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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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Vuik, Cornelis (author), Vermolen, F.J. (author), van Gijzen, M.B. (author), Vuik, Thea (author)In this book we discuss several numerical methods for solving ordinary differential equations. We emphasize the aspects that play an important role in practical problems. We confine ourselves to ordinary differential equations with the exception of the last chapter in which we discuss the heat equation, a parabolic partial differential equation....book 2023
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Zhang, Z. (author), Wang, Y. (author), Vuik, Cornelis (author), Hajibeygi, H. (author)We present an efficient compositional framework for simulation of CO2 storage in saline aquifers with complex geological geometries during a lifelong injection and migration process. To improve the computation efficiency, the general framework considers the essential hydrodynamic physics, including hysteresis, dissolution and capillarity, by...conference paper 2023
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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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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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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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Wang, L. (author), Golfier, Fabrice (author), Tinet, Anne-Julie (author), Chen, Weizhong (author), Vuik, Cornelis (author)This work investigates numerical method and equivalent continuum approach (ECA) of fluid flow in fractured porous media. The commonly used discrete fracture model (DFM) without upscaling needs full discretization of all fractures. It enjoys the merit of capturing each fracture accurately but will get in trouble with mesh partition and low...journal article 2022
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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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- Danczul, Tobias (author), Hetebrij, Wouter (author), Khalighi, Faeze (author), Kogler, Lukas (author), Lahaye, D.J.P. (author), Luckins, Ellen (author), Munters, Wim (author), Neunteufel, Michael (author), Vuik, Cornelis (author) conference paper 2022
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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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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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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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Hosseinimehr, S.M. (author), Piguave Tomala, Janio (author), Vuik, Cornelis (author), Al Kobaisi, Mohammed (author), Hajibeygi, H. (author)We present the projection-based embedded discrete fracture model (pEDFM) for hexahedral corner-point grid (CPG) geometries, for the simulation of hydrothermal processes in fractured porous media. Unlike the previously-developed pEDFM for structured box grids, our new development allows for the modeling of complex geometries defined with...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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Wang, Lu Yu (author), Chen, Wei Zhong (author), Zhang, Yan Jun (author), Zhang, Xiao Dong (author), Vuik, Cornelis (author)Modeling of fluid flow in porous media is a pillar in geoscience applications. Previous studies have revealed that heterogeneity and fracture distribution have considerable influence on fluid flow. In this work, a numerical investigation of two-phase flow in heterogeneous fractured reservoir is presented. First, the discrete fracture model is...journal article 2022
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Vakili, Seryas (author), Ebadi, G. (author), Vuik, Cornelis (author)In this article, a parameterized extended shift-splitting (PESS) method and its induced preconditioner are given for solving nonsingular and nonsymmetric saddle point problems with nonsymmetric positive definite (1,1) part. The convergence analysis of the (Formula presented.) iteration method is discussed. The distribution of eigenvalues of...journal article 2022
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Lahaye, D.J.P. (author), Nakate, P.A. (author), Vuik, Cornelis (author), Juretic, F. (author), Talice, Marco (author)The operation of large industrial furnaces will continue to rely on hydrocarbon fuels in the near foreseeable future. Mathematical modeling and numerical simulation is expected to deliver key insights to implement measures to further reduce pollutant emissions. These measures include the design optimization of the burners, the dilution of...journal article 2022
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Wang, L. (author), Vuik, Cornelis (author), Hajibeygi, H. (author)Simulation of fracture contact mechanics in deformable fractured media is of paramount important in computational mechanics. Previous studies have revealed that compressive loading may produce mode II fractures, which is quite different from mode I fractures induced by tensile loading. Furthermore, fractures can cross each other. This will...journal article 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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Kootte, M.E. (author), Vuik, Cornelis (author)Power system simulations should be adapted to be applicable to the trends that are currently evoked by the energy transition. This transition is pushing our power system from a traditional hierarchical system to a modern interactive system. In order to keep the supply and transport of energy safe and reliant, we need to change the way we perform...book chapter 2022