Iterative methods for Navier-Stokes equations (Krylov methods, preconditioning, multigrid)

• H. Hornikova and C. Vuik and J. Egermaier (pdf, bibtex)
  A comparison of block preconditioners for isogeometric analysis discretizations of the incompressible Navier-Stokes equations
  International Journal for Numerical Methods in Fluids, 93, pp. 1788-1815, 2021


• H. Hornikova and C. Vuik ( bibtex)
  Preconditioning for Linear Systems Arising from IgA Discretized Incompressible Navier-Stokes Equations
  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. 76-97, 2021


• 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


• 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


• A.A. Lukyanov and C. Vuik (pdf, bibtex)
  A stable SPH discretization of the elliptic operator with heterogeneous coefficients
  Journal of Computational and Applied Mathematics, 374, 2020


• X. Li and J.K. Ryan and R.M. Kirby and C. Vuik (pdf, bibtex)
  Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering for Discontinuous Galerkin Solutions over Nonuniform Meshes: Superconvergence and Optimal Accuracy
  Journal of Scientific Computing, 81, pp. 1150-1180, 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


• M. Atsma and C. Vuik (pdf, bibtex)
  Determining water speed of ships: Establishing the delivered power needed as a function of the ship's speed in relation to the water
  Delft University of Technology
  Delft Institute of Applied Mathematics
  Report 19-04, 2019
  ISSN 1389-6520


• J. Hinz and M. Moeller and C. Vuik (pdf, bibtex)
  Spline-Based Parameterization Techniques for Twin-Screw Machine Geometries
  IOP Conference Series: Materials Science and Engineering, 425, 012030, 2018


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


• J. Hinz and M. Moeller and C. Vuik (pdf, bibtex)
  Elliptic grid generation techniques in the framework of isogeometric analysis applications
  Computer Aided Geometric Design, 65, pp. 48-75, 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


• X. He and C. Vuik and C. Klaij (pdf, bibtex)
  Combining the Augmented Lagrangian Preconditioner with the Simple Schur Complement Approximation
  SIAM Journal on Scientific Computing, 40, pp. A1362-A1385, 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


• G.B. Diaz Cortes and C. Vuik and J.D. Jansen (pdf, bibtex)
  On POD-based Deflation Vectors for DPCG applied to porous media problems
  Journal of Computational and Applied Mathematics, 330, pp. 193-213, 2018


• M. HosseiniMehr and M. Cusini and C. Vuik and H. Hajibeygi (pdf, bibtex)
  Algebraic Dynamic Multilevel Method for Single-phase Flow in Heterogeneous Geothermal Reservoirs
  ECMOR XVI - 16th European Conference on the Mathematics of Oil Recovery, September 3-6, 2018
  Editor: D. Gunasekera
  EAGE, Barcelona, pp. 1-11, 2018


• G.B. Diaz Cortes and J.D. Jansen and C. Vuik (pdf, bibtex)
  On The Acceleration Of Ill-Conditioned Linear Systems: A Pod-Based Deflation Method For The Simulation Of Two-Phase Flow
  ECMOR XVI - 16th European Conference on the Mathematics of Oil Recovery, September 3-6, 2018
  Editor: D. Gunasekera
  EAGE, Barcelona, pp. 1-22, 2018


• X. He and C. Vuik and C. Klaij (pdf, bibtex)
  Combining the Augmented Lagrangian Preconditioner with the Simple Schur Complement Approximation
  SIAM Journal on Scientific Computing, 40, pp. A1362-A1385, 2018


• M.H. Aissa and T. Verstraete and C. Vuik (pdf, bibtex)
  Toward a GPU-aware comparison of explicit and implicit CFD simulations on structured meshes
  Computers and Mathematics with Applications, 74, pp. 201-217, 2017


• C.M. Klaij and X. He and C. Vuik (pdf, bibtex)
  On the design of block preconditioners for maritime engineering
  Proceedings of the Seventh International Conference on Computational Methods in Marine Engineering MARINE
  Editors: M. Visonneau and P. Queutey and D. Le Touze
  May 15-17, Nantes, France, pp. 893-904, 2017


• X. He and C. Vuik and C. Klaij( bibtex)
  Block-preconditioners for the incompressible Navier-Stokes equations discretized by a finite volume method
  Journal of Numerical Mathematics, 25, pp. 89-105, 2017
  https://doi.org/10.1515/jnma-2015-0120


• 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


• M.H. Aissa and T. Verstraete and C. Vuik (pdf, bibtex)
  Aerodynamic optimization of supersonic compressor cascade using differential evolution on GPU
  International Conference of Numerical Analysis and Applied Mathematics, 22-28 September 2015, Rhodos, AIP Conference Proceedings 1738 Editors: Theodore Simos and Charalambos Tsitouras AIP Publishing, Melville, pp. 480077-1-4, 2016


• P. van Slingerland and C. Vuik (pdf, bibtex)
  Scalable two-level preconditioning and deflation based on a piecewise constant subspace for (SIP)DG systems for diffusion problems
  Journal of Computational and Applied Mathematics, 275, pp. 61-78, 2015


• X. He and M. Neytcheva and C. Vuik (pdf, bibtex)
  On preconditioning of incompressible non-Newtonian flow problems Journal of Computational Mathematics, 33, pp. 33-58, 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


• M.H. Aissa and T. Verstraete and C. Vuik (pdf, bibtex)
  Use of modern GPUs in Design Optimisation The 10th ASMO UK / ISSMO conference on Engineering Design Optimization Product and Process Improvement Delft University of Technology, Delft, The Netherlands June 30th - July 1st, 2014
  Editors: F. van Keulen and M. Guffens and G. van der Veen and M. Langelaar
  Delft University of Technology, Delft, pp. 1-11, 2014


• S.P. Pereira and C. Vuik and F.T. Pinho and J. M. Nobrega (pdf, bibtex)
  On the performance of a 2D unstructured computational rheology code on a GPU AIP Conference Proceedings, 1526 (72), Novel Trends in Rheology V, 30-31 July 2013, Zlin, Czech Republic Editors: M. Zatloukal Pages: 72-89 American Institute of Physics, New York, 2013


• R. Gupta and M.B. van Gijzen and C. Vuik (pdf, bibtex)
  3D Bubbly Flow Simulation on the GPU - Iterative Solution of a Linear System Using Sub-domain and Level-Set Deflation
  2013 21st Euromicro International Conference on Parallel, Distributed and Network-Based Processing Feb. 27 2013-March 1 2013, Belfast, UK
  Editors: Peter Kilpatrick and Peter Milligan and Rainer Stotzka
  IEEE Computer Society, Los Alamitos, pp. 359-366, 2013


• M. de Jong and A. van der Ploeg and A. Ditzel and C. Vuik (pdf, bibtex)
  Real-time computation of interactive waves using the GPU
  15th Numerical Towing Tank Symposium 2012 (NuTTS 2012), Proceedings of a meeting held 7-9 October 2012, Cortona, Italy
  Editors: Volker Bertram
  Curran Associates, Red Hook, pp. 106-111, 2013


• C.M. Klaij and C. Vuik (pdf, bibtex)
  SIMPLE-type preconditioners for cell-centered, colocated finite volume discretization of incompressible Reynolds-averaged Navier-Stokes equations
  International Journal for Numerical Methods in Fluids, 71, pp. 830-849, 2013


• M. ur Rehman and T. Geenen and C. Vuik and G. Segal and S.P. MacLachlan (pdf, bibtex)
  On iterative methods for the incompressible Stokes problem
  Int. J. Num. Meth. in Fluids, 65, pp. 1180-1200, 2011


• A. Segal and M. ur Rehman and C. Vuik (pdf, bibtex)
  Preconditioners for Incompressible Navier-Stokes Solvers
  Numerical Mathematics: Theory, Methods and Applications, 3, pp. 245-275, 2010


• M.H. Carpenter and C. Vuik and P. Lucas and M.B. van Gijzen and H. Bijl (pdf, bibtex)
  A General Algorithm for Reusing Krylov Subspace Information. I. Unsteady Navier-Stokes NASA, Langley Research Center, 2010 NASA/TM2010216190
  
  
• M. ur Rehman and C. Vuik and G. Segal (pdf, bibtex)
  Block Preconditioners for the Incompressible Stokes Problem
  In: Large-Scale Scientific Computing Editors: I. Lirkov and S. Margenov and J. Wasniewski Lecture Notes in Computer Science, Vol. 5910 Springer, Berlin, 2010, pp. 829-836


• T. Geenen and M. ur Rehman and S.P. MacLachlan and G. Segal and C. Vuik and A. P. van den Berg and W. Spakman (pdf, bibtex)
  Scalable robust solvers for unstructured FE geodynamic modeling applications: Solving the Stokes equation for models with large localized viscosity contrasts
  Geochemistry Geophysics Geosystems, 10, pp. 1-12, 2009
  
  
• M. ur Rehman and C. Vuik and G. Segal (pdf, bibtex)
  SIMPLE-type preconditioners for the Oseen problem
  Int. J. Num. Meth. in Fluids, 61, pp. 432-452, 2009
  
  
• M. ur Rehman and C. Vuik and G. Segal (pdf, bibtex)
  Preconditioners for the steady incompressible Navier-Stokes problem
  International Journal of Applied Mathematics,38, pp. 223-232, 2008
  
  
• M. ur Rehman and C. Vuik and G. Segal (pdf, bibtex)
  A comparison of preconditioners for incompressible Navier-Stokes solvers
  Int. J. Num. Meth. in Fluids, 57, pp. 1731-1751, 2008
  
  
• M. ur Rehman and C. Vuik and G. Segal, ( pdf , bibtex)
  SIMPLE-type preconditioners for the Oseen problem
  Delft University of Technology
  Delft Institute of Applied Mathematics
  Report 08-09
  
  
• M. ur Rehman and C. Vuik and G. Segal ( pdf, bibtex)
  Solution of the incompressible Navier Stokes equations with preconditioned Krylov subspace methods
  Delft University of Technology
  Delft Institute of Applied Mathematics
  Report 06-05
  ISSN 1389-6520
  
  
• M. ur Rehman and C. Vuik and G. Segal ( pdf, bibtex)
  Study Report of IFISS Package (version 2.1)
  Delft University of Technology
  Delft Institute of Applied Mathematics
  Report 06-06
  ISSN 1389-6520
  
  
• C. Li and C. Vuik ( pdf-file, bibtex item)
  The GCR-SIMPLE solver and the SIMPLE-type preconditioning for incompressible Navier Stokes equations
  Proceedings of the 4th European Congress on Computational Methods in Applied Sciences and Engineering, Volume II, ECCOMAS 2004, Jyvaskyla, Finland, July 24-28, 2004 editor: P. Neittaanmaki and T. Rossi and S. Korotov and E. Onate and J. Periaux and D. Knorzer University of Jyvaskyla, Jyvaskyla, 2004 pages: CD ISBN 951-39-1869-6
  
  
• C. Li and C. Vuik ( pdf-file, bibtex item)
  Eigenvalue analysis of the SIMPLE preconditioning for incompressible flow
  Numerical Linear Algebra with Applications, 11, pp.511-523, 2004
  
  
• Chunguang Li and Kees Vuik ( pdf-file, bibtex item)
  Eigenvalue Analysis of the SIMPLE Preconditioning for Incompressible Flow
  Delft University of Technology
  Department of Applied Mathematical Analysis
  Report 02-15
  ISSN 1389-6520
  
  
• C. Vuik and A. Saghir ( pdf-file, bibtex item)
  The Krylov accelerated SIMPLE(R) method for incompressible flow
  Delft University of Technology
  Department of Applied Mathematical Analysis
  Report 02-01
  ISSN 1389-6520
  
  
• C. Vuik and J. Frank and A. Segal ( pdf-file, bibtex item)
  A parallel block-preconditioned GCR method for incompressible flow problems
  Future Generation Computer Systems, 18, pp. 31--40, 2001
  
  
• J. van Kan and C. Vuik and P. Wesseling ( pdf-file, bibtex item)
  Fast pressure calculation for 2D and 3D time dependent incompressible flow
  Num. Lin. Alg. with Appl., 7 pp. 429-447, 2000
  
  
• C. Vuik and A. Saghir and G.P. Boerstoel ( pdf-file, bibtex item)
  The Krylov accelerated SIMPLE(R) method for flow problems in industrial furnaces
  International Journal for Numerical methods in fluids, 33 pp. 1027-1040, 2000
  see also TNO-Report FSP-RPT-990010
  
  
• C. Vuik, J.J.I.M. van Kan and P. Wesseling ( pdf file, bibtex item)
  A black box multigrid preconditioner for second order elliptic partial differential equations
  Proceedings European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000, Barcelona, Spain, September 11-14, 2000
  editors: E. Oñate, G. Bugeda and B. Suárez
  CIMNE, Barcelona, 2000
  CDROM ISBN 84-89925-70-4
  
  
• C. Vuik (pdf, bibtex item)
  Fast iterative solvers for the discretized incompressible Navier-Stokes equations
  Int. J. for Num. Meth. Fluids, 22, pp. 195-210, 1996.
  
  
• C. Vuik, P. Wesseling and S. Zeng
  Krylov subspace and multigrid methods for the incompressible Navier-Stokes equations
  Seventh Copper Mountain Conference on Multigrid Methods, Copper Mountain, Colorado, April 2-7, 1995
  NASA Conference Publication 3339 pp. 737-753
  editors: N. Duane Melson and T.A. Manteuffel and S.F. McCormick
  NASA, Hampton VA., 1996
  
  
• C. Vuik
  Iterative solution methods for flow problems
  Proceedings of the Second IMACS International Symposium on Iterative Methods in Linear Algebra Blagoevgrad, Bulgaria June 17-20,1995
  Iterative methods in linear algebra II pp. 453--461
  editors: S.D. Margenov and P.S. Vassilevski
  IMACS, Piscataway, 1996
  
  
• Guus Segal, Kees Vuik
  A simple iterative linear solver for the 3D incompressible Navier-Stokes equations discretized by the finite element method
  Faculty of Technical Mathematics and Informatics
  Delft University of Technology,1995
  TUD Report 95-64.
  
  
• C. Vuik, A. Segal
  Solution of the coupled Navier-Stokes equations
  Proceedings of the Eleventh GAMM-Seminar Kiel, January 20-22, 1995
  Numerical treatment of coupled systems pp. 186--197
  editors: W. Hackbusch, G. Wittum
  Vieweg, Braunschweig, 1995
  ISBN 3 528 07651 8
  
  
• S. Zeng, C. Vuik, P. Wesseling ( pdf-file, bibtex item)
  Numerical solution of the incompressible Navier-Stokes equations by Krylov subspace and multigrid methods
  Adv. Comp. Math., 4, pp. 27-49, 1995.
  
  
• C. Vuik
  Solution of the discretized incompressible Navier-Stokes equations with the GMRES method
  International Journal Numerical Methods in Fluids, 16, pp.507-523, 1993.
  
  

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