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Astudillo, R. (author), Van Gijzen, M.B. (author)This work presents an algorithm to approximate eigenpairs of large, sparse and nonsymmetric matrices based on the Induced Dimension Reduction method (IDR(s)) introduced in [1]. We obtain a Hessenberg relation from IDR(s) computations and in conjunction with Implicitly Restarting and shift-and-invert techniques [2] we created a short recurrence...conference paper 2013
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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 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
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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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Jönsthövel, T.B. (author), Van Gijzen, M.B. (author), MacLachlan, S. (author), Vuik, C. (author), Scarpas, A. (author)Many applications in computational science and engineering concern composite materials, which are characterized by large discontinuities in the material properties. Such applications require fine-scale finite-element meshes, which lead to large linear systems that are challenging to solve with current direct and iterative solutions algorithms....journal article 2012
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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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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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Van Gijzen, M.B. (author), Sleijpen, G.L.G. (author), Zemke, J.P. (author)We give two important generalizations of the Induced Dimension Reduction (IDR) approach for the solution of linear systems. We derive a flexible and a multi-shift Quasi-Minimal Residual IDR (QMRIDR) variant. Numerical examples are presented to show the effectiveness of these new IDR variants compared to existing ones and to other Krylov subspace...report 2011
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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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Sleijpen, G.L.G. (author), Van Gijzen, M.B. (author)IDR(s) [P. Sonneveld and M. B. van Gijzen, SIAM J. Sci. Comput., 31 (2008), pp. 1035–1062] and BiCGstab(?) [G. L. G. Sleijpen and D. R. Fokkema, Electron. Trans. Numer. Anal., 1 (1993), pp. 11–32] are two of the most efficient short-recurrence iterative methods for solving large nonsymmetric linear systems of equations. Which of the two is best...journal article 2010
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Van Gijzen, M.B. (author), Sonneveld, P. (author)The IDR(s) method that is proposed in [18] is a very efficient limited memory method for solving large nonsymmetric systems of linear equations. IDR(s) is based on the induced dimension reduction theorem, that provides a way to construct subsequent residuals that lie in a sequence of shrinking subspaces. The IDR(s) algorithm that is given in [18...report 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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Van Gijzen, M.B. (author), Collignon, T.P. (author)The IDR(s) method that is proposed in [26] is an efficient limited memory method for solving large nonsymmetric systems of linear equations. In [11] an IDR(s) variant is described that has a single synchronisation point per iteration step, which makes this variant well-suited for parallel and grid computing. In this paper, we combine this IDR(s)...report 2010
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- Collignon, T.P. (author), Van Gijzen, M.B. (author) report 2009
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- Sleijpen, G.L.G. (author), Van Gijzen, M.B. (author) report 2009
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- Van Gijzen, M.B. (author), Sonneveld, P. (author) report 2008
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- Sleijpen, G.L.G. (author), Sonneveld, P. (author), Van Gijzen, M.B. (author) report 2008
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- Collignon, T. (author), Van Gijzen, M.B. (author) report 2008
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- Collignon, T.P. (author), Van Gijzen, M.B. (author) report 2008
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- Collignon, T.P. (author), Van Gijzen, M.B. (author) report 2007