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Chen, J. (author), Dwarka, V.N.S.R. (author), Vuik, Cornelis (author)The Helmholtz equation is related to seismic exploration, sonar, antennas, and medical imaging applications. It is one of the most challenging problems to solve in terms of accuracy and convergence due to the scalability issues of the numerical solvers. For 3D large-scale applications, high-performance parallel solvers are also needed. In this...journal article 2024
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Wiersma, R.T. (author), Nasikun, A. (author), Eisemann, E. (author), Hildebrandt, K.A. (author)We introduce a geometric multigrid method for solving linear systems arising from variational problems on surfaces in geometry processing, Gravo MG. Our scheme uses point clouds as a reduced representation of the levels of the multigrid hierarchy to achieve a fast hierarchy construction and to extend the applicability of the method from triangle...conference paper 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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Nasikun, A. (author)Research in geometry processing concerns the design of algorithms and mathematical models for the analysis and manipulation of geometric data. Examples of its applications are shape projection (e.g. smoothing and filtering), shape correspondence (e.g. functional maps), shape descriptors (e.g. heat and wave kernel signatures), segmentation, and...doctoral 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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Nasikun, A. (author), Hildebrandt, K.A. (author)Sparse eigenproblems are important for various applications in computer graphics. The spectrum and eigenfunctions of the Laplace–Beltrami operator, for example, are fundamental for methods in shape analysis and mesh processing. The Subspace Iteration Method is a robust solver for these problems. In practice, however, Lanczos schemes are often...journal article 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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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)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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Maquelin, Eva (author)Numerical methods are investigated for solving large-scale sparse linear systems of equations, that can be applied to thermo-mechanical models and wafer-slip models. This thesis examines efficient numerical methods, in terms of memory, number of iterations required for convergence, and computation time. To be more specific, algebraic multigrid ...master thesis 2021
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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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Kumar, P. (author), Rodrigo, Carmen (author), Gaspar, Francisco J. (author), Oosterlee, C.W. (author)We present a multilevel Monte Carlo (MLMC) method for the uncertainty quantification of variably saturated porous media flow that is modeled using the Richards equation. We propose a stochastic extension for the empirical models that are typically employed to close the Richards equations. This is achieved by treating the soil parameters in...journal article 2019
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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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Lathouwers, D. (author), Perko, Z. (author)In a previous paper (Hennink and Lathouwers, 2017) we developed a finite element discretization for the Boltzmann transport equation with forward peaked scatter modeled by the Fokker–Planck approximation. The discretization was based on the discontinuous Galerkin method in both space and angle. It was expected and found that the regular...journal article 2019
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Kumar, P. (author), Luo, P. (author), Gaspar, Francisco J. (author), Oosterlee, C.W. (author)A multilevel Monte Carlo (MLMC) method for Uncertainty Quantification (UQ) of advection-dominated contaminant transport in a coupled Darcy–Stokes flow system is described. In particular, we focus on high-dimensional epistemic uncertainty due to an unknown permeability field in the Darcy domain that is modelled as a lognormal random field....journal article 2018
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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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Qiu, Y. (author), van Gijzen, M.B. (author), van Wingerden, J.W. (author), Verhaegen, M.H.G. (author), Vuik, Cornelis (author)This paper studies a new preconditioning technique for sparse systems arising from discretized partial differential equations in computational fluid dynamics problems. This preconditioning technique exploits the multilevel sequentially semiseparable (MSSS) structure of the system matrix. MSSS matrix computations give a data-sparse way to...journal article 2018
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Knibbe, H. (author), Vuik, C. (author), Oosterlee, C.W. (author)In geophysical applications, the interest in least-squares migration (LSM) as an imaging algorithm is increasing due to the demand for more accurate solutions and the development of high-performance computing. The computational engine of LSM in this work is the numerical solution of the 3D Helmholtz equation in the frequency domain. The...journal article 2015
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Knibbe, H.P. (author), Vuik, Cornelis (author), Oosterlee, C.W. (author)In geophysical applications, the interest in least-squares migration (LSM) as an imaging algorithm is increasing due to the demand for more accurate solutions and the development of high-performance computing. The computational engine of LSM in this work is the numerical solution of the 3D Helmholtz equation in the frequency domain. The...journal article 2015
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Zhao, J. (author)Rail transportation plays an important role in our everyday life, and there is fast development and modernization in the railway industry to meet the growing demand for swifter, safer and more comfortable trains. At the same time, the security of train operation and the maintenance of rails have to be considered. A lot of research on these...doctoral thesis 2015