Searched for: author%3A%22Tielen%2C+R.P.W.M.%22
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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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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)
Since its introduction in [20], Isogeometric Analysis (IgA) has established itself as a viable alternative to the Finite Element Method (FEM). Solving the resulting linear systems of equations efficiently remains, however, challenging when high-order B-spline basis functions of order p> 1 are adopted for approximation. The use of...
book chapter 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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Dwarka, V.N.S.R. (author), Tielen, R.P.W.M. (author), Möller, M. (author), Vuik, Cornelis (author)
Finding fast yet accurate numerical solutions to the Helmholtz equation remains a challenging task. The pollution error (i.e. the discrepancy between the numerical and analytical wave number k) requires the mesh resolution to be kept fine enough to obtain accurate solutions. A recent study showed that the use of Isogeometric Analysis (IgA)...
journal article 2021
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Tielen, R.P.W.M. (author), Möller, M. (author), Vuik, Cornelis (author)
Isogeometric Analysis (IgA) can be considered as the natural extension of the Finite Element Method (FEM) to high-order B-spline basis functions. The development of efficient solvers for discretizations arising in IgA is a challenging task, as most (standard) iterative solvers have a detoriating performance for increasing values of the...
conference paper 2021
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Tielen, R.P.W.M. (author), Möller, M. (author), Vuik, Cornelis (author)
Isogeometric Analysis can be considered as the natural extension of the Finite Element Method (FEM) to higher-order spline based discretizations simplifying the treatment of complex geometries with curved boundaries. Finding a solution of the resulting linear systems of equations efficiently remains, however, a challenging task. Recently, p...
conference paper 2021
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Wobbes, Elizaveta (author), Tielen, R.P.W.M. (author), Möller, M. (author), Vuik, Cornelis (author)
Both the material-point method (MPM) and optimal transportation meshfree (OTM) method have been developed to efficiently solve partial differential equations that are based on the conservation laws from continuum mechanics. However, the methods are derived in a different fashion and have been studied independently of one another. In this...
journal article 2020
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de Koster, P.B.J. (author), Tielen, R.P.W.M. (author), Wobbes, Elizaveta (author), Möller, M. (author)
The Material Point Method (MPM) is a numerical technique that combines a fixed Eulerian background grid and Lagrangian point masses to simulate materials which undergo large deformations. Within the original MPM, discontinuous gradients of the piecewise-linear basis functions lead to the so-called grid-crossing errors when particles cross...
journal article 2020
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Tielen, R.P.W.M. (author), Möller, M. (author), Göddeke, D. (author), Vuik, Cornelis (author)
Over the years, Isogeometric Analysis has shown to be a successful alternative to the Finite Element Method (FEM). However, solving the resulting linear systems of equations efficiently remains a challenging task. In this paper, we consider a p-multigrid method, in which coarsening is applied in the spline degree p instead of the mesh width h...
journal article 2020
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Tielen, R.P.W.M. (author), Möller, M. (author), Vuik, Cornelis (author)
The Material Point Method (MPM) has been applied successfully to problems in engineering which involve large deformations and history-dependent material behavior. However, the classical method suffers from some shortcomings which influence the quality of the numerical solution significantly. High-order B-spline basis functions solve the problem...
conference paper 2019
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Wobbes, Elizaveta (author), Tielen, R.P.W.M. (author), Möller, M. (author), Vuik, Cornelis (author), Galavi, Vahid (author)
Both the Material Point Method (MPM) and meshfree schemes based on optimal transport theory have been developed for efficient and robust integration of the weak form equations originating from computational mechanics. Although the methods are derived in a different fashion, their algorithms share many similarities. In this paper, we outline the...
conference paper 2019
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Wobbes, Elizaveta (author), Tielen, R.P.W.M. (author), Möller, M. (author), Vuik, Cornelis (author), Galavi, Vahid (author)
book chapter 2019
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Tielen, R.P.W.M. (author), Möller, M. (author), Vuik, Cornelis (author)
Introduced in [1], Isogeometric Analysis (IgA) has become widely accepted in academia and industry. However, solving the resulting linear systems remains a challenging task. For instance, the condition number of the Poisson operator scales quadratically with the mesh width h, but, in contrast to standard Finite Elements, exponentially with the...
conference paper 2018
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Tielen, R.P.W.M. (author), Wobbes, Elizaveta (author), Möller, M. (author), Beuth, Lars (author)
The classical material point method (MPM) developed in the 90s is known for drawbacks which affect the quality of results. The movement of material points from one element to another leads to non-physical oscillations known as ‘grid crossing errors’. Furthermore, the use of material points as integration points renders a numerical quadrature...
journal article 2017
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Tielen, R.P.W.M. (author)
The material point method (MPM) is a meshfree mixed Lagrangian-Eulerian method which utilizes moving Lagrangian material points that store physical properties of a deforming continuum and a fixed Eulerian finite elementmesh to solve the equations of motion for individual time steps. MPM proved to be successful in simulating mechanical problems...
master thesis 2016
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Tielen, R.P.W.M. (author)
bachelor thesis 2013
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