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- Thomas, R. (author), Lahaye, D.J.P. (author), Vuik, C. (author), Van der Sluis, L. (author) report 2013
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He, X. (author), Neytcheva, M. (author), Vuik, C. (author)This paper deals with fast and reliable numerical solution methods for the incompressible non-Newtonian Navier-Stokes equations. To handle the nonlinearity of the governing equations, the Picard and Newton methods are used to linearize these coupled partial differential equations. For space discretization we use the finite element method and...report 2013
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- Lingen, F.J. (author), Bonnier, P.G. (author), Brinkgreve, R.B.J. (author), Van Gijzen, M.B. (author), Vuik, C. (author) report 2012
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- Van Slingerland, P. (author), Vuik, C. (author) report 2012
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- Van Slingerland, P. (author), Vuik, C. (author) report 2012
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Idema, R. (author), Papaefthymiou, G. (author), Lahaye, D.J.P. (author), Vuik, C. (author), Van der Sluis, L. (author)Current and future developments in the power system industry demand fast power flow solvers for larger power flow problems. The established methods are no longer viable for such problems, as they are not scalable in the problem size. In this paper, the use of Newton-Krylov power flow methods is proposed, and a multitude of preconditioning...report 2012
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Raees, F. (author), Van der Heul, D.R. (author), Vuik, C. (author)The Mass-Conserving Level-Set method combines the efficiency of a Level-Set algorithm with the mass conserving properties of the Volume Of Fluid method. It avoids the work intensive interface construction of the former method and imposes a mass-conserving correction to the distance function of the latter. The interface capturing algorithm...report 2011
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Jönsthövel, T.B. (author), Van Gijzen, M.B. (author), MacLachlan, S. (author), Vuik, C. (author), Scarpas, A. (author)The demand for large FE meshes increases as parallel computing becomes the standard in FE simulations. Direct and iterative solution methods are used to solve the resulting linear systems. Many applications concern composite materials, which are characterized by large discontinuities in the material properties. An example of such a material is...report 2011
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Gupta, R. (author), Van Gijzen, M.B. (author), Vuik, K. (author)We present an implementation of Two-Level Preconditioned Conjugate Gradient Method for the GPU. We investigate a Truncated Neumann Series based preconditioner in combination with deflation and compare it with Block Incomplete Cholesky schemes. This combination exhibits fine-grain parallelism and hence we gain considerably in execution time. It’s...report 2011
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Van Slingerland, P. (author), Vuik, C. (author)Despite their geometric flexibility and high accuracy, an important drawback of Discontinuous Galerkin (DG) methods is that the resulting linear systems cannot be solved efficiently by standard iterative solution methods. In search of an effective preconditioning strategy for these systems, we cast a uniform spectral two-level preconditioner...report 2011
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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 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 (PCG) method. This paper...report 2011
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Vuik, K. (author), Daalderop, F. (author), Van Kints, R. (author), Baksteen, T. (author), Schaap, B. (author)This report gives an overview of the development and experiences of using Mumie [1] at TU Delft during the academic year 2010-2011. Mumie is an e-learning platform that can be used for mathematical courses and acquired the interest of TU Delft at the beginning of 2009 in order to be used in their first years mathematical courses, in particular...report 2011
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Vuik, K. (author), Daalderop, F. (author), Van Kints, R. (author), Schaap, B. (author)In this document the Mumie pilot that took place in March 2010 for the Linear Algebra course (wi1403lr) at Aerospace Engineering will be evaluated. This pilot is the result of an interest in using an e-learning platform that can improve the level of education for first year mathematical courses at TU Delft. In order to be successful with such...report 2011
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- Vermolen, F.J. (author), Vuik, C. (author) report 2011
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Idema, R. (author), Lahaye, D.J.P. (author), Vuik, C. (author)The inexact Newton method is widely used to solve systems of non-linear equations. It is well-known that forcing terms should be chosen relatively large at the start of the process, and be made smaller during the iteration process. This paper explores the mechanics behind this behavior theoretically using a simplified problem, and presents...report 2011
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Sheikh, A.H. (author), Lahaye, D. (author), Vuik, C. (author)A Helmholtz solver whose convergence is parameter independent can be obtained by combining the shifted Laplace preconditioner with multigrid deflation. To proof this claim, we develop a Fourier analysis of a two-level variant of the algorithm proposed in [1]. In this algorithm those eigenvalues that prevent the shifted Laplace preconditioner...report 2011
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- Vermolen, F.J. (author), Vuik, C. (author) report 2010
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Idema, R. (author), Lahaye, D.J.P. (author), Vuik, C. (author), Van der Sluis, L. (author)The power flow problem is generally solved by the Newton-Raphson method with a sparse direct solver for the linear system of equations in each iteration. While this works fine for small power flow problems, we will show that for very large problems the direct solver is very slow and we present alternatives that scale much better in the problem...report 2010
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- Van Slingerland, P. (author), Vuik, C. (author) report 2010
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- Gupta, R. (author), Vuik, C. (author), Lemmens, C.W.J. (author) report 2010