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Li, Jingya (author)Finite element analysis and multibody dynamics are popular mathematical modeling techniques for sev- eral mechanical applications. The finite element method is a costly method from a runtime standpoint. Moreover, both multibody dynamics and finite element methods require approximating the geometry of the application either by meshing or by...master thesis 2023
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Takacs, Thomas (author), Toshniwal, D. (author)Isogeometric Analysis generalizes classical finite element analysis and intends to integrate it with the field of Computer-Aided Design. A central problem in achieving this objective is the reconstruction of analysis-suitable models from Computer-Aided Design models, which is in general a non-trivial and time-consuming task. In this article,...journal article 2023
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Mederos, Victoria Hernández (author), Ugalde, Isidro Abelló (author), Alfonso, Rolando M.Bruno (author), Lahaye, D.J.P. (author), Ones, Valia Guerra (author)In this paper we use the Isogeometric Analysis (IgA) to solve the Helmholtz equation with Dirichlet boundary condition over a bounded physical 2D domain. Starting from the variational formulation of the problem, we show how to apply IgA to obtain an approximated solution based on biquadratic B-spline functions. We focus the attention on...journal article 2023
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Unnikrishnan, Gokul Krishna (author), Sharma, S. (author), Pathak, Himanshu (author), Chauhan, Vishal Singh (author), Jain, Satish Chandra (author)To accurately analyze the fracture behavior of piezoceramics at small length scales, flexoelectricity must be considered along with piezoelectricity. Due to its dependence on size, flexoelectricity predominates at the micro- and nano-length scales. Additionally, crack tips having the largest strain gradient state cause large flexoelectricity...journal article 2023
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Dwarka, V.N.S.R. (author)The bottleneck in designing iterative solvers for the Helmholtz equation lies in balancing the trade-off between accuracy and scalability. Both the accuracy of the numerical solution and the number of iterations to reach convergence deteriorate in higher dimensions and increase with the wavenumber. To address these issues in this dissertation,...doctoral thesis 2022
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Bosma, Douwe (author)An isogeometric finite element method for incompressible fluid film equations is presented. The method can be applied to numerically model the behaviour of thin cellular membranes, such as lipid bilayers. The membranes are represented by infinitely thin closed surfaces. Both the surface parametrization and analysis are based on state-of-the-art...master thesis 2022
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Volker, Thijs-Gerrit (author)Implementation of an Explicit Algebraic Reynolds Stress Model in Isogeometric Analysis for seperating flows using a two-equation k-omega model. The model is verified for simple cases such as homogeneous isotropic decaying turbulence, and the turbulent backward facing stepmaster thesis 2022
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Looije, Mark (author)Isogeometric Analysis (IgA) is an extension of the more well known Finite Element Method (FEM). It allows for more accurate descriptions of boundary value problems on irregular domains. However, many of the traditional iterative solution strategies that are known to work well in FEM do not show the same behavior in IgA, especially for increasing...master thesis 2022
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Toshniwal, D. (author)Given an unstructured mesh consisting of quadrilaterals and triangles (we allow both planar and non-planar meshes of arbitrary topology), we present the construction of quadratic splines of mixed smoothness — C<sup>1</sup> smooth away from the unstructured regions of T and C<sup>0</sup> smooth otherwise. The splines have several useful B...journal article 2022
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Tielen, R.P.W.M. (author), Möller, M. (author), Vuik, Cornelis (author)Isogeometric Analysis (IgA) can be seen as the natural extension of the Finite Element Method (FEM) to high-order B-spline basis functions. Combined with a time inte- gration scheme within the method of lines, IgA has become a viable alternative to FEM for time-dependent problems. However, as processors' clock speeds are no longer increasing but...conference paper 2022
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Tielen, R.P.W.M. (author), Möller, M. (author), Vuik, Cornelis (author)The use of sequential time integration schemes becomes more and more the bottleneck within large-scale computations due to a stagnation of processor’s clock speeds. In this study, we combine the parallel-in-time Multigrid Reduction in Time method with a p-multigrid method to obtain a scalable solver specifically designed for Isogeometric...journal article 2022
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Hille, Helge C. (author), Kumar, Siddhant (author), De Lorenzis, Laura (author)We propose Floating Isogeometric Analysis (FLIGA), which extends IGA to extreme deformation analysis. The method is based on a novel tensor-product construction of B-Splines for the update of the basis functions in one direction of the parametric space. With basis functions “floating” deformation-dependently in this direction, mesh distortion...journal article 2022
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Koh, Kim Jie (author), Toshniwal, D. (author), Cirak, Fehmi (author)Easy to construct and optimally convergent generalisations of B-splines to unstructured meshes are essential for the application of isogeometric analysis to domains with non-trivial topologies. Nonetheless, especially for hexahedral meshes, the construction of smooth and optimally convergent isogeometric analysis basis functions is still an...journal article 2022
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Wang, Dandan (author), Xu, Jinlan (author), Gao, Fei (author), Wang, C.C. (author), Gu, Renshu (author), Lin, Fei (author), Rabczuk, Timon (author), Xu, Gang (author)In this paper, a deep learning framework combined with isogeometric analysis (IGA for short) called IGA-Reuse-Net is proposed for efficient reuse of numerical simulation on a set of topology-consistent models. Compared with previous data-driven numerical simulation methods only for simple computational domains, our method can predict high...journal article 2022
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Tielen, R.P.W.M. (author)Isogeometric Analysis is a methodology that bridges the gap between Computer Aided Design (CAD) and the Finite Element Method (FEM) by adopting the building blocks used in CAD, namely Non-UniformRational B-Splines and B-splines, as a basis for FEM. The use of these high-order spline functions does not only lead to an accurate representation of...doctoral thesis 2021
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van Schie, Sebastiaan (author)This thesis poses a new geometric formulation for compressible Euler flows. A partial decomposition of this model into Roe variables is applied; this turns mass density, momentum and kinetic energy into product quantities of the Roe variables. Lie derivative advection operators of weak forms constructed with this decomposed model naturally...master thesis 2021
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Herrera Clapera, Miquel (author)Computational fluid dynamics is nowadays one of the pillars of modern aircraft design, just as important as experimental wind tunnel testing. Very ambitious goals in regards to performance, efficiency and sustainability are being asked of the aviation industry, the kind that warrant a virtual exploration of the edges of the flight envelope....master thesis 2021
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Casquero, Hugo (author), Bona-Casas, Carles (author), Toshniwal, D. (author), Hughes, Thomas J.R. (author), Gomez, Hector (author), Zhang, Yongjie Jessica (author)We extend the recently introduced divergence-conforming immersed boundary (DCIB) method [1] to fluid-structure interaction (FSI) problems involving closed co-dimension one solids. We focus on capsules and vesicles, whose discretization is particularly challenging due to the higher-order derivatives that appear in their formulations. In two...journal article 2021
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ten Eikelder, M.F.P. (author), Akkerman, I. (author)Two well-established classes of the interface capturing models are the level-set and phase-field models. Level-set formulations satisfy the maximum principle for the density but are not energy-stable. On the other hand, phase-field models do satisfy the second law of thermodynamics but lack the maximum principle for the density. In this paper...journal article 2021
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Hinz, J.P. (author), Jaeschke, Andrzej (author), Möller, M. (author), Vuik, Cornelis (author)This paper proposes a shape optimization algorithm based on the principles of Isogeometric Analysis (IGA) in which the parameterization of the geometry enters the problem formulation as an additional PDE-constraint. Inspired by the isoparametric principle of IGA, the parameterization and the governing state equation are treated using the same...journal article 2021