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- Van Borselen, R.G. (author), Fokkema, J.T. (author), Van den Berg, P.M. (author), Van der Weiden, R.M. (author), Tan, T.H. (author) journal article 1994
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- Vuik, C. (author), Segal, A. (author), el Yaakoubi, L. (author), Dufour, E. (author) report 2001
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Vermolen, F.J. (author), Vuik, C. (author)We investigate the influence of the value of deflation vectors at interfaces on the rate of convergence of preconditioned conjugate gradient methods. Our set-up is a Laplace problem in two dimensions with continuous or discontinuous coeffcients that vary in several orders of magnitude. In the continuous case we are interested in the convergence...report 2001
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Vermolen, F.J. (author), Vuik, C. (author), Segal, A. (author)We investigate the influence of the value of deflation vectors at interfaces on the rate of convergence of preconditioned conjugate gradient methods applied to a Finite Element discretization for an elliptic equation. Our set-up is a Poisson problem in two dimensions with continuous or discontinuous coefficients that vary in several orders of...report 2002
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Nabben, R. (author), Vuik, C. (author)In this paper we compare various preconditioners for the numerical solution of partial dierential equations. We compare a coarse grid correction preconditioner used in domain decomposition methods with a so-called deflation preconditioner. We prove that the effective condition number of the de ated preconditioned system is always, i.e. for all...report 2003
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Nabben, R. (author), Vuik, C. (author)In this paper we compare various preconditioners for the numerical solution of partial differential equations. We compare the well-known balancing Neumann Neumann preconditioner used in domain decomposition methods with a so-called deflation preconditioner. We prove that the effective condition number of the deflated preconditioned system is...report 2004
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Tang, J.M. (author)In this report we give a short overview of aspects on parallel deflated conjugate gradient method which is applied on large, sparse, symmetric and semi-positive definite linear systems obtained from moving boundary problems. Moreover, we present some results of small numerical experiments. After introducing the Navier-Stokes equations for...report 2005
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Tang, J.M., (author), Vuik, C. (author)In this report we give new insights into the properties of invertible and singular deflated and preconditioned linear systems where the coefficient matrices are also symmetric and positive (semi-) definite. First we prove that the invertible de ated matrix has always a more favorable effeective condition number compared to the original matrix....report 2005
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Tang, J.M. (author), Vuik, C. (author)For various applications, it is well-known that deflated ICCG is an efficient method for solving linear systems with invertible and singular co-efficient matrix. This deflated ICCG with subdomain deflation vectors is used by us to solve linear systems with singular coefficient matrix, arising from a discretization of the Poisson equation with...report 2006
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Riyanti, C.D. (author), Erlangga, Y.A. (author), Plessix, R.E. (author), Mulder, W.A. (author), Vuik, C. (author), Oosterlee, C. (author)The time-harmonic wave equation, also known as the Helmholtz equation, is obtained if the constant-density acoustic wave equation is transformed from the time domain to the frequency domain. Its discretization results in a large, sparse, linear system of equations. In two dimensions, this system can be solved efficiently by a direct method. In...journal article 2006
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Tang, J.M. (author), Vuik, C. (author)Simulating bubbly flows is a very popular topic in CFD. These bubbly flows are governed by the Navier-Stokes equations. In many popular operator splitting formulations for these equations, solving the linear system coming from the discontinuous diffusion equation takes the most computational time, despite of its elliptic origins. Sometimes these...conference paper 2006
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Tang, J.M. (author), Vuik, C. (author)Simulating bubbly flows is a very popular topic in CFD. These bubbly flows are governed by the Navier-Stokes equations. In many popular operator splitting formulations for these equations, solving the linear system coming from the discontinuous diffusion equation takes the most computational time, despite of its elliptic origins. Sometimes these...conference paper 2006
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Tang, J.M. (author)The Preconditioned Conjugate Gradient (PCG) method is one of the most popular iterative methods for solving large linear systems with a symmetric and positive semi-definite coefficient matrix. However, if the preconditioned coefficient matrix is ill-conditioned, the convergence of the PCG method typically deteriorates. Instead, a two-level PCG...doctoral thesis 2008
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Tang, J.M. (author), Nabben, R. (author), Vuik, C. (author), Erlangga, Y.A. (author)For various applications, it is well-known that a multi-level, in particular two-level, preconditioned CG (PCG) method is an efficient method for solving large and sparse linear systems with a coefficient matrix that is symmetric positive definite. The corresponding two-level preconditioner combines traditional and projection-type...journal article 2009
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- Van 't Wout, E. (author) master thesis 2009
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Tang, J.M. (author), MacLachlan, S.P. (author), Nabben, R. (author), Vuik, C. (author)It is well known that two-level and multilevel preconditioned conjugate gradient (PCG) methods provide efficient techniques for solving large and sparse linear systems whose coefficient matrices are symmetric and positive definite. A two-level PCG method combines a traditional (one-level) preconditioner, such as incomplete Cholesky, with a...journal article 2010
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Van 't Wout, E. (author), Van Gijzen, M.B. (author), Ditzel, A. (author), Van der Ploeg, A. (author), Vuik, C. (author)Ship simulators are used for training purposes and therefore have to calculate realistic wave patterns around the moving ship in real time. We consider a wave model that is based on the variational Boussinesq formulation, which results in a set of partial differential equations. Discretization of these equations gives a large system of linear...journal article 2010
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Gupta, R. (author)In this work we have implemented the Iterative Method of Conjugate Gradients with two levels of Preconditioning to solve a System of Linear Equations on Graphical Processing Unit (GPU). This system represents the discretized Pressure equation resulting from the Level Set Method Solution of the Incompressible Navier Stokes Equation used to...master thesis 2010
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Kaliszka, K.B. (author)In this master thesis I investigate the case of solving linear systems which correspond to mechanical problems with the use of Deflated Preconditioned Conjugate Method (DPCG), where the creation of the preconditioner is based on Additive Schwarz method (ASM). This approach allows us to perform several computation steps in parallel, which leads...master thesis 2010
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- Gupta, R. (author), Vuik, C. (author), Lemmens, C.W.J. (author) report 2010