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publications

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(For list of publications, see also: CWI Repository, )

Submitted

  1. J. Bajars, J. Frank & L. R. M. Maas, "On the appearance of internal wave attractors due to an initial or parametrically excited disturbance", J. Fluid Mech., submitted 2012.

  2. W. Wadman, B. Bloemhof, D. Crommelin & J. Frank, "Probablistic Power Flow Simulations Allowing Temporary Current Overloading", PMAPS 2012, (Probabilistic Methods Applied to Power Systems), submitted.

Refereed journal publications

  1. J. Bajars, J. Frank & B. Leimkuhler, "Stochastic-Dynamical Thermostats for Constraints and Stiff Restraints", Euro. Phys. J. 200 (2011) 131–152. (DOI: 10.1140/epjst/e2011-01522-0)

  2. S. Shin, S. Reich & J. Frank, "Hydrostatic Hamiltonian particle-mesh (HPM) methods for atmospheric modeling", Q. J. R. Meteorol. Soc. (2011), online Dec. 5. (doi:10.1002/qj.982)

  3. J. Frank & G.A. Gottwald, "The Langevin Limit of the Nosé-Hoover-Langevin Thermostat", J. Stat. Phys. 143 (2011) 715–724. (DOI: 10.1007/s10955-011-0203-1)

  4. S. Dubinkina, J. Frank, and B. Leimkuhler, "Simplified Modelling of a Thermal Bath, with Application to a Fluid Vortex System", SIAM Multiscale Model. Simul. 8 (2010) 1882–1901.
    [Related CWI Report MAS-E0909]
    Animations referenced in this paper: anim1.avi anim2.avi

  5. S. Dubinkina and J. Frank, "Statistical relevance of vorticity conservation with the Hamiltonian particle-mesh method", J. Comput. Phys. 229 (2010) 2634–2648. (doi:10.1016/j.jcp.2009.12.012)
    [CWI Report MAS-E0907]

  6. S. Dubinkina and J. Frank, "Statistical mechanics of Arakawa's discretizations", J. Comput. Phys. 227 (2007) 1286–1305.
    [CWI Report MAS-E0712]

  7. B. N. Ryland, R. I. McLachlan and J. Frank, "On multisymplecticity of partitioned Runge-Kutta and splitting methods", Int. J. Comput. Math. 84 (2007) 847–869.
    [Preprint]

  8. C. Cotter, J. Frank and S. Reich, "A remapped particle-mesh semi-Lagrangian advection scheme", Q. J. R. Meteorol. Soc. 133 (2007) 251–260.
    [Preprint]

  9. J. Frank, "Conservation of wave action under multisymplectic discretizations", J. Phys. A: Math. Gen.39 (2006) 5479–5493. (Special issue on Geometric Integration).
    [CWI Report MAS-R0602]

  10. J. Frank, B. E. Moore and S. Reich, "Linear PDEs and numerical methods that preserve a multi-symplectic conservation law", SIAM J. Sci. Comput., 28 (2006) 260–277.
    [Preprint]

  11. J. Frank, S. Reich, A. Staniforth, A. White, N. Wood, "Analysis of a regularized, time-staggered discretization method and its link to the semi-implicit method", Atmospheric Science Letters, 6 (2005) 97–104.
    [Preprint]

  12. J. Frank and S. Reich, "The Hamiltonian Particle-Mesh Method for the Spherical Shallow Water Equations", Atmospheric Science Letters, 5 (2004) 89–95.
    [CWI Report MAS-E0317]

  13. C. Cotter, J. Frank and S. Reich, "Hamiltonian Particle-Mesh Method for Two-Layer Shallow-Water Equations Subject to the Rigid-Lid Approximation", SIAM J. Appl. Dyn. Syst., 3 (2004) 69–83.
    [Link to the e-publication (with movies!)]
    [Preprint]

  14. J. Frank, "Geometric space-time integration of ferromagnetic materials", Applied Numerical Mathematics, 48 (2004) 307–322.
    [CWI Report MAS-E0301, Revised]

  15. J. Frank and S. Reich, "Conservation properties of smoothed particle hydrodynamics applied to the shallow water equations", BIT 43 (2003) 40–54.
    [CWI Report MAS-R0111, Revised]

  16. J. Frank, G. Gottwald and S. Reich, "A Hamiltonian Particle-Mesh Method for the Rotating Shallow Water Equations", in M. Griebel and M.A. Schweitzer, eds., Meshfree Methods for Partial Differential Equations, Lecture Notes in Computational Science and Engineering, Vol. 26, pp. 131–142, Springer, 2002.
    [Preprint]

  17. J. Frank and S. Reich, "A Particle-Mesh Method for the Shallow Water Equations Near Geostrophic Balance", J. Comput. Phys. 180 (2002) 407–426.
    [CWI Report MAS-R0102, Revised]

  18. C. Vuik, J. Frank, F.J. Vermolen, "Parallel deflated Krylov methods for incompressible flow," Parallel computational fluid dynamics (Egmond aan Zee, 2001) Elsevier, Amsterdam, 2002. pp. 381–388.

  19. J. Frank and C. Vuik, "On the construction of deflation-based preconditioners", SIAM J. Sci. Comp. 23 (2001) 442–462.
    [CWI Report MAS-R0009, Revision]

  20. C. Vuik, J. Frank, and A. Segal, "A parallel block-preconditioned GCR method for incompressible flow problems", Future Generation Computer Systems 18 (2001) 31–40.

  21. C. Vuik and J. Frank, "Coarse grid acceleration of a parallel block preconditioner," Future Generation Computer Systems 17 (2001) 933–940.

  22. C. Vuik and J. Frank, "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, Rutgers University, New Brunswick, 2000, (CDROM). ISBN 3-9522075-1-9.

  23. C. Vuik and J. Frank, "A Parallel Block Preconditioner Accelerated by Coarse Grid Correction," in M. Bubak, H. Afsarmanesh, R. Williams and B. Hertzberger, eds., High-Performance Computing and Networking, Proceedings of the 7th International Conference, HPCN Europe 2000, Amsterdam, the Netherlands, May 8–10, 2000, Lecture notes in Computer Science 1823, Springer, Berlin, 2000, 99–108. ISBN 3-540-67553-1

  24. C. Vuik and J. Frank, "A parallel implementation of the block preconditioned GCR method," in P. Sloot, M. Bubak, A. Hoekstra and B. Hertzberger, eds., High-Performance Computing and Networking, Proceedings of the 7th International Conference, HPCN Europe 1999, Amsterdam, the Netherlands, April 12–14, 1999, Lecture notes in Computer Science 1593, Springer, Berlin, 1999, 1052–1060

  25. J. Frank and C. Vuik, "Parallel implementation of a multiblock method with approximate subdomain solution," Applied Numerical Mathematics 30 (1999) 403–423.
    [Related T.U. Delft Technical Report DUT-TWI-98-11, Delft University of Technology, 1998. PDF (281K)]

  26. J. Frank, A. Segal and C. Vuik, "Parallel Domain Decomposition with Incomplete Subdomain Solution," T.U. Delft Technical Report DUT-TWI-96-83, Delft University of Technology, 1996.

  27. Robert van Liere, Juriaan Mulder, Jason Frank, and Jacques de Swart, "Virtual Fekete Point Configurations: a Case Study in Perturbing Complex Systems," Proceedings of IEEE Virtual Reality 2000, S. Feiner and D. Thalmann, eds., IEEE Computer Society Press, Los Alamitos, California, USA, 2000, pp. 189-196. ISBN 0-7695-0478-7

  28. J.E. Frank and P.J. van der Houwen, "Diagonalizable Extended Backward Differentiation Formulas," BIT 40 (2000) 497–512.
    [CWI Report MAS-R9917]

  29. J.E. Frank and P.J. van der Houwen, "Parallel iteration of the extended backward differentiation formulas," IMA J. Numer. Anal. 21 (2001) 367–385.
    [CWI Report MAS-R9913]

  30. J. Frank, W. Huang and B. Leimkuhler, "Geometric Integrators for Classical Spin Systems," J. Comput. Phys., 133 (1997) 160–172.
    [Related U. Kansas Math. Report 96-10-02, 1996. Preprint .]

  31. J. Frank, W. Hundsdorfer and J. G. Verwer, "Stability of Implicit-Explicit Linear Multistep Methods", Applied Numerical Mathematics 25 (1997) 193–205.
    [CWI Report NM-R9623]

  32. J. Frank and R. Taghavi, "Supersonic jets with swirling shear layers," in G. Raman, S. Kaji and C. Freitas, eds., High Speed Jet Flows-1995 FED214, number G00964, American Society of Mechanical Engineers.

Non-refereed

  1. J. Frank (with S. Dubinkina & B. Leimkuhler), "Statistically consistent model reduction for point vortices", Geometric Numerical Integration, Mathematisches Forschungsinstitut Oberwolfach, Report No. 16/2011. (DOI: 10.4171/OWR/2011/16)

  2. J. Frank (with S. Dubinkina & B. Leimkuhler), "Thermostats for point vortices", Mathematical Theory and Modelling in Atmosphere-Ocean-Science, Mathematisches Forschungsinstitut Oberwolfach, Report No. 34/2010. (DOI: 10.4171/OWR/2010/34)

  3. M. van den Akker, G. Bloemhof, J. Bosman, D. Crommelin, J. Frank & G. Yang, "Optimal distributed power generation under network load constraints", Proceedings of the 72nd European Study Group Mathematics with Industry, Centrum Wiskunde & Informatica (2010), 30–44.

  4. J. Frank and S. Reich, "Energy-conserving semi-discretizations and spurious numerical reflections", CWI Report MAS-E0608, Center for Mathematics and Computer Science, 2006.

  5. J. Frank, "A note on semi-discrete conservation laws and conservation of wave action by multisymplectic Runge-Kutta box schemes", CWI Report MAS-E0603, Center for Mathematics and Computer Science, 2006.

  6. J. Frank and S. Reich, "On spurious reflections, nonuniform grids and finite difference discretizations of wave equations", CWI Report MAS-E0406, Center for Mathematics and Computer Science, 2004.

For a broader audience

  1. J. Frank, "The nature of prediction (and the prediction of nature)", Nieuw Archief voor Wiskunde, 13:1 (2012) 18–24.

  2. J. Frank, W. Hundsdorfer & B. Koren, In memoriam. Jan Verwer (1946-2011), Nieuw Archief voor de Wiskunde, 2 June 2011.

  3. D. Crommelin & J. Frank, "Stochastics and computation for turbulent systems", ERCIM News No. 81, 28–29. [Link.]

  4. J. Frank "Chaos, Voorspelbaarheid, en Bemonstering", Wiskunde: de Uitdaging. Vakantiecursus 2010, CWI Syllabus 60, Centrum Wiskunde & Informatica, 2010.

  5. J. Frank, "Better Weather Forecasts with Use of Conservation Laws", ERCIM News No. 61, April 2005. [Link.]

  6. J. Frank, "Geometric Numerical Methods for Continuum Dynamics", ERCIM News No. 53, April 2003. [Link.]

Theses, oratie

  1. J. Frank, "The Nature of Prediction (and the Prediction of Nature)", Inaugural Lecture, 412 in the series, Amsterdam University Press, 2011. Download my slides: Apple Keynote (35MB), or PDF (4MB)

  2. J. Frank, Efficient Algorithms for the Numerical Solution of Differential Equations. Dissertation, Technische Universiteit Delft, 17 April 2000. Summary.]

  3. J. Frank, An Experimental Investigation of the Effects of Swirl on Mixing Enhancement of Supersonic Rectangular Jets, Masters thesis, University of Kansas, 1994.

erdös number = 4

I have two papers with Pieter van der Houwen, who in turn co-authored papers with Herman te Riele, who has written articles with Peter Montgomery (as well with Erdös co-authors Deshouillers, Granville, Ivic, and Odlyzko), who is a co-author of Paul Erdös.