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document
Jönsthövel, T.B. (author), Van Gijzen, M.B. (author), Vuik, C. (author), Scarpas, A. (author)
Large discontinuities in material properties, such as those 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 method. This paper...
journal article 2013
document
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
document
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