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On the convergence of GMRES with invariant-subspace deflation

Yeung, M.C. (author), Tang, J.M. (author), Vuik, C. (author)

We consider the solution of large and sparse linear systems of equations by GMRES. Due to the appearance of unfavorable eigenvalues in the spectrum of the coefficient matrix, the convergence of GMRES may hamper. To overcome this, a deflated variant of GMRES can be used, which treats those unfavorable eigenvalues effectively. In the literature,...

report 2010

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Application of the numerical density-enthalpy method to the multi-phase flow through a porous medium

Ibrahim, D. (author), Vermolen, F.J. (author), Vuik, C. (author)

In this paper we apply a new method to solve multi-phase fluid flow problem for 1D1D and 2D2D fluid systems. This method is developed at TNO and presented in [1] for spatially homogeneous systems. We call this method the numerical density-enthalpy method (or ??-hh method) because density-enthalpy phase diagrams (or ??-hh diagrams) play an...

journal article 2010

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The Deflated Relaxed Incomplete Cholesky CG method for use in a real-time ship simulator

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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A Comparison of Two-Level Preconditioners Based on Multigrid and Deflation

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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Numerical methods for industrial problems with phase changes

Vermolen, F.J. (author), Vuik, C. (author), Hegen, D. (author)

report 2009

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Fast iterative solution methods for the Helmholtz equation

Sheikh, A.H. (author), Vuik, C. (author), Lahaye, D. (author)

report 2009

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Modelling Biogrout: A new ground improvement method based on microbial induced carbonate precipitation

Van Wijngaarden, W.K. (author), Vermolen, F.J. (author), Van Meurs, G.A.M. (author), Vuik, C. (author)

report 2009

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Comparison of Two-Level Preconditioners Derived from Deflation, Domain Decomposition and Multigrid Methods

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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Load flow literature survey

Idema, R. (author), Lahaye, D.J.P. (author), Vuik, C. (author)

report 2009

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Smoothness-increasing convergence-conserving spline filters applied to streamline visualisation of DG approximations

Van Slingerland, P. (author), Ryan, J.K. (author), Vuik, C. (author)

report 2009

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A mathematical analysis of physiological and morphological aspects of wound closure

Javierre, E. (author), Vermolen, F.J. (author), Vuik, C. (author), Van der Zwaag, S. (author)

A computational algorithm to study the evolution of complex wound morphologies is developed based on a model of wound closure by cell mitosis and migration due to Adam [Math Comput Model 30(5–6):23–32, 1999]. A detailed analysis of the model provides estimated values for the incubation and healing times. Furthermore, a set of inequalities are...

journal article 2008

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Berekend in Delft

Vuik, C. (author)

public lecture 2008

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Fast and robust solvers for pressure correction in bubbly flow problems

MacLachlan, S.P. (author), Tang, J.M. (author), Vuik, C. (author)

report 2008

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Numerical methods for industrial flow problems

Vuik, C. (author), Vermolen, F.J. (author), Hegen, D. (author)

report 2008

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Theoretical comparison of two-level preconditioners based on multigrid and deflation

Tang, J.M. (author), MacLachlan, S.P. (author), Nabben, R. (author), Vuik, C. (author)

report 2008

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A local theta scheme for advection problems with strongly varying meshes and velocity profiles

Van Slingerland, P. (author), Borsboom, M. (author), Vuik, C. (author)

report 2008

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A class of projected Newton methods to solve laminar reacting flow problems

Van Veldhuizen, S. (author), Vuik, C. (author), Kleijn, C.R. (author)

report 2008

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SIMPLE-type preconditioners for the Oseen problem

Ur Rehman, M. (author), Vuik, C. (author), Segal, G. (author)

report 2008

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Core-annular flow through a horizontal pipe: Hydrodynamic counterbalancing of buoyancy force on core

Ooms, G. (author), Vuik, C. (author), Poesio, P. (author)

A theoretical investigation has been made of core-annular flow: the flow of a high-viscosity liquid core surrounded by a low-viscosity liquid annular layer through a horizontal pipe. Special attention is paid to the question of how the buoyancy force on the core, caused by a density difference between the core and the annular layer, is...

journal article 2007

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A comparison of abstract versions of deflation, balancing and additive coarse grid correction preconditioners

Nabben, R. (author), Vuik, C. (author)

report 2007