Martin van Gijzen - Publications

Publications

Book

Numerical Methods for Ordinary Differential Equations

Refereed Publications

2022

M.L. de Leeuw den Bouter, G. Ippolito, T.P.A. O’Reilly, R.F. Remis, M.B. van Gijzen and A.G. Webb. Deep Learning-Based Single Image Super-Resolution for Low-Field MR Brain Images. Scientific Reports, 12, Article 6362, 2022.
X. Shan and M.B van Gijzen. Deflated Preconditioned Conjugate Gradient Methods for Noise Filtering of Low-Field MR Images. Journal of Computational and Applied Mathematics, 400, Article 113730, 2022.

2021

E. Ahishakiye, M.B. van Gijzen, J. Tumwiine, R. Wario, and J. Obungoloch. A Survey on Deep Learning in Medical Image Reconstruction. Intelligent Medicine, 1(3):118-127, 2021.
L. Steverink, T. Veugen, and M. van Gijzen. Approximating Eigenvectors with Fixed-Point Arithmetic: a Step Towards Secure Spectral Clustering. Lecture Notes in Computational Science and Engineering, 139:1129-1136, 2021.
M. de Leeuw den Bouter, M. van Gijzen, and R. Remis. CG Variants for General-Form Regularization with an Application to Low-Field MRI. Lecture Notes in Computational Science and Engineering, 139:673-681, 2021.
X. Shan and M. van Gijzen. Deflated Preconditioned Conjugate Gradients for Nonlinear Diffusion Image Enhancement. Lecture Notes in Computational Science and Engineering, 139:459-468, 2021.
Y. Qiu, M.B. van Gijzen, J.-W. van Wingerden, M. Verhaegen, and C. Vuik. Preconditioning Navier-Stokes Control Using Multilevel Sequentially Semiseparable Matrix Computations. Numerical Linear Algebra with Applications, 28(2):e2349, 2021.
M. de Leeuw den Bouter, M.B. van Gijzen, and R.F. Remis. Low-Field Magnetic Resonance Imaging Using Multiplicative Regularization. Magnetic Resonance Imaging, 75:21-33, 2021.

2020

F. van Doesum, J.C. Diehl, M. Bakker, M. van Gijzen, T. O'Reilly, I. Muhumuza, J. Obungoloch, and E. Mbabazi Kabachelor. The Embodiment of Low-Field MRI for the Diagnosis of Infant Hydrocephalus in Uganda. Proceedings of the 2020 IEEE Global Humanitarian Technology Conference, pages 150-157, 2020.
M. de Leeuw den Bouter, D. Geçmen, A. Meijer, D. de Gans, L. Middelplaats, R. Remis, and M. van Gijzen. Description of a Low-Field MRI Scanner Based on Permanent Magnets. CEUR Workshop Proceedings, vol. 2688, paper 15, 2020.
E. Ahishakiye, M.B. van Gijzen, J. Tumwiine, and J. Obungoloch. Adaptive-Size Dictionary Learning Using Information Theoretic Criteria for Image Reconstruction from Undersampled k-space Data in Low Field Magnetic Resonance Imaging. BMC Medical Imaging, 20(1):1-12, 2020.
E. Ahishakiye, M.B. van Gijzen, J. Tumwiine, and J. Obungoloch. A Dictionary Learning Approach for Noise-Robust Image Reconstruction in Low Field Magnetic Resonance Imaging. In 2020 IST-Africa Conference (IST-Africa) Proceedings, pages 1-12, 2020.
M. Pari, W. Swart, M.B. van Gijzen, M.A.N. Hendriks, and J.G. Rots. Two Solution Strategies to Improve the Computational Performance of Sequentially Linear Analysis for Quasi-brittle Structures. International Journal for Numerical Methods in Engineering, 121(10):2128-2146, 2020.

2019

M.L. de Leeuw den Bouter, M.B. van Gijzen, and R.F. Remis. Conjugate Gradient Variants for \(\ell_p\)-regularized Image Reconstruction in Low-Field MRI. SN Applied Sciences, 1, article 1736, 2019.
A. Vijn, E. Lepelaars, J. Dubbeldam, M. van Gijzen, and A. Heemink. Magnetic Susceptibility Estimation for Magnetostatics. IEEE Transactions on Magnetics, 55(3):1-9, 2019.
R. Astudillo, J.M. de Gier, and M.B. van Gijzen. Accelerating the Induced Dimension Reduction Method Using Spectral Information. Journal of Computational and Applied Mathematics, 345:33-47, 2019.
M. Baumann and M.B. van Gijzen. An Efficient Two-Level Preconditioner for Multi-frequency Wave Propagation Problems. Applied Numerical Mathematics, 135:316-332, 2019.

2018

M. Baumann and M.B. van Gijzen. Convergence and Complexity Study of GMRES Variants for Solving Multi-frequency Elastic Wave Propagation Problems. Journal of Computational Science, 26:285-293, 2018.
E.C.H. van Dongen, N. Kirchner, M.B. van Gijzen, R.S.W. van De Wal, T. Zwinger, G. Cheng, P. Lötstedt, and L. von Sydow. Dynamically Coupling Full Stokes and Shallow Shelf Approximation for Marine Ice Sheet Flow Using Elmer/Ice (v8. 3). Geoscientific Model Development, 11(11):4563-4576, 2018.
Y. Qiu, M.B. van Gijzen, J.-W. van Wingerden, M. Verhaegen, and C. Vuik. Evaluation of Multilevel Sequentially Semiseparable Preconditioners on CFD Benchmark Problems Using Incompressible Flow and Iterative Solver Software. Mathematical Methods in the Applied Sciences, Special Issue: Trends in Applied Mathematics, 41(3):888-903, 2018.
M. Baumann, R. Astudillo, Y. Qiu, E.Y.M. Ang, M.B. van Gijzen, and R.-É. Plessix. An MSSS-Preconditioned Matrix Equation Approach for the Time-Harmonic Elastic Wave Equation at Multiple Frequencies. Computational Geosciences, 22:43-61, 2018.

2017

M.I. Ahmad, D.B. Szyld, and M.B. van Gijzen. Preconditioned Multishift BiCG for \(\mathcal{H}_2\)-Optimal Model Reduction. SIAM Journal on Matrix Analysis and Applications, 38(2):401-424, 2017. © 2017 SIAM
M. Baumann and M.B. van Gijzen. Efficient Iterative Methods for Multi-Frequency Wave Propagation Problems: A Comparison Study. Procedia Computer Science, 108:645-654, 2017.
R. Astudillo and M.B. van Gijzen. Induced Dimension Reduction Method to Solve the Quadratic Eigenvalue Problem. Lecture Notes in Computer Science, 10187:203-211, 2017.

2016

M. Baumann and M.B. van Gijzen. A Fast Iterative Solution of the Time-harmonic Wave Equation with MSSS-preconditioned IDR(s). In Proceedings of the 78th EAGE Conference and Exhibition 2016, 2016:1-5, 2016.
R. Astudillo and M.B. van Gijzen. A Restarted Induced Dimension Reduction Method to Approximate Eigenpairs of Large Unsymmetric Matrices. Journal of Computational and Applied Mathematics, 296:24-35, 2016.
R. Gupta, D. Lukarski. M.B. van Gijzen, and C. Vuik. Evaluation of the Deflated Preconditioned CG Method to Solve Bubbly and Porous Media Flow Problems on GPU and CPU. International Journal for Numerical Methods in Fluids, 80:666-683, 2016.
R. Astudillo and M.B. van Gijzen. Induced Dimension Reduction Method for Solving Linear Matrix Equations. Procedia Computer Science, 80:222-232, 2016.
R. Astudillo and M.B. van Gijzen. The Induced Dimension Reduction Method Applied to Convection-Diffusion-Reaction Problems. Lecture Notes in Computational Science and Engineering, 112:295-303, 2016.

2015

M. Baumann and M.B. van Gijzen. Nested Krylov Methods for Shifted Linear Systems. SIAM Journal on Scientific Computing, 37(5):S90-S112, 2015. © 2015 SIAM
A. Sangers 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, 277:192-201, 2015.
M.B. van Gijzen, G.L.G. Sleijpen, and J.-P.M. Zemke. Flexible and Multi-shift Induced Dimension Reduction Algorithms for Solving Large Sparse Linear Systems. Numerical Linear Algebra with Applications, 22(1):1-25, 2015.
Y. Qiu, M.B. van Gijzen, J.-W. van Wingerden, M. Verhaegen, and C. Vuik. Efficient Preconditioners for PDE-Constrained Optimization Problems with a Multilevel Sequentially Semiseparable Matrix Structure. Electronic Transactions on Numerical Analysis, 44:367-400, 2015.

2014

R. Gupta, M.B. van Gijzen, and K. Vuik. Multi-GPU/CPU Deflated Preconditioned Conjugate Gradient for Bubbly Flow Solver. In HPC'14: Proceedings of the High Performance Computing Symposium, article 14, pages 1-8, 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, 18:913-926, 2014.
Y. 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. In Proceedings of the 13th European Control Conference ECC14, pages 2750-2755, 2014.

2013

T.B. Jönsthövel, 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, 35(1):B207-B225, 2013. © 2013 SIAM
R. Astudillo and M.B. van Gijzen. An Induced Dimension Reduction Algorithm to Approximate Eigenpairs of Large Nonsymmetric Matrices. AIP Conference Proceedings, 1558(1):2277-2280, 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. AIP Conference Proceedings, 1558(1):2253-2256, 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. In Proceedings of the 2013 21st Euromicro International Conference on Parallel, Distributed and Network-Based Processing (PDP 2013), pages 359-366, 2013.
R. Gupta, M.B. van Gijzen, and C.K. Vuik. Efficient Two-Level Preconditioned Conjugate Gradient Method on the GPU. Lecture Notes in Computer Science, 7851:36-49, 2013.

2012

T.B. Jönsthövel, M.B. van Gijzen, S. MacLachlan, C. Vuik, and A. Scarpas. Comparison of the Deflated Preconditioned Conjugate Gradient Method and Algebraic Multigrid for Composite Materials. Computational Mechanics, 50:321-333, 2012.

2011

T.P. Collignon and M.B. van Gijzen. Minimizing Synchronization in IDR(s). Numerical Linear Algebra with Applications, 18(5):805-825, 2011. © 2011 John Wiley & Sons, Ltd.
M.B. van Gijzen and P. Sonneveld. Algorithm 913: An Elegant IDR(s) Variant that Efficiently Exploits Bi-orthogonality Properties. ACM Transactions on Mathematical Software, 38(1), article 5, 19 pages, 2011. © 2011 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, 25(4): 440-450, 2011.
J.S.B. van Zwieten, M.B. van Gijzen, C. Vuik, J. van Male, and J.G.E.M. Fraaije. Efficient Solution Method for the Stokes Equations with Variable Viscosity and Periodic Boundary Conditions. In Proceedings of the 8th International Conference on Computational Fluid Dynamics in the Oil & Gas, Metallurgical and Process Industries CFD 2011, pages 1-10, 2011.

2010

G.L.G. Sleijpen and M.B. van Gijzen. Exploiting BiCGstab(\(\ell\)) Strategies to Induce Dimension Reduction. SIAM Journal on Scientific Computing, 32(5):2687-2709, 2010. © 2010 SIAM
G.L.G. Sleijpen, P. Sonneveld, and M.B. van Gijzen. Bi-CGSTAB as an Induced Dimension Reduction Method. Applied Numerical Mathematics, 60:1100-1114, 2010. © 2010 Elsevier
T. Collignon and M. van Gijzen. Two Implementations of the Preconditioned Conjugate Gradient Method on a Heterogeneous Computing Grid. International Journal of Applied Mathematics and Computer Science (AMCS), 20(1):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. In Proceedings of ENUMATH 2009, the 8th European Conference on Numerical Mathematics and Advanced Applications, pages 261-268, 2010.
T.P. Collignon and M.B. van Gijzen. Parallel Scientific Computing on Loosely Coupled Networks of Computers. Lecture Notes in Computational Science and Engineering, 71:79-106, 2010.
E. van 't Wout, M.B. van Gijzen, A. Ditzel, 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(1):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. Mathematics in Industry, 15:875-880, 2010.

2009

T.B. Jönsthövel, 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, 47(2):97-118, 2009. © 2009 Tech Science Press
P. Arbenz, M. van Gijzen, P. Amestoy, and P. D’Ambra. Introduction. Lecture Notes in Computer Science, 5704:717-720, 2009.

2008

P. Sonneveld and M.B. van Gijzen. IDR(s): A Family of Simple and Fast Algorithms for Solving Large Nonsymmetric Linear Systems. SIAM Journal on Scientific Computing, 31(2):1035-1062, 2008. © 2008 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, 56(8):1481-1487, 2008.
M.B. van Gijzen and P. Sonneveld. The IDR(s) method for solving nonsymmetric systems: a performance study for CFD problems. In Proceedings of RIMS Workshop 2007, volume 1614, pages 53-63, Research Institute for Mathematical Sciences, Kyoto University, 2008.

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, 29:1942-1958, 2007. © 2007 SIAM
T.P. Collignon 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, 2007.

2006

F. Chaitin-Chatelin and M.B. van Gijzen. Analysis of Parameterized Quadratic Eigenvalue Problems in Computational Acoustics with Homotopic Deviation Theory. Numerical Linear Algebra with Applications, 13(6):487-512, 2006.
D. Loghin, M. van Gijzen, and E. 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, 189(1):304-323, 2006.
M.B. van Gijzen and Y. A. Erlangga. Convergence Bounds for Preconditioned GMRES Using Element-by-Element Estimates of the Field of Values. In ECCOMAS CFD 2006, Proceedings of the European Conference on Computational Fluid Dynamics, 9 pages, 2006.

2005

J. van den Eshof, G.L.G. Sleijpen, and M.B. van Gijzen. Restarted GMRES with Inexact Matrix-Vector Products. Lecture Notes in Computer Science, 3401:494-502, 2005.
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, 177(2):347-365, 2005.
J. van den Eshof, G.L.G. Sleijpen, and M.B. van Gijzen. Iterative Linear System Solvers with Approximate Matrix-Vector Products. Lecture Notes in Computational Science and Engineering, 47:133-142, 2005.

2004

L. Giraud and M.B. van Gijzen. Large Scale Acoustic Simulations on Clusters of SMPs. In C. Constande, M. Ahues, and A. Largillier, eds., Integral Methods in Science and Engineering, pages 61-66, Birkhauser, Boston, 2004.
M. van Gijzen. Two-Level Parallelism in a Stream-Function Model for Global Ocean Circulation. Lecture Notes in Computer Science, 2790:820-829, 2004.
J. van den Eshof, G.L.G. Sleijpen, and M.B. van Gijzen. Efficient Iteration Methods for Schur Complement Systems. In Proceedings of NACoM-2003, pages 65-68, 2004.

2002

P. van Walree, M. van Gijzen, and M. Pattipeilohy. Acoustic Communication Experiments in the Westerschelde Shipping Lane Using Direct Sequence Spread Spectrum Signals. In Proceedings of the Sixth European Conference on Underwater Acoustics ECUA 2002, pages 543-548, 2002.

2000

P.A. van Walree, M.B. van Gijzen, and D.G. Simons. Analysis of a Shallow-Water Acoustic Communication Channel. In Proceedings of the Fifth European Conference on Underwater Acoustics ECUA 2000, volume 1, pages 561-566, 2000.
M.B. van Gijzen, P.A. van Walree, D. Cano, J.-M. Passerieux, A. Waldhorst, R.B. Weber, and C. Maillard. The ROBLINKS Underwater Acoustic Communication Experiments. In Proceedings of the Fifth European Conference on Underwater Acoustics ECUA 2000, volume 1, pages 555-560, 2000.
M. van Gijzen, P. 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. In Project Synopses of EurOCEAN 2000, the European Conference on Marine Science and Ocean Technology, volume II, pages 589-599, 2000.
M.B. van Gijzen and P.A. van Walree. Shallow-Water Acoustic Communication with High Bit Rate BPSK Signals. In Proceedings of the Oceans 2000 MTS/IEEE Conference and Exhibition (Cat. No.00CH37158), pages 1621-1624, 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(6):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. Journal of Computational Physics, 140:30-46, 1998. © 1998 Academic Press
J. Barkmeijer, F. Bouttier, and M. van Gijzen. Singular Vectors and Estimates of the Analysis-Error Covariance Metric. Quarterly Journal of the Royal Meteorological Society, 124:1695-1713, 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. In Proceedings of the 15th IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics, pages 479-484, 1997.

1996

M.B. van Gijzen. GMRES-Like Methods on Distributed Memory Computers. IMACS Series in Computational and Applied Mathematics, 3:45-56, 1996.
M.B. van Gijzen. Parallel Ocean Flow Computations on a Regular and on an Irregular Grid. Lecture Notes in Computer Science, 1067:207-212, 1996.
G. Sleijpen, H. van der Vorst, and M. van Gijzen. Quadratic Eigenproblems Are No Problem. SIAM News, 29(7):8-9, 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(1-4):121-136, 1995.
M.B. van Gijzen. A Polynomial Preconditioner for the GMRES Algorithm. Journal of Computational and Applied Mathematics, 59:91-107, 1995.
M.B. van Gijzen. Large Scale Finite Element Computations with GMRES-Like Methods on a Cray Y-MP. Applied Numerical Mathematics, 19(1-2):51-62, 1995.
M. van Gijzen. Parallel Iterative Solution Methods for Linear Finite Element Computations on the CRAY T3D. Lecture Notes in Computer Science, 919:723-728, 1995.

1994

M.B. van Gijzen. Iterative solution methods for linear equations in finite element computations. PhD. Thesis, Delft University of Technology, Delft, The Netherlands, 1994.
M.B. van Gijzen. Clustering of Elements in EBE-Preconditioners. In Proceedings of the First International DIANA Conference on Computational Mechanics, DIANA Computational Mechanics '94, pages 297-306, 1994.

1993

M.B. van Gijzen. An Analysis of Element-by-Element Preconditioners for Nonsymmetric Problems. Computer Methods in Applied Mechanics and Engineering, 105(1):23-40, 1993.

1990

M.B. van Gijzen and P. Nauta. An Element-by-Element Solution Algorithm for Nonsymmetric Linear Systems of Equations. In Integration of Theory and Applications in Applied Mechanics, Proceedings of the First National Mechanics Congress, pages 295-304, 1990.