Publications in journals and refereed proceedings

2015

A. Sanger and M.B. Van Gijzen, The eigenvectors corresponding to the second eigenvalue of the Google matrix and their relation to link spamming, Journal of Computational and Applied Mathematics, Vol 227, pp. 192-201, 2015

M.B. van Gijzen, G.L.G. Sleijpen, and JPM Zemke, Flexible and multi‐shift induced dimension reduction algorithms for solving large sparse linear systems. Numerical Linear Algebra with Applications, to appear

2014

R. Gupta, M.B. van Gijzen, and C. Vuik, Multi-GPU/CPU deflated preconditioned conjugate gradient for bubbly flow solver. Proceeding HPC '14 Proceedings of the High Performance Computing Symposium Article No. 14, 2014

J. Lingen, P.G. Bonnier, R.B.J. Brinkgreve, M.B. van Gijzen and C. Vuik, A parallel linear solver exploiting the physical properties of the underlying mechanical problem, Computational Geosciences, Vol 18, pp. 913-926, 2014

Yue Qiu, M.B. Van Gijzen, J-W. Van Wingerden and M. Verhaegen,On the application of a novel model order reduction algorithm for sequentially semi-separable matrices to the identification of one-dimensional distributed systems , IEEE Xplore Digital Library, Proceedings of ECC 2014, pp. 2750-2755, 2014

2013

T.B. Jonsthovel, M.B. van Gijzen, C.Vuik and A. Scarpas, On the Use of Rigid Body Modes in the Deflated Preconditioned Conjugate Gradient Method. SIAM Journal on Scientific Computing, Vol. 35, pp. B207-B225, 2013
R. Astudillo and M.B. Van Gijzen, An induced dimension reduction algorithm to approximate eigenpairs of large nonsymmetric matrices , Proceedings of ICNAAM2013, AIP Conf. Proc. 1558, 2277, 2013
Y. Qiu, M.B. van Gijzen, J-W. Van Wingerden and M. Verhaegen, A class of efficient preconditioners with multilevel sequentially semiseparable matrix structure, Proceedings of ICNAAM2013, AIP Conf. Proc. 1558, 2253, 2013
R. Gupta, M.B. van Gijzen, and C. Vuik, 3D Bubbly Flow Simulation on the GPU - Iterative Solution of a Linear System Using Sub-domain and Level-Set Deflation, Proceedings of the 21th Euromicro conference on Parallel, Distributed and Network-Based Processing (PDP), pp. 359-366, 2013
R. Gupta, M.B. van Gijzen, and C. Vuik,Efficient Two-Level Preconditioned Conjugate Gradient Method on the GPU, Proceedings of VECPAR 2012, Lecture Notes in Computer Science, Vol. 7851, pp. 36-49, 2013

2012

T.B. Jonsthovel and M.B. van Gijzen and S. MacLachlan and C.Vuik and A. Scarpas, Comparison of the deflated preconditioned conjugate gradient method and algebraic multigrid for composite materials. Computational Mechanics, Vol. 50, pp. 321-333, 2012

2011

T.P. Collignon and M.B. van Gijzen, Minimizing synchronization in IDR(s). Numerical Linear Algebra with Applications, Vol. 18, No. 5, pp. 805–825, 2011 (Copyright John Wiley & Sons, Ltd.)


Martin B. van Gijzen and Peter Sonneveld, Algorithm 913: An Elegant IDR(s) Variant that Efficiently Exploits Bi-orthogonality Properties. ACM Transactions on Mathematical Software, Vol. 38, No. 1, pp. 5:1-5:19, 2011 (copyright ACM)


T.P. Collignon and M.B. van Gijzen, Fast iterative solution of large sparse linear systems on geographically separated clusters. International Journal of High Performance Computing Applications, Vol. 25, No 4, pp. 440-450, 2011

J.S.B. van Zwieten and M.B. van Gijzen and C. Vuik and J. van Male and J.G.E.M. Fraaije. Efficient solution method for the Stokes equations with variable viscosity and periodic boundary conditions. In: JE Olsen et al (eds.), Proceedings 8th International Conference on Computational Fluid Dynamics in Oil & Gas, Metallurgical and Process Industries (CFD 2011), June 21 - 23, 2011; SINTEF/NTNU, Trondheim, Norway, 2011, p. 1 - 10

2010

Gerard L.G. Sleijpen and Martin B. van Gijzen, Exploiting BiCGstab(ℓ) strategies to induce dimension reduction. SIAM J. Sci. Comput. Vol. 32, No. 5, pp. 2687-2709, 2010 (copyright SIAM)

Gerard L.G. Sleijpen, Peter Sonneveld and Martin B. van Gijzen, Bi-CGSTAB as an induced dimension reduction method, Applied Numerical Mathematics. Vol 60, pp. 1100-1114, 2010 (copyright Elsevier)

Collignon, T.P., van Gijzen, M.B., Two Implementations of the Preconditioned Conjugate Gradient Method on a Heterogeneous Computing Grid, International Journal of Applied Mathematics and Computer Science (AMCS), Vol. 20, No. 1, pp. 109-121 (2010)

T.P. Collignon and M.B. van Gijzen, Solving Large Sparse Linear Systems Efficiently on Grid Computers Using an Asynchronous Iterative Method as a Preconditioner. Numerical Mathematics and Advanced Applications 2009.
Proceedings of ENUMATH 2009, the 8th European Conference on Numerical Mathematics and Advanced Applications, Uppsala, July 2009, Gunilla Kreiss, Per Lötstedt, Axel Målqvist and Maya Neytcheva (eds), Springer, pp. 261-268, 2010

Collignon, T.P., van Gijzen, M.B.: Parallel Scientific Computing on Loosely Coupled Networks of Computers. In Koren, B., Vuik, C., eds.: Advanced Computational Methods in Science and Engineering. Lecture Notes in Computational Science and Engineering, Vol. 71, pp. 79-106, ISBN 978-3-642-03343-8 (2010).

E. van 't Wout and M.B. van Gijzen and A. Ditzel and A. van der Ploeg and C. Vuik, The Deflated Relaxed Incomplete Cholesky CG method for use in a real-time ship simulator, Procedia Computer Science, 1, pp. 249-257, 2010

P.A. van Heerbeek, M.B. van Gijzen, C. Vuik, and M.R. de la Fonteijne. Numerical Modelling of a Pulse Combustion Burner: Limiting Conditions of Stable Operation. In: Fitt, A.D.; Norbury, J.; Ockendon, H.; Wilson, E., eds. Progress in Industrial Mathematics at ECMI 2008. Mathematics in Industry, Vol. 15, pp. 875-880, ISBN: 978-3-642-12109-8 (2010)

2009

T.B. Jonsthovel, M.B. van Gijzen, C.Vuik, C. Kasbergen, and A. Scarpas, Preconditioned conjugate gradient method enhanced by deflation of rigid body modes applied to composite materials. Computer Modeling in Engineering and Sciences, vol. 47, pp. 97-118, 2009.

Peter Arbenz, Martin van Gijzen, Patrick Amestoy and Pasqua D’Ambra. Introduction. In: Euro-Par 2009 Parallel Processing.
Lecture Notes in Computer Science Vol. 5704, pp 719-720 (2009)

2008

Peter Sonneveld and Martin B. van Gijzen, IDR(s): a family of simple and fast algorithms for solving large nonsymmetric linear systems. SIAM J. Sci. Comput. Vol. 31, No. 2, pp. 1035-1062. (copyright SIAM)


C. Sensiau, F. Nicoud, M. van Gijzen, and J.W. van Leeuwen, A comparison of solvers for quadratic eigenvalue problems from combustion. International Journal for Numerical Methods in Fluids, vol. 56, issue 8, pp. 1481-1487

The IDR(s) method for solving nonsymmetric systems: a performance study for CFD problems. Martin B. van Gijzen and Peter Sonneveld. Proceedings of RIMS 2007.

2007

M.B. van Gijzen, Y.A. Erlangga, and C. Vuik. Spectral analysis of the discrete Helmholtz operator preconditioned with a shifted Laplacian. SIAM Journal on Scientific Computing, Vol. 29, pp. 1942-1958. (copyright SIAM)

T. Collignon, T. and M.B. van Gijzen. Implementing the Conjugate Gradient Method on a grid computer. In:  Proceedings of the International Multiconference on Computer Science and Information Technology, pages 361-370. (CD-ROM).


Pieter van Heerbeek, Martin van Gijzen, Kees Vuik, and Marcel de la Fonteijne, Numerical modeling of a pulse combustor. Limiting conditions of stable operation. Proceedings of COMBURA 2007, pages 49-50.

M.B. van Gijzen, Y.A. Erlangga, and C. Vuik, Estimation of the optimal shift for the discrete Helmholtz operator preconditioned with a shifted Laplacian.  PAMM Proc. Appl. Math. Mech. 7, 2020075–2020076 (2007). Proceedings of ICIAM07, 2007.

2006

F. Chaitin-Chatelin and M.B. van Gijzen, Analysis of parameterised Quadratic Eigenvalue Problems in Computational Acoustics with Homotopic Deviation Theory. Numerical Linear Algebra with Applications. Vol 13, 2006, pp. 487-512


Daniel Loghin, Martin van Gijzen, and Eline Jonkers, Bounds on the eigenvalue range and on the Field of Values of non-Hermitian and indefinite finite element matrices.  Journal of Computational and Applied Mathematics. Vol 189 Issue 1-2, 2006  pp 304-323

M.B. van Gijzen and Y. A. Erlangga, Convergence bounds for preconditioned GMRES using element-by-element estimates of the field of values, Proceedings of the ECCOMAS-CFD 2006 conference (CD-ROM).

2005

J. van den Eshof, G.L.G. Sleijpen, and M.B. van Gijzen, Restarted GMRES with inexact matrix-vector products. Proceedings of NAA2004, Lecture Notes in  Computer Science, Vol 3401, 2005, pp. 494-501


J. van den Eshof, G.L.G. Sleijpen, and M.B. van Gijzen, Relaxation strategies for nested Krylov methods.  Journal of Computational and  Applied Mathematics. Vol 177, Issue 2, 2005, pp. 347-365

J. van den Eshof, G.L.G. Sleijpen, and M.B. van Gijzen, Iterative linear system solvers with approximate matrix-vector products.  In: QCD and Numerical Analysis III , Lecture Notes in  Computational Science (Artan Borici, Andreas Frommer, Balint Joo, Anthony D. Kennedy, and Brian Pendleton Editors), Vol. 47, Springer, Berlin, Heidelberg, New York (2005)

2004

L. Giraud and M.B. van Gijzen, Large scale acoustic simulations on clusters of SMPs, In: Integral Methods in Science and Engineering (C. Constande, M. Ahues, and A. Largillier Editors),
Birkhauser, Boston, (2004), pp. 61 – 66.

2003

M.B. van Gijzen. Two level parallelism in a stream-function model for global ocean circulation.
Proceedings of EURO-PAR 2003, Lecture Notes in Computer Science, 2790, 2003, pp. 820-829.

J. van den Eshof, G.L.G. Sleijpen, and M.B. van Gijzen, Efficient iteration methods for Schur complement systems, Proceedings of NACoM 2003, pp. 65-68, 2003.

2002

P.A. van Walree, M.B. van Gijzen, and M. Pattipeilohy, Acoustic communication experiments in the Westerschelde shipping lane using direct sequence spread spectrum signals, Proceedings of the 6th European Conference on Underwater Acoustics ECUA 2002, Gdansk, Poland, 2002.

2000

P.A. van Walree, M.B. van Gijzen, D.G. Simons, Analysis of a shallow-water acoustic communication channel, Proceedings of the fifth European Conference on Underwater Acoustics, pp. 561-566, Lyon, July 2000.

M.B. van Gijzen, P.A. van Walree, D. Cano, J.M. Passerieux, A. Waldhorst, R. Weber, and C. Maillard. The ROBLINKS underwater acoustic communication experiments, Proceedings of the fifth European Conference on Underwater Acoustics, pp. 555-560, Lyon, 2000.

M. B. van Gijzen, P.A.van Walree, D. Cano, J.M. Passerieux, A. Waldhorst, and R. Weber. Advances in the ROBLINKS project on long-range shallow-water robust acoustic communication links, Proceedings of EurOCEAN 2000, Hamburg, 2000.

M.B. van Gijzen, and P.A. van Walree, Shallow-water acoustic communication with high bit rate BPSK signals, Proceedings Oceans 2000, pp. 1621-1624, Providence, RI, 2000.

1999

M.B. van Gijzen, The parallel computation of the smallest eigenpair of an acoustic problem with damping. International journal for numerical methods in engineering, 45, 1999, pp. 765-777.

1998

M. B. van Gijzen, C. B. Vreugdenhil, and H. Oksuzoglu, The Finite Element Discretization for Stream-Function Problems on Multiply Connected Domains, J. Comp. Phys., 140, 1998, pp. 30-46. (copyright JCP)

Jan Barkmeijer, Martin van Gijzen and Francois Bouttier, Singular vectors and estimates of the analysis-error covariance metric, Q.J.R. Meteorol. Soc., 124, 1998, pp. 1695-1713.


Daniel Cano, Martin van Gijzen, Andreas Waldhorst, Long Range Shallow Water Robust Acoustic Communication Links ROBLINKS, In: Third European Marine Science and Technology Conference, Lisbon, Volume III, pp. 1133-1136, 1998.

1997

M.B. van Gijzen, G.L.G. Sleijpen, and A.J. van der Steen, The data-parallel iterative solution of the finite element discretization of stream-function models for global ocean circulation, Proceedings 15th IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics, Part III, Computational Physics, Biology, and Chemistry, pp. 479-484, edited by A. Sydow, et. al, Wissenschaft and Technik Verlag, August 24-29, Berlin 1997.

1996

M.B. van Gijzen, GMRES-like methods on distributed memory computers. IMACS Series in Computational and Applied Mathematics, 3, 1996, pp. 45-56.

M.B. van Gijzen, Parallel ocean flow computations on a regular and on an irregular grid. Lecture Notes in Computer Science, 1067, 1996, pp. 207-212.

Gerard Sleijpen, Henk van der Vorst, and Martin van Gijzen, Quadratic eigenproblems are no problem. SIAM News, Vol. 29, Nr. 7, 1996.

1995

M.B. van Gijzen, Conjugate Gradient-like solution algorithms for the Mixed Finite Element Approximation of the Biharmonic Equation applied to Plate Bending Problems. Computer Methods in Applied Mechanics and Engineering, 121, 1995, pp. 121-136.

M.B. van Gijzen, A Polynomial Preconditioner for the GMRES algorithm. Journal of Computational and Applied Mathematics, 59, 1995, pp. 91-107.

M.B. van Gijzen, Large scale finite element computations with GMRES-like methods on a Cray Y-MP. Applied Numerical Mathematics, 19, 1995, pp. 51-62.

M.B. van Gijzen, Parallel iterative solution methods for linear finite element computations on the CRAY T3D. Lecture Notes in Computer Science, 919, 1995, pp. 723-728.

1994

M.B. van Gijzen, Iterative solution methods for linear equations in finite element computations, PhD-thesis, Delft University of Technology, Delft, 1994.


M.B. van Gijzen, Clustering of Elements in EBE-Preconditioners. In: DIANA Computational Mechanics '94, edited by G.M.A. Kusters and M.A.N Hendriks, Dordrecht, 1994, pp. 297-306.

1993

M.B. van Gijzen, An analysis of element-by-element preconditioners for nonsymmetric problems. Computer Methods in Applied Mechanics and Engineering, 105, 1993, pp. 23-40.

1990