Skip to: Site menu | Main content


Google Scholar, Scopus

Articles (refereed unless indicated otherwise)

  1. H.E. de Swart, S.T. van der Wal, J.E. Frank & G.P. Schramkowski, Sensitivity of modeled tracer motion in tidal areas to numerics and to non-Hamiltonian perturbations, Chaos, Solitons and Fractals 161 (2022) 112318.
  2. X. Liu & J. Frank, Symplectic Runge-Kutta discretization of a regularized forward-backward sweep iteration for optimal control problems, J. Comput. Appl. Math. 383 (2021) 113133., arXiv:1912.07028
  3. S.K.J. Falkena, C. Quinn, J. Sieber, J. Frank & H.A. Dijkstra, Derivation of delay equation climate models using the Mori-Zwanzig formalism, Proc. R. Soc. A 475 (2019) 20190075. arXiv:1902.03198,
  4. K.G. Helwegen, C.E. Wieners, J. Frank & H.A. Dijkstra, Complementing CO2 emission reduction by solar radiation management might strongly enhance future welfare, Earth System Dynamics 10 (2019) 453-472.
  5. J. Frank & S. Zhuk, A detectability criterion and data assimilation for non-linear differential equations, Nonlinearity 31 (2018) 5235. arXiv:1711.05039, doi:10.1088/1361-6544/aaddcb
  6. B. M. de Leeuw, S. Dubinkina, J. Frank, A. Steyer, X. Tu & E.S. van Vleck, "Projected Shadowing-based Data Assimilation", SIAM Journal on Applied Dynamical Systems 17 (2018) 2446–2477 arXiv:1707.09264. doi:10.1137/17M1141163
  7. J. Frank & G. A. Gottwald, "A note on statistical consistency of numerical integrators for multi-scale dynamics", Multiscale Modelling and Simulation 16 (2018) 1017–1033. doi:10.1137/17M1154709
  8. J. Frank & S. Zhuk, "Exponentially convergent data assimilation algorithm for Navier-Stokes equations", Proceedings of the American Control Conference, art. no. 7963448, pp. 3249–3256, 2017.
  9. K. Myerscough, J. Frank & B. Leimkuhler, "Observation-based correction of dynamical models using thermostats", Proc. R. Soc. A 473 (2017) 20160730.
  10. J. Frank, B. J. Leimkuhler & K. W. Myersough, "A generic thermostat for smooth vector fields and smooth target densities", Proceedings of the Workshop "Geometric Integration and Its Applications", Melbourne, Australia, December 5–7, 2016. (non-refereed)
  11. H. Dijksta, A. Tantet, J. Viebahn, E. Mulder, M. Hebbink, D. Castellana, H. van den Pol, J. Frank, S. Baars, F. Wubs, M. Chekroun & C. Kuehn, "A numerical framework to understand transitions in high-dimensional stochastic dynamical systems", Dynamics and Statistics of the Climate System, 2016.
  12. K. Myerscough & J. Frank, "Explicit, parallel Poisson integration of point vortices on the sphere", J. Comput. Appl. Math. 304 (2016) 100–119.
  13. J. Frank, B, Leimkuhler & K. W. Myerscough, "Direct control of the small-scale energy balance in 2D fluid dynamics", J. Fluid Mech. 782 (2015) 240–259. doi:10.1017/jfm.2015.526.
  14. S. Zhuk, J. Frank, I. Herlin & R. Shorten, "State estimation for linear parabolic equations: minimax projection method", SIAM J. Sci. Comput., 37 (2015) A1174–A1196. doi:10.1137/13094709X.
  15. J. Frank, & S. Zhuk, "Symplectic Möbius integrators for LQ optimal control problems", IEEE 53rd Annual Conference on Decision and Control (CDC), 15–17 Dec 2014, pp. 6377–6382. DOI:10.1109/CDC.2014.7040389
  16. W. Wadman, D. Crommelin & J. Frank, "A Separated Splitting Technique for Disconnected Rare Event Sets", Proceedings of the 2014 Winter Simulation Conference, IEEE Press, pp. 522–532, 2014.

  17. W. Wadman, D. Crommelin & J. Frank, "Applying a splitting technique to estimate electrical grid reliability", Proceedings of the 13th Winter Simulation Conference (WSC 2013), Washington DC, USA, Dec. 8–11, 2013, pp. 577–588.

  18. J. Bajars, J. Frank & B. Leimkuhler, "Weakly coupled heat bath models for Gibbs-like invariant states in nonlinear wave equations", Nonlinearity 26 (2013) 1945–1973. doi:10.1088/0951-7715/26/7/1945.
  19. J. Frank & G.A. Gottwald, "Stochastic homogenization for an energy conserving multi-scale toy model of the atmosphere", Physica D 254 (2013) 45–56. doi:10.1016/j.physd.2013.03.010.
  20. 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., 714 (2013) 283–311. doi:10.1017/jfm.2012.479

  21. W. Wadman, G. Bloemhof, D. Crommelin & J. Frank, "Probablistic Power Flow Simulations Allowing Temporary Current Overloading", Proceedings of the 12th International Conference on Probabilistic Methods Applied to Power Systems (PMAPS 2012), Istanbul, Turkey, June 10–14, 2012, pp. 494–499.

  22. 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)

  23. S. Shin, S. Reich & J. Frank, "Hydrostatic Hamiltonian particle-mesh (HPM) methods for atmospheric modeling", Q. J. R. Meteorol. Soc. 138 (2011) 1388–1399. (online Dec. 5i, 2011)x. (doi:10.1002/qj.982)

  24. 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)

  25. S. Dubinkina, J. Frank, & 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

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

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

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

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

  30. 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]

  31. 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. (non-refereed)

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

  33. J. Frank & S. Reich, "Energy-conserving semi-discretizations and spurious numerical reflections", CWI Report MAS-E0608, Center for Mathematics and Computer Science, 2006. (non-refereed)

  34. 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.

  35. J. Frank & 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. (non-refereed)

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

  37. C. Cotter, J. Frank & 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!)]

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

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

  40. J. Frank, G. Gottwald & 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.

  41. J. Frank & 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]

  42. 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.

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

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

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

  46. C. Vuik & J. Frank, "Deflated ICCG method applied to problems with extreme contrasts in the coefficients," in M. Deville & 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.

  47. C. Vuik & J. Frank, "A Parallel Block Preconditioner Accelerated by Coarse Grid Correction," in M. Bubak, H. Afsarmanesh, R. Williams & 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

  48. C. Vuik & J. Frank, "A parallel implementation of the block preconditioned GCR method," in P. Sloot, M. Bubak, A. Hoekstra & 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

  49. J. Frank & 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)]

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

  51. Robert van Liere, Juriaan Mulder, Jason Frank & 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

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

  53. J.E. Frank & 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]

  54. J. Frank, W. Huang & 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 .]

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

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

Summaries and other 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.

For a broader audience

  1. Formulas for Insight and Innovation: Dutch Mathematical Sciences in 2025. Platform Wiskunde Nederland, 2014.

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

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

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

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

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

  7. 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.