

Bibliography S. 186-204

„… / simulia/portfolio/abaqus/overview/, 2012. [2] A. Aitken. On Bernoulli’s numerical solution of algebraic equations. Proceedings of …” „… Numerical Methods in Engineering, 35:737–766, 1992. [4] F. Armero and J.C. Simo. A priori stability …” „… , 122(1-2):1–21, 2000. Numerical Analysis in the 20th Century Vol. II: Interpolation and Extrapolation. [18] C …”

Conclusions and outlook S. 171-173

„… for several numerical computations. Apart from academic examples serving to test the partitioned …” „… , different numerical models for the radiative transfer are discussed. For the special case of vacuum …” „… , the three different numerical radiation models are investigated and compared to the standard, but the …”

Titelei/Inhaltsverzeichnis S. I-XVI

„… – Numerical thermal radiation – Convergence acceleration – Fluid-structure interaction – Coupled problems …” „… (CFD) solvers. The numerical results are compared to experiments. Moreover, an in-depth study of …” „… . . . . . . . . . . . . . . . . 39 2.3.4 Coupling to other fields . . . . . . . . . . . . . . . . . . . . . 41 3 Numerical methods 45 …”

Solution of coupled problems S. 79-144

„… coupling algorithm is generally embedded in a time integration procedure, as shown in Figure 4.1. This …” „… applying an implicit time integration procedure [3]. 4.1. Coupling algorithms: an introduction 81 tn Solve …” „… Newton-Raphson procedure might become extremely large and also unsymmetrical. For some cases, the numerical …”

Governing equations S. 8-44

„… the numerical solution process. More specifically, this part does not fulfil the material 2.1. Basic …” „… continuum mechanics 13 objectivity requirement, which is why it is not suitable for further numerical …” „… often neglected or only treated approximately in numerical analysis. With increasing temperature …”

doi.org/10.51202/9783186345189

Matthias Jüttner - Softwareagenten-basierte Berechnung interdisziplinärer gekoppelter Simulation

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Matthias Jüttner

Softwareagenten-basierte Berechnung interdisziplinärer gekoppelter Simulation

Series: Rechnerunterstützte Verfahren

Volume 469 2017

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Literaturverzeichnis S. 98-110

„… , J. Hoeflinger, L. Kale und M. Bhandarkar, „A New Approach to Software Integration Frameworks for …” „… Stuttgart, Institut für Theorie der Elektrotechnik, 2015. [64] M. Nikraz, „Agent-Based Integration of …” „… ] M. Kaltenbacher, Numerical Simulation of Mechatronic Sensors and Actuators. Springer, 2015, Bd. 3 …”

doi.org/10.51202/9783186469205

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