Iterative methods for general systems (Krylov methods, preconditioning)

• S. Vakili and G. Ebadi and C. Vuik (pdf, bibtex)
  A parameterized extended shift-splitting preconditioner for nonsymmetric saddle point problems
  Numerical Linear Algebra with Applications, 30, e2478, 2023


• Reijer Idema and Cornelis Vuik (pdf)
  A comparison of Krylov methods for Shifted Skew-Symmetric Systems
  https://arxiv.org/abs/2304.04092


• R. Tielen and M. Moller and C. Vuik (pdf, bibtex)
  Combining p-multigrid and Multigrid Reduction in Time methods to obtain a scalable solver for Isogeometric Analysis
  SN Applied Sciences, 4, 163, 2022


• R. Tielen and M. Moller and C. Vuik (pdf, bibtex)
  Multigrid Reduced in Time for Isogeometric Analysis in YIC2021 Scientific Committee editors, Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference, Editorial Universitat Politecnica de Valencia, Valencia, 47-56, 2022


• R. Tielen and M. Moller and C. Vuik (pdf, bibtex)
  A Block ILUT Smoother for Multipatch Geometries in Isogeometric Analysis
  In Carla Manni and Hendrik Speleers editors, Geometric Challenges in Isogeometric Analysis
  Springer, Cham, 259-278, 2022


• R. Tielen and M. Moller and C. Vuik ( bibtex)
  A Direct Projection to Low-Order Level for p-Multigrid Methods in Isogeometric Analysis
  Numerical Mathematics and Advanced Applications ENUMATH 2019 European Conference, Egmond aan Zee, The Netherlands, September 30 - October 4, 2019
  Lecture Notes in Computational Science and Engineering 139
  Springer, Cham, pp. 1001-1010, 2021


• R. Tielen and M. Moller and C. Vuik ( bibtex)
  Efficient p-Multigrid Based Solvers for Isogeometric Analysis on Multipatch Geometries
  Isogeometric Analysis and Applications 2018
  Editors: H. van Brummelen and C. Vuik and M. Moler and C. Verhoosel and b. Simeon and B. Juttler
  Lecture Notes in Computational Science and Engineering 133
  Springer, Cham, pp. 209-225, 2021


• Roel Tielen, Matthias Moller, Cornelis Vuik (pdf)
  Combining p-multigrid and multigrid reduced in time methods to obtain a scalable solver for Isogeometric Analysis
  https://arxiv.org/abs/2107.05337


• Luyu Wang, Cornelis Vuik, Hadi Hajibeygi (pdf)
  A preconditioned mixed-FE scheme with stabilized Lagrange multiplier for frictional contact mechanics of crossing fractures in porous media
  https://arxiv.org/abs/2105.13179


• Mousa HosseiniMehr, Janio Piguave Tomala, Cornelis Vuik, Mohammed Al Kobaisi, Hadi Hajibeygi (pdf)
  Projection-based embedded discrete fracture model (pEDFM) for flow and heat transfer in real-field geological formations with corner-point grid geometries
  https://arxiv.org/abs/2105.05888


• M. HosseiniMehr and C. Vuik and H. Hajibeygi (pdf, bibtex)
  Adaptive Dynamic Multilevel Simulation of Fractured Geothermal Reservoirs
  Journal of Computational Physics: X, 7, 100061, 2020


• R. Tielen and M. Moller and D. Goddeke and C. Vuik (pdf, bibtex)
  p-multigrid methods and their comparison to h-multigrid methods within Isogeometric Analysis
  Computer Methods in Applied Mechanics and Engineering, 372, 113347, 2020


• Yue Qiu and Martin B. van Gijzen and Jan-Willem van Wingerden and Michel Verhaegen and Cornelis Vuik (pdf, bibtex)
  Preconditioning Navier-Stokes control using multilevel sequentially semiseparable matrix computations
  Numerical Linear Algebra with Applications, 21, e2349, 2020


• X. He and C. Vuik (pdf, bibtex)
  Efficient and robust Schur complement approximations in the augmented Lagrangian preconditioner for the incompressible laminar flows
  Journal of Computational Physics Volume 408, 1 May 2020, 109286


• J. Knipping and J. du Toit and C. Vuik (pdf, bibtex)
  Comparison of Wavelets for Adaptive Mesh Refinement
  Technical Report TR1/20 NAG, Oxford, 2020


• R. Tielen and M. Moller and D. Goddeke and C. Vuik (pdf, bibtex)
  p-multigrid methods and their comparison to h-multigrid methods within Isogeometric Analysis
  Computer Methods in Applied Mechanics and Engineering, 372, 113347, 2020


• M. Moeller and C. Vuik (pdf, bibtex)
  A conceptual framework for quantum accelerated automated design optimization
  Microprocessors and Microsystems, 66, pp. 67-71, 2019


• M. HosseiniMehr and R. Arbarim and M. Cusini and C. Vuik and H. Hajibeygi (bibtex)
  Algebraic Dynamic Multilevel Method for Fractured Geothermal Reservoir Simulation
  SPE Reservoir Simulation Conference, 10-11 April, 2019 Galveston, Texas, USA
  SPE, pp. 1-16, 2019


• R. Tielen and M. Moeller and C. Vuik (pdf, bibtex)
  Efficient multigrid based solvers for B-spline MPM
  2nd International Conference on the Material Point Method for Modelling Soil-Water-Structure Interaction, Anura3D, MPM Research Community
  Deltares, Delft pp. 161-165, 2019


• C. Vuik (pdf, bibtex)
  Krylov Subspace Solvers and Preconditioners
  ESAIM: Proceedings and Surveys, 63, pp. 1-43, 2018


• Yue Qiu and Martin B. van Gijzen and Jan-Willem van Wingerden and Michel Verhaegen and Cornelis Vuik (pdf, bibtex)
  Evaluation of multilevel sequentially semiseparable preconditioners on computational fluid dynamics benchmark problems using Incompressible Flow and Iterative Solver Software
  Mathematical Methods in the Applied Sciences, 41, pp. 888-903, 2018


• M. HosseiniMehr and M. Cusini and C. Vuik and H. Hajibeygi (pdf, bibtex)
  Algebraic dynamic multilevel method for embedded discrete fracture model (F-ADM)
  Journal of Computational Physics, 373, pp. 324-345, 2018


• J. Chen and C. Vuik (pdf, bibtex)
  Globalization technique for projected Newton-Krylov methods
  International Journal for Numerical Methods in Engineering, 110, pp. 661-674, 2017


• B. Sereeter and C. Vuik and C. Witteveen (pdf, bibtex)
  Newton Power Flow Methods for Unbalanced Three-Phase Distribution Networks
  Energies, 10, pp. 1658-1677, 2017


• Yue Qiu and Martin B. van Gijzen and Jan-Willem van Wingerden and Michel Verhaegen and Cornelis Vuik (pdf, bibtex)
  Efficient preconditioners for PDE-constrained optimization problem with a multilevel sequentially semiseparable matrix structure
  ETNA, 44, pp. 367-400, 2015


• P. van Slingerland and C. Vuik (pdf, bibtex)
  Fast linear solver for diffusion problems with applications to pressure computation in layered domains
  Computational Geosciences, 18, pp. 343-356, 2014


• T.B. Jonsthovel and M.B. van Gijzen and C.Vuik and A. Scarpas (pdf, bibtex)
  On the Use of Rigid Body Modes in the Deflated Preconditioned Conjugate Gradient Method
  SIAM Journal on Scientific Computing, 35, pp. B207-B225, 2013


• R. Idema and G. Papaefthymiou and D.J.P. Lahaye and C. Vuik and L. van der Sluis (pdf, bibtex)
  Towards Faster Solution of Large Power Flow Problems
  IEEE Transactions on Power Systems, 28, pp. 4918-4925, 2013


• T.B. Jonsthovel and A.A. Lukyanov and E.D. Wobbes and C. Vuik (pdf, bibtex)
  Monotone Non-Galerkin Algebraic Multigrid Method Applied to Reservoir Simulations
  ECMOR XV - 15th European Conference on the Mathematics of Oil Recovery, August 29 - September 1, 2016 Editor: J.D. Jansen EAGE, Houten, 2016 DOI: 10.3997/2214-4609.201601896


• Y.A. Erlangga and C.W. Oosterlee and C. Vuik ( pdf-file, bibtex item)
  A Novel Multigrid Based Preconditioner For Heterogeneous {H}elmholtz Problems
  Delft University of Technology
  Department of Applied Mathematical Analysis
  Report 04-05
  ISSN 1389-6520
  
  
• C. Vuik and Y.A. Erlangga and C.W. Oosterlee ( pdf-file, bibtex item)
  Shifted Laplace preconditioners for the Helmholtz equations
  Delft University of Technology
  Department of Applied Mathematical Analysis
  Report 03-18
  ISSN 1389-6520
  
  
• Y.A. Erlangga and C. Vuik and C.W. Oosterlee ( bibtex item)
  On a class of preconditioners for solving the discrete Helmholtz equation
  Proceedings of The Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation Held at Jyvaskyla, Finland, 30 June - 4 July, 2003
  editor: G.C. Cohen and E. Heikkola and P. Joly and P. Neittaanmaki Springer, Berlin, 2003, pages 788-793
  ISBN 3-540-40127-X
  
  
• Y.A. Erlangga and C. Vuik and C.W. Oosterlee ( pdf-file, bibtex item)
  On a class of preconditioners for solving the Helmholtz equation
  Delft University of Technology
  Department of Applied Mathematical Analysis
  Report 03-01
  ISSN 1389-6520
  
  
• F. Vermolen and C. Vuik (pdf-file, bibtex item)
  The influence of deflation vectors at interfaces on the deflated Conjugate Gradient method
  Delft University of Technology
  Department of Applied Mathematical Analysis
  Report 01-13
  ISSN 1389-6520
  
  
• J. Frank and C. Vuik ( pdf-file, bibtex item)
  On the construction of deflation-based preconditioners
  SIAM Journal on Scientific Computing, 23, pp. 442--462, 2001
  see also CWI Report MAS-R0009
  
  
• C. Vuik, A. Segal, L. El Yaakoubi and E. Dufour (pdf-file, bibtex item)
  A comparison of various deflation vectors applied to elliptic problems with discontinuous coefficients
  Delft University of Technology
  Department of Applied Mathematical Analysis
  Report 01-03
  ISSN 1389-6520
  to appear in: Applied Numerical Mathematics
  
  
• C. Vuik and J. Frank ( bibtex item, pdf file)
  Deflated ICCG method applied to problems with extreme contrasts in the coefficients
  In: M. Deville and R. Owens (eds.): Proceedings of the 16th IMACS World Congress 2000. Lausanne, August 2000.
  CDROM ISBN 3-9522075-1-9,
  Rutgers University, New Brunswick, 2000
  
  
• C. Vuik and A. Segal and J.A. Meijerink and J. Frank ( bibtex item)
  Deflated ICCG applied to problems with extreme contrasts in the coefficients
  Sixth Copper Mountain Conference on Iterative Methods, (virtual proceedings)
  Copper Mountain, Colorado, April 2 - April 7, 2000
  editors: T.A. Manteuffel and S.F. McCormick
  
  
• C. Vuik and A. Segal and J.A. Meijerink and G.T. Wijma ( bibtex item)
  The construction of projection vectors for a Deflated ICCG method applied to problems with extreme contrasts in the coefficients
  Shell, 2000
  Shell Report EP2000-8019
  to appear in: Journal of Computational Physics
  
  
• C. Vuik and A. Segal and J.A. Meijerink (pdf file, bibtex item)
  An efficient preconditioned CG method for the solution of a class of layered problems with extreme contrasts in the coefficients
  J. Comp. Phys., 152, pp. 385-403, 1999.
  see also TUD Report 98-20.
  
  
• C. Vuik and A. Segal and J.A. Meijerink and G.T. Wijma ( bibtex item)
  The construction of projection vectors for a deflated ICCG method used in problems with a layered structure
  1999 International Conference on Preconditioning Techniques for Large Sparse Matrix Problems in Industrial Applications, Minneapolis, USA, June 10-12, 1999, pp. 225-231
  editors: Y. Saad and D. Pierce and W.P. Tang
  University of Minnesota Supercomputing Institute, Minneapolis, 1999
  related poster
  
  
• Kees Vuik, Guus Segal and Koos Meijerink,
  An efficient CG method for layered problems with large contrasts in the coefficients
  Fifth Copper Mountain Conference on Iterative Methods, (virtual proceedings)
  Copper Mountain, Colorado, March 30 - April 3, 1998
  editors: T.A. Manteuffel and S.F. McCormick
  
  
• E.F.F. Botta, K. Dekker, Y. Notay, A. van der Ploeg, C. Vuik, F.W. Wubs, P.M. de Zeeuw, ( pdf-file, bibtex item)
  How fast the Laplace equation was solved in 1995
  Appl. Num. Meth., 24, pp. 439-455, 1997.
  see also Report W-9701
  
  
• C. Vuik ( pdf-file, bibtex item)
  New insights in GMRES-like methods with variable preconditioners
  J. Comp. Appl. Math., 61, pp. 189-204, 1995.
  
  
• T. Jongen, X. Costantini, C. Vuik
  BIGMRESR: a combination of a GCR outerloop and a BICGSTAB innerloop
  Faculty of Technical Mathematics and Informatics Delft University of Technology, 1994
  TUD Report 94-62.
  
  
• H.A. van der Vorst, C. Vuik ( pdf-file, bibtex item)
  GMRESR: a family of nested GMRES methods
  Num. Lin. Alg. Appl., 1, pp. 369-386, 1994.
  
  
• C. Vuik
  Further experiences with GMRESR
  Supercomputer, 55, pp. 13-27, 1993.
  
  
• H.A. van der Vorst, C. Vuik
  The superlinear convergence behaviour of GMRES
  J. Comp. Appl. Math., 48, pp. 327-341, 1993.
  
  
• C. Vuik and H.A. van der Vorst ( pdf-file)
  A comparison of some GMRES-like methods
  Linear Alg. Appl., 160, pp.131-162, 1992.
  
  

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