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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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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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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 pmultigrid method, in which coarsening is applied in the spline degree p instead of the mesh width h...journal article 2020
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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 datasparse 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 leastsquares migration (LSM) as an imaging algorithm is increasing due to the demand for more accurate solutions and the development of highperformance 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 leastsquares migration (LSM) as an imaging algorithm is increasing due to the demand for more accurate solutions and the development of highperformance 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
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Sheikh, A.H. (author)The Helmholtz equation is the simplest possible model for the wave propagation. Perhaps this is the reason, despite denying traditional iterative methods like Krylov subspace methods, Multigrids, etcetera, numerical solution of the Helmholtz equation has been an interesting and abundant problem to researchers since years. The work in this...doctoral thesis 2014
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Qiu, Y. (author), Van Gijzen, M.B. (author), Van Wingerden, J. (author), Verhaegen, M. (author), Vuik, C. (author)This paper studies a new preconditioning technique for sparse systems arising from discretized partial differential equations (PDEs) in computational fluid dynamics (CFD), which exploit the multilevel sequentially semiseparable (MSSS) structure of the system matrix. MSSS matrix computations give a datasparse way to approximate the LU...report 2013
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Diao, H. (author)This thesis attempts to explain the convergence behaviour of solving Helmholtz problem by investigating its spectral properties. Fourier analysis is employ to solve the eigenvalues of the matrices that are involved in the iterative methods. The numerical experiment is conducted to verify the conclusions by Fourier analysis and also to reveal...master thesis 2012
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Wan, J.W.L. (author)In the paper, we present multigrid methods for solving scalar conservation laws and convection diffusion equations that frequently arise from fluid flow problems. For scalar conservation laws, we present monotonicity preserving and total variation diminishing multigrid methods. We generalize the upwindbiased residual restriction and...conference paper 2006
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De Borst, R. (author), Hulshoff, S.J. (author), Lenz, S. (author), Munts, E.A. (author), Van Brummelen, E.H. (author), Wall, W.A. (author)The basic idea of multiscale methods, namely the decomposition of a problem into a coarse scale and a fine scale, has in an intuitive manner been used in engineering for many decades, if not for centuries. Also in computational science, largescale problems have been solved, and local data, for instance displacements, forces or velocities, have...conference paper 2006
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De Borst, R. (author), Hulshoff, S.J. (author), Lenz, S. (author), Munts, E.A. (author), Van Brummelen, E.H. (author), Wall, W.A. (author)The basic idea of multiscale methods, namely the decomposition of a problem into a coarse scale and a fine scale, has in an intuitive manner been used in engineering for many decades, if not for centuries. Also in computational science, largescale problems have been solved, and local data, for instance displacements, forces or velocities, have...conference paper 2006
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Köstler, H. (author), Popa, C. (author), Prümmer, M. (author), Rüde, U. (author)In this paper we introduce a multigrid method for sparse, possibly rankdeficient and inconsistent least squares problems arising in the context of tomographic image reconstruction. The key idea is to construct a suitable AMG method using the Kaczmarz algorithm as smoother. We first present some theoretical results about the correction step and...conference paper 2006
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 Wesseling, P. (author), Zijlema, M. (author), Segal, A. (author), Kassels, C.G.M. (author) journal article 1997
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 Zeng, S. (author), Wesseling, P. (author) journal article 1995
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 Zeng, S. (author), Wesseling, P. (author) journal article 1994
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 Oosterlee, C.W. (author), Wesseling, P. (author) journal article 1993
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 Oosterlee, C.W. (author), Wesseling, P. (author), Segal, A. (author), Brakkee, E. (author) journal article 1993
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 Khalil, M. (author) doctoral thesis 1989
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