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Wang, Luyu (author), Chen, Weizhong (author), Vuik, Cornelis (author)Developing numerical method of fractured porous media is of paramount importance in geoscience applications. Previous studies have revealed that the discrete fractures and cavities as well as the heterogeneity have considerable influences on hydraulic property of porous media. This work presents a numerical investigation on fluid flow in...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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Vermolen, F.J. (author), Bakker, D.R. (author), Vuik, Cornelis (author)The discretisation of the Laplacian results into the well-known Laplace matrix. In the case of a one dimensional problem, an explicit formula for its inverse is derived on the basis of fundamental solutions (Green’s functions) for general boundary conditions. For a linear reaction–diffusion equation, approximations of the inverse are given.journal article 2022
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Kootte, M.E. (author), Vuik, Cornelis (author)This paper compares and assesses several numerical methods that solve the steady-state power flow problem on integrated transmission-distribution networks. The integrated network model consists of a balanced transmission and an unbalanced distribution network. It is important to analyze these integrated electrical power systems due to the...journal article 2021
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Markensteijn, A.S. (author), Romate, J.E. (author), Vuik, Cornelis (author)Optimization is an important tool for the operation of an energy system. Multi-carrier energy systems (MESs) have recently become more important. Load flow (LF) equations are used within optimization to determine if physical network limits are violated. Due to nonlinearities, the solvability of the OF problem and the convergence of the...journal article 2021
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Sereeter, B. (author), Markensteijn, A.S. (author), Kootte, M.E. (author), Vuik, Cornelis (author)Power flow computations are important for operation and planning of the electricity grid, but are computationally expensive because of nonlinearities and the size of the system of equations. Linearized methods reduce computational time but often have the disadvantage that they are not applicable to general grids. In this paper we propose a novel...journal article 2021
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Vandenplas, Jérémie (author), Calus, Mario P.L. (author), Eding, Herwin (author), van Pelt, Mathijs (author), Bergsma, Rob (author), Vuik, Cornelis (author)Background<br/>The preconditioned conjugate gradient (PCG) method is the current method of choice for iterative solving of genetic evaluations. The relative difference between two successive iterates and the relative residual of the system of equations are usually chosen as a termination criterion for the PCG method in animal breeding. However,...journal article 2021
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Dwarka, V.N.S.R. (author), Vuik, Cornelis (author)In researching the Helmholtz equation, the focus has either been on the accuracy of the numerical solution (pollution) or the acceleration of the convergence of a preconditioned Krylov-based solver (scalability). While it is widely recognized that the convergence properties can be investigated by studying the eigenvalues, information from the...journal article 2021
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El Abbassi, M. (author), Lahaye, D.J.P. (author), Vuik, Cornelis (author)One of the quickest ways to influence both the wall temperature and thermal NOx emissions in rotary kilns is to change the air–fuel ratio (AFR). The normalized counterpart of the AFR, the equivalence ratio, is usually associated with premixed flames and studies of its influence on diffusion flames are inconsistent, depending on the application....journal article 2021
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Lahaye, D.J.P. (author), El Abbassi, M. (author), Vuik, Cornelis (author), Talice, Marco (author), Juretic, F. (author)This work studies how non-premixed turbulent combustion in a rotary kiln depends on the<br/>geometry of the secondary air inlet channel. We target a kiln in which temperatures can reach values above 1800 degrees Kelvin. Monitoring and possible mitigation of the thermal nitric-oxide (NOx) formation is of utmost importance. The performed reactive...journal article 2021
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Wang, Y. (author), Vuik, Cornelis (author), Hajibeygi, H. (author)CO2 injection into deep saline aquifers has shown to be a feasible option, as for their large storage capacity under safe operational conditions. Previous studies have revealed that CO2 can be trapped in the subsurface by several mechanisms. Despite the major advances in studying these trapping mechanisms, their dynamic interactions in different...journal article 2022
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Nakate, P.A. (author), Lahaye, D.J.P. (author), Vuik, Cornelis (author)Thermal nitric-oxide (NOx) formation in industrial furnaces due to local overheating is a widely known problem. Various industries made significant investments to reduce thermal NOx by varying the operating conditions and designs of the furnace. It is difficult to find the optimal operating conditions that minimize NOx formation in the...journal article 2021
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Dwarka, V.N.S.R. (author), Vuik, Cornelis (author)Recent research efforts aimed at iteratively solving time-harmonic waves have focused on a broad range of techniques to accelerate convergence. In particular, for the famous Helmholtz equation, deflation techniques have been studied to accelerate the convergence of Krylov subspace methods. In this work, we extend the two-level deflation method...journal article 2022
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Buwalda, F.J.L. (author), de Goede, Erik (author), Knepflé, Maxim (author), Vuik, Cornelis (author)The accuracy, stability and computational efficiency of numerical methods on central processing units (CPUs) for the depth-averaged shallow water equations were well covered in the literature. A large number of these methods were already developed and compared. However, on graphics processing units (GPUs), such comparisons are relatively scarce....journal article 2023
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Gaiko, V. (author), Ginoux, Jean-Marc (author), Vuik, Cornelis (author)We carry out the global bifurcation analysis of the Kukles system representing a planar polynomial dynamical system with arbitrary linear and cubic right-hand sides and having an anti-saddle at the origin. Using the <br/>Wintner–Perko termination principle of multiple limit cycles, we solve the problem on the maximum number and distribution of...journal article 2017
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Vuik, Cornelis (author)In these lecture notes an introduction to Krylov subspace solvers and preconditioners is presented. After a discretization of partial differential equations large, sparse systems of linear equations have to be solved. Fast solution of these systems is very urgent nowadays. The size of the problems can be 1013 unknowns and 1013 equations....journal article 2018
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Gaiko, V. (author), Vuik, Cornelis (author), Reijm, Huibert A.J. (author)In this paper, we study a multi-parameter Liénard polynomial system carrying out its global bifurcation analysis. To control the global bifurcations of limit cycle in this systems, it is necessary to know the properties and combine the effects of all its field rotation parameters. It can be done by means of the development of our...journal article 2018
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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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Wang, Y. (author), Vuik, Cornelis (author), Hajibeygi, H. (author)Natural or induced fractures are typically present in subsurface geological formations. Therefore, they need to be carefully studied for reliable estimation of the long-term carbon dioxide storage. Instinctively, flow-conductive fractures may undermine storage security as they increase the risk of CO2 leakage if they intersect the CO2 plume. In...journal article 2022
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Kemna, Maarten (author), Heinlein, A. (author), Vuik, Cornelis (author)Surrogate models based on convolutional neural networks (CNNs) for computational fluid dynamics (CFD) simulations are investigated. In particular, the flow field inside two-dimensional channels with a sudden expansion and an obstacle is predicted using an image representation of the geometry as the input. Generative adversarial neural networks ...journal article 2023