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Chen, Kewang (author), Vuik, Cornelis (author)Although Anderson acceleration AA(m) has been widely used to speed up nonlinear solvers, most authors are simply using and studying the stationary version of Anderson acceleration. The behavior and full potential of the non-stationary version of Anderson acceleration methods remain an open question. Motivated by the hybrid linear solver...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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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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Diaz Cortes, Gabriela Berenice (author), Vuik, Cornelis (author), Jansen, J.D. (author)We explore and develop a Proper Orthogonal Decomposition (POD)-based deflation method for the solution of ill-conditioned linear systems, appearing in simulations of two-phase flow through highly heterogeneous porous media. We accelerate the convergence of a Preconditioned Conjugate Gradient (PCG) method achieving speed-ups of factors up to...journal article 2021
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He, Xin (author), Vuik, Cornelis (author)This paper introduces three new Schur complement approximations for the augmented Lagrangian preconditioner. The incompressible Navier-Stokes equations discretized by a stabilized finite element method are utilized to evaluate these new approximations of the Schur complement. A wide range of numerical experiments in the laminar context...journal article 2020
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Lukyanov, A. (author), Vuik, Cornelis (author)Smoothed particle hydrodynamics (SPH) has been extensively used to model high and low Reynolds number flows, free surface flows and collapse of dams, study pore-scale flow and dispersion, elasticity, and thermal problems. In different applications, it is required to have a stable and accurate discretization of the elliptic operator with...journal article 2020
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Wobbes, E. D. (author), Möller, M. (author), Galavi, V. (author), Vuik, Cornelis (author)The material point method (MPM) is an effective computational tool for simulating problems involving large deformations. However, its direct mapping of the material-point data to the background grid frequently leads to severe inaccuracies. The standard function reconstruction techniques can considerably decrease these errors, but do not...conference paper 2020
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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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Tran, Quoc-Anh (author), Wobbes, Elizaveta (author), Sołowski, Wojciech (author), Möller, M. (author), Vuik, Cornelis (author)The paper shows a moving least squares reconstruction technique applied to the B-spline Material Point Method (B-spline MPM). It has been shown previously that B-spline MPM can reduce grid-crossing errors inherent in the original Material Point Method. However, in the large deformation regime where the gridcrossing occurs more frequently, the...conference paper 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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Wobbes, Elizaveta (author), Tielen, R.P.W.M. (author), Möller, M. (author), Vuik, Cornelis (author), Galavi, Vahid (author)Both the Material Point Method (MPM) and meshfree schemes based on optimal transport theory have been developed for efficient and robust integration of the weak form equations originating from computational mechanics. Although the methods are derived in a different fashion, their algorithms share many similarities. In this paper, we outline the...conference paper 2019
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Linear power flow method improved with numerical analysis techniques applied to a very large networkSereeter, B. (author), van Westering, W.H.P. (author), Vuik, Cornelis (author), Witteveen, C. (author)In this paper, we propose a fast linear power flow method using a constant impedance load model to simulate both the entire Low Voltage (LV) and Medium Voltage (MV) networks in a single simulation. Accuracy and efficiency of this linear approach are validated by comparing it with the Newton power flow algorithm and a commercial network design...journal article 2019
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Wobbes, Elizaveta (author), Möller, M. (author), Galavi, Vahid (author), Vuik, Cornelis (author)Within the standard material point method (MPM), the spatial errors are partially caused by the direct mapping of material-point data to the background grid. In order to reduce these errors, we introduced a novel technique that combines the least squares method with the Taylor basis functions, called the Taylor least squares (TLS), to...journal article 2019
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Sereeter, B. (author), Vuik, Cornelis (author), Witteveen, C. (author)A general framework is given for applying the Newton–Raphson method to solve power flow problems, using power and current-mismatch functions in polar, Cartesian coordinates and complex form. These two mismatch functions and three coordinates, result in six possible ways to apply the Newton–Raphson method for the solution of power flow...journal article 2019
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Li, Xiaozhou (author), Ryan, J.K. (author), Kirby, Robert M. (author), Vuik, Cornelis (author)Smoothness-increasing accuracy-conserving (SIAC) filtering is an area of increasing interest because it can extract the “hidden accuracy” in discontinuous Galerkin (DG) solutions. It has been shown that by applying a SIAC filter to a DG solution, the accuracy order of the DG solution improves from order k+ 1 to order 2 k+ 1 for linear...journal article 2019
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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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He, X. (author), Vuik, Cornelis (author), Klaij, Christiaan M. (author)The augmented Lagrangian (AL) preconditioner and its variant have been successfully applied to solve saddle point systems arising from the incompressible Navier-Stokes equations discretized by the finite element method. Attractive features are the purely algebraic construction and robustness with respect to the Reynolds number and mesh renement....journal article 2018
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Hosseinimehr, S.M. (author), Cusini, M. (author), Vuik, Cornelis (author), Hajibeygi, H. (author)We present an algebraic dynamic multilevel method for multiphase flow in heterogeneous fractured porous media (F-ADM), where fractures are resolved at fine scale with an embedded discrete modelling approach. This fine-scale discrete system employs independent fine-scale computational grids for heterogeneous matrix and discrete fractures,...journal article 2018
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Chen, Jinhai (author), Vuik, Cornelis (author)Large-scale systems of nonlinear equations appear in many applications. In various applications, the solution of the nonlinear equations should also be in a certain interval. A typical application is a discretized system of reaction diffusion equations. It is well known that chemical species should be positive otherwise the solution is not...journal article 2017
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van Zwieten, J.S.B. (author), Sanderse, B. (author), Hendrix, M.H.W. (author), Vuik, Cornelis (author), Henkes, R.A.W.M. (author)One-dimensional models for multiphase flow in pipelines are commonly discretised using first-order Finite Volume (FV) schemes, often combined with implicit time-integration methods. While robust, these methods introduce much numerical diffusion depending on the number of grid points. In this paper we propose a high-order, space-time...journal article 2017