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Vandenplas, Jeremie (author), Nguyen, B. (author), Vuik, Cornelis (author)In this paper, we consider a block Jacobi preconditioner and various deflation techniques applied in the Deflated Preconditioned Conjugate Gradient (DPCG) method for solving a sparse system of linear equations derived from a statistical linear mixed model that analyses simultaneously phenotypic and pedigree information of genotyped and...journal article 2023
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CHENG, ZHIMIN (author)A wide range of practical problems involve computing multi-dimensional integrations. However, in most cases, it is hard to find analytical solutions to these multi-dimensional integrations. Their numerical solutions always suffer from the `curse of dimension', which means the computational complexity grows exponentially with respect to the...master thesis 2022
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Mooiman, Arthur (author)In this thesis the Conjugate Gradient method used in the forecasting of the number of students in the Netherlands is investigated. The addition of international students to the forecasting led to mathematical problem of which a solution could not be computed. While the numerical method is working as intended, the work presented in this thesis...master thesis 2022
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Hoofwijk, Jorn (author)In finite element software one has to solve a system of non-linear equations, which is commonly simplified to a sequence of linear system. We research the possibility to solve these systems on a GPU to improve the solve time. We are particularly interested in systems arising from geotechnical models. We compare several combinations of Krylov...master thesis 2022
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Nguyen, Buu-Van (author)The single-step single nucleotide polymorphism best linear unbiased prediction (ssSNPBLUP) model can potentially be used in animal breeding for genetic evaluations. It has been reported that this model has convergence issues when the Preconditioned Conjugate Gradient (PCG) method is applied. This is due to the linear system being ill-conditioned...master thesis 2021
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Keer, Pim (author)Level-set percolation on the Discrete Gaussian Free Field (DGFF) turned out to be a hot topic within mathematical physics over the last couple of years. In particular, the DGFF on Z^d , with homogeneously weighted nearest-neighbour interactions, i.e. all conductances equal to 1, has been studied in detail. These models can be simulated with...bachelor 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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Ippolito, Giulia (author)This work is part of the low-fieldMRI project, which aims to bring portable, affordable, low-fieldMRI scanners to low-income countries. Replacing the superconducting magnets of conventional scanners with standard ones can significantly reduce the costs, but it also has a negative impact on the Signal-to-Noise Ratio (SNR). In order to circumvent...master thesis 2020
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Buwalda, Floris (author)In the past 15 years the field of general purpose computing on graphics processing units, or GPUs, has become well developed and the practice is becoming more mainstream. Computational demands of simulation software are continuously increasing. As such for many applications traditionally computed on the central processing unit the question...master thesis 2020
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de Leeuw den Bouter, M.L. (author), van Gijzen, M.B. (author), Remis, R.F. (author)We consider the MRI physics in a low-field MRI scanner, in which permanent magnets are used to generate a magnetic field in the millitesla range. A model describing the relationship between measured signal and image is derived, resulting in an ill-posed inverse problem. In order to solve it, a regularization penalty is added to the least...journal article 2019
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Cheng, L. (author)Modern computational and experimental techniques can represent the detailed dynamics of complex systems using large numbers of degrees of freedom. To facilitate human interpretation or the optimal design of control systems, however, reduced-order models (ROMs) are required. Conventional reduced-order modeling techniques, such as those based on...doctoral thesis 2017
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Gorter, Wilbert (author)Allerlei diffusieverschijnselen in de natuurkunde kunnen omschreven worden<br/>met de Poissonvergelijking op een gebied met te kiezen randvoorwaarden. Er zijn echter ook verschijnselen waarin er een gelaagdheid optreedt zodat er in verticale<br/>richting minder makkelijk diffusie kan plaatsvinden. Dit leidt tot een vergelijking<br/>met...bachelor thesis 2017
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De Leeuw den Bouter, M.L. (author)The quality of magnetic resonance images produced by conventional MRI scanners is guaranteed by the strength and homogeneity of the magnetic field. However, the superconducting magnets required to produce such a field make MRI scanners large and expensive and hence inaccessible to a large number of people in developing countries. Our partners...master thesis 2017
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Hong, Z. (author), Abdalla, M.M. (author)Optimisation algorithms used to automatically size structural members commonly involve stress constraints to avoid material failure. Therefore the cost of optimisation grows rapidly as the number of structural members is increased due to the corresponding increase in the number of constraints. In this work, an efficient method for large scale...conference paper 2016
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He, D. (author)The main objective of this thesis project is to establish an optimization framework that can carry out robust aerodynamic design tasks. The work is based on the single-point optimization module of the SU2 code, which contains the partial differential equation solver for flow evaluation and gradient calculation based on the adjoint method. The...master thesis 2015
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Gupta, R. (author)In this work we study the implementations of deflation and preconditioning techniques for solving ill-conditioned linear systems using iterative methods. Solving such systems can be a time-consuming process because of the jumps in the coefficients due to large difference in material properties. We have developed implementations of the iterative...doctoral thesis 2015
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Zhao, J. (author), Vollebregt, E.A.H. (author), Oosterlee, C.W. (author)This paper presents a fast numerical solver for a nonlinear constrained optimization problem, arising from a 3D frictional contact problem. It incorporates an active set strategy with a nonlinear conjugate gradient method. One novelty is to consider the tractions of each slip element in a polar coordinate system, and use azimuth angles as...report 2014
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Jönsthövel, T.B. (author), Van Gijzen, M.B. (author), Vuik, C. (author), Scarpas, A. (author)Large discontinuities in material properties, such as those encountered in composite materials, lead to ill-conditioned systems of linear equations. These discontinuities give rise to small eigenvalues that may negatively affect the convergence of iterative solution methods such as the preconditioned conjugate gradient method. This paper...journal article 2013
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Kloek, T. (author)This research investigates iterative methods for solving large and sparse least squares problems, as those encountered in tomography. A widely used method for such systems is the Conjugate Gradients method for Least Squares problems (CGLS), which is derived from the popular Conjugate Gradient method. The Conjugate Residuals method can also be...bachelor thesis 2012
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Jönsthövel, T.B. (author), Van Gijzen, M.B. (author), MacLachlan, S. (author), Vuik, C. (author), Scarpas, A. (author)Many applications in computational science and engineering concern composite materials, which are characterized by large discontinuities in the material properties. Such applications require fine-scale finite-element meshes, which lead to large linear systems that are challenging to solve with current direct and iterative solutions algorithms....journal article 2012