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- Vuik, C. (author), Segal, A. (author), el Yaakoubi, L. (author), Dufour, E. (author) report 2001
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Collignon, T.P. (author), Sleijpen, G.L.G. (author), Van Gijzen, M.B. (author)In this paper the IDR(s) method is interpreted in the context of deflation methods. It is shown that IDR(s) can be seen as a Richardson iteration preconditioned by a variable deflation–type preconditioner. The main result of this paper is the IDR projection theorem, which relates the spectrum of the deflated system in each IDR(s) cycle to all...report 2010
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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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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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- Gupta, R. (author), Vuik, C. (author), Lemmens, C.W.J. (author) report 2010
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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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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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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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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