Publicaties
2021
Wetenschappelijke publicaties
Arnold, M., Podhaisky, H., Weiner, R., Celledoni, E., Frank, J., & Lang, J. (2021). Numerical Solution of Differential and Differential–Algebraic Equations. Selected Papers from NUMDIFF-15. Journal of Computational and Applied Mathematics, 387, [112611]. https://doi.org/10.1016/j.cam.2019.112611
Liu, X., & Frank, J. (2021). Symplectic Runge–Kutta discretization of a regularized forward–backward sweep iteration for optimal control problems. Journal of Computational and Applied Mathematics, 383, [113133]. https://doi.org/10.1016/j.cam.2020.113133
2019
Wetenschappelijke publicaties
Falkena, S. K. J., Quinn, C., Sieber, J., Frank, J., & Dijkstra, H. A. (2019). Derivation of delay equation climate models using the Mori-Zwanzig formalism. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 475(2227), [20190075]. https://doi.org/10.1098/rspa.2019.0075
Helwegen, K. G., Wieners, C. E., Frank, J. E., & Dijkstra, H. A. (2019). Complementing CO2 emission reduction by solar radiation management might strongly enhance future welfare. Earth System Dynamics, 10(3), 453-472. https://doi.org/10.5194/esd-10-453-2019
2018
Wetenschappelijke publicaties
Frank, J., & Gottwald, G. A. (2018). A note on statistical consistency of numerical integrators for multiscale dynamics. Multiscale Modeling and Simulation, 16(2), 1017-1033. https://doi.org/10.1137/17M1154709
De Leeuw, B., Dubinkina, S., Frank, J., Steyer, A., Tu, X., & Van Vleck, E. (2018). Projected shadowing-based data assimilation. SIAM Journal on Applied Dynamical Systems, 17(4), 2446-2477. https://doi.org/10.1137/17M1141163
Frank, J., & Zhuk, S. (2018). A detectability criterion and data assimilation for nonlinear differential equations. Nonlinearity, 31(11), 5235-5257. https://doi.org/10.1088/1361-6544/aaddcb
2017
Wetenschappelijke publicaties
Frank, J., & Zhuk, S. (2017). A detectability criterion and data assimilation for non-linear differential equations. arXiv.
Leeuw, B. D., Dubinkina, S., Frank, J., Steyer, A., Tu, X., & Vleck, E. V. (2017). Projected Shadowing-based Data Assimilation. arXiv.
Myerscough, K. W., Frank, J., & Leimkuhler, B. (2017). Observation-based correction of dynamical models using thermostats. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 473(2197), [20160730]. https://doi.org/10.1098/rspa.2016.0730
Zhuk, S., Tchrakian, T. T., & Frank, J. (2017). Exponentially convergent data assimilation algorithm for Navier-Stokes equations. In 2017 American Control Conference, ACC 2017 (pp. 3249-3256). [7963448] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/ACC.2017.7963448
2016
Wetenschappelijke publicaties
Dijkstra, H. A., Tantet, A. J. J., Viebahn, J. P., Mulder, T. E., Hebbink, M., Castellana, D., van den Pol, H., Frank, J. E., Baars, S., Wubs, F. W., Chekroun, M., & Kuehn, C. (2016). A numerical framework to understand transitions in high-dimensional stochastic dynamical systems. Dynamics and Statistics of the Climate System: An Interdisciplinary Journal, 1(1), [dzw003]. https://doi.org/10.1093/climsys/dzw003
Myerscough, K. W., & Frank, J. (2016). Explicit, parallel Poisson integration of point vortices on the sphere. Journal of Computational and Applied Mathematics, 304, 100-119. https://doi.org/10.1016/j.cam.2016.02.053
Vakpublicaties
Bisseling, R. H., Frank, J. E., Gavranovic, H., van Heugten, J., Kruseman, A. M. S., van Leeuwen, D., & Reinhardt, C. (2016). Inferring transportation modes from smartphone sensors. In Proceedings 106th European Study Group Mathematics with Industry (pp. 21-34)
https://dspace.library.uu.nl/bitstream/handle/1874/346282/smartphone.pdf?sequence=2
https://dspace.library.uu.nl/bitstream/handle/1874/346282/smartphone.pdf?sequence=2
2015
Wetenschappelijke publicaties
Zhuk, S., Frank, J. E., Herlin, I., & Shorten, R. (2015). Data assimilation for linear parabolic equations: minimax projection method. SIAM journal on scientific computing, 37(3), A1174-A1196. https://doi.org/10.1137/13094709X
Frank, J., Leimkuhler, B., & Myerscough, K. W. (2015). Direct control of the small-scale energy balance in two-dimensional fluid dynamics. Journal of Fluid Mechanics, 782, 240-259. https://doi.org/10.1017/jfm.2015.526
Wadman, W. J., Crommelin, D. T., & Frank, J. (2015). A Separated Splitting Technique for Disconnected Rare Event Sets. In A. Tolk, & S. Y. Diallo (Eds.), WSC '14: Proceedings of the 2014 Winter Simulation Conference (Vol. 2015-January, pp. 522-532). [7019917] IEEE Press.
https://dspace.library.uu.nl/bitstream/handle/1874/304714/wadman.pdf?sequence=1
https://dspace.library.uu.nl/bitstream/handle/1874/304714/wadman.pdf?sequence=1
2014
Wetenschappelijke publicaties
Koren, B., Abgrall, R., Bochev, P., Frank, J., & Perot, B. (2014). Physics-compatible numerical methods. Journal of Computational Physics, 257(PB), 1039. https://doi.org/10.1016/j.jcp.2013.10.015
Frank, J., & Zhuk, S. (2014). Symplectic Möbius integrators for LQ optimal control problems. In Decision and Control (CDC), 2014 IEEE 53rd Annual Conference on (pp. 6377-6382). [7040389] IEEE. https://doi.org/10.1109/CDC.2014.7040389
2013
Wetenschappelijke publicaties
Bajars, J., Frank, J. E., & Maas, L. R. M. (2013). On The Appearance Of Internal Wave Attractors Due To An Initial Or Parametrically Excited Disturbance. Journal of Fluid Mechanics, 714, 283 - 311. https://doi.org/10.1017/jfm.2012.479
Frank, J. E., & Gottwald, G. A. (2013). Stochastic Homogenization For An Energy Conserving Multi-Scale Toy Model Of The Atmosphere. Physica. D, nonlinear phenomena, 254, 45 - 56. https://doi.org/10.1016/j.physd.2013.03.010
Bajars, J., Frank, J. E., & Leimkuhler, B. J. (2013). Weakly Coupled Heat Bath Models For Gibbs-Like Invariant States In Nonlinear Wave Equations. Nonlinearity, 26, 1945 - 1973.
Wadman, W. S., Crommelin, D. T., & Frank, J. E. (2013). Applying A Splitting Technique To Estimate Electrical Grid Reliability. In R. Pasupathy, S-H. Kim, A. Tolk, R. Hill, & M. E. Kuhl (Eds.), Proceedings of the Winter Simulation Conference (WSC, 2013) (pp. 577-588). IEEE Press. http://informs-sim.org/wsc13papers/includes/files/049.pdf
2012
Wetenschappelijke publicaties
Wadman, W. S., Bloemhof, G., Crommelin, D. T., & Frank, J. E. (2012). Probabilistic Power Flow Simulation Allowing Temporary Current Overloading. In Proceedings of Probabilistic Methods Applied to Power Systems 2012 (PMAPS ) (pp. 494-499). IEEE. http://oai.cwi.nl/oai/asset/18828/18828B.pdf
Vakpublicaties
Frank, J. E. (2012). The Nature Of Prediction (and The Prediction Of Nature). Nieuw archief voor wiskunde. Serie 5, 13(1), 18 - 24. http://oai.cwi.nl/oai/asset/21097/21097D.pdf
2011
Wetenschappelijke publicaties
Frank, J. E., & Gottwald, G. A. (2011). The Langevin Limit Of The Nosé-Hoover-Langevin Thermostat. Journal of Statistical Physics, 143, 715 - 724. http://oai.cwi.nl/oai/asset/18775/18775D.pdf
Bajars, J., Frank, J. E., & Leimkuhler, B. J. (2011). Stochastic-Dynamical Thermostats For Constraints And Stiff Restraints. European Physical Journal Special Topics, 200, 131 - 152. http://oai.cwi.nl/oai/asset/18806/18806D.pdf
Shin, S., Reich, S., & Frank, J. E. (2011). Hydrostatic Hamiltonian Particle-Mesh (HPM) Methods For Atmospheric Modelling. Quarterly Journal of the Royal Meteorological Society, 138, 1388-1399. https://doi.org/10.1002/qj.982
2010
Wetenschappelijke publicaties
Dubinkina, S., Frank, J. E., & Leimkuhler, B. J. (2010). Simplified Modelling Of A Thermal Bath, With Application To A Fluid Vortex System. Multiscale Modeling and Simulation, 8, 1882 - 1901. http://oai.cwi.nl/oai/asset/17083/17083A.pdf
Dubinkina, S., & Frank, J. E. (2010). Statistical Relevance Of Vorticity Conservation With The Hamiltonian Particle-Mesh Method. Journal of Computational Physics, 229(7), 2634 - 2648. http://oai.cwi.nl/oai/asset/17084/17084D.pdf
van den Akker, J. M., Bloemhof, G., Bosman, J. W., Crommelin, D. T., Frank, J. E., & Yang, G. (2010). Optimal Distributed Power Generation Under Network-Load Constraints. In Proceedings of 72nd European Study Group Science with Industry 2010 (pp. 25 - 38). CWI.
Overige resultaten
den Boer, A. V., Bosman, J. W., Bouman, N. J., van Dam, S., Frank, J. E., van der Mei, R. D., Verhoef, C., & Ma, H. (Eds.) (2010). 72nd European Study Group.
2007
Wetenschappelijke publicaties
Cotter, C. J., Frank, J., & Reich, S. (2007). The remapped particle-mesh semi-Lagrangian advection scheme. Quarterly Journal of the Royal Meteorological Society, 133(622), 251-260. https://doi.org/10.1002/qj.11
Ryland, B. N., Mclachlan, R. I., & Frank, J. (2007). On the multisymplecticity of partitioned Runge-Kutta and splitting methods. International Journal of Computer Mathematics, 84(6), 847-869. https://doi.org/10.1080/00207160701458633
Dubinkina, S., & Frank, J. (2007). Statistical mechanics of Arakawa's discretizations. Journal of Computational Physics, 227(2), 1286-1305. https://doi.org/10.1016/j.jcp.2007.09.002
2006
Wetenschappelijke publicaties
Frank, J. (2006). Conservation of wave action under multisymplectic discretizations. Journal of Physics A: Mathematical and General, 39(19), 5479-5493. https://doi.org/10.1088/0305-4470/39/19/S09
Frank, J., Moore, B. E., & Reich, S. (2006). Linear PDEs and numerical methods that preserve a multisymplectic conservation law. SIAM journal on scientific computing, 28(1), 260-277. https://doi.org/10.1137/050628271
2005
Wetenschappelijke publicaties
Frank, J., Reich, S., Staniforth, A., White, A., & Wood, N. (2005). Analysis of a regularized, time-staggered discretization method and its link to the semi-implicit method. Atmospheric Science Letters, 6(2), 97-104. https://doi.org/10.1002/asl.97
2004
Wetenschappelijke publicaties
Frank, J., & Reich, S. (2004). The Hamiltonian particle-mesh method for the spherical shallow water equations. Atmospheric Science Letters, 5(5), 89-95. https://doi.org/10.1002/asl.70
Frank, J. (2004). Geometric space-time integration of ferromagnetic materials. Applied Numerical Mathematics, 48(3-4), 307-322. https://doi.org/10.1016/j.apnum.2003.11.003
Cotter, C. J., Frank, J., & Reich, S. (2004). Hamiltonian particle-mesh method for two-layer shallow-water equations subject to the rigid-lid approximation. SIAM Journal on Applied Dynamical Systems, 3(1), 69-83. https://doi.org/10.1137/030600076
2003
Wetenschappelijke publicaties
Frank, J., & Reich, S. (2003). Conservation properties of Smoothed Particle Hydrodynamics applied to the shallow water equation. BIT Numerical Mathematics, 43(1), 41-55. https://doi.org/10.1023/A:1023620100065
2002
Wetenschappelijke publicaties
Frank, J., & Vuik, C. (2002). On the construction of deflation-based preconditioners. SIAM journal on scientific computing, 23(2), 442-462. https://doi.org/10.1137/S1064827500373231
Frank, J., & Reich, S. (2002). A particle-mesh method for the shallow water equations near geostrophic balance. Journal of Computational Physics, 180(2), 407-426. https://doi.org/10.1006/jcph.2002.7058
2001
Wetenschappelijke publicaties
Frank, J. E., & Van Der Houwen, P. J. (2001). Parallel iteration of the extended backward differentiation formulas. IMA Journal of Numerical Analysis, 21(1), 367-385. https://doi.org/10.1093/imanum/21.1.367
Vuik, C., Frank, J., & Segal, A. (2001). A parallel block-preconditioned GCR method for incompressible flow problems. Future Generation Computer Systems, 18(1), 31-40. https://doi.org/10.1016/S0167-739X(00)00073-X
Vuik, C., & Frank, J. (2001). Coarse grid acceleration of a parallel block preconditioner. Future Generation Computer Systems, 17(8), 933-940. https://doi.org/10.1016/S0167-739X(01)00035-8
2000
Wetenschappelijke publicaties
Vuik, C., & Frank, J. (2000). A parallel block preconditioner accelerated by coarse grid correction. In M. Bubak, H. Afsarmanesh, B. Hertzberger, & R. Williams (Eds.), High Performance Computing and Networking - 8th International Conference, HPCN Europe 2000, Proceedings (pp. 99-108). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1823). Springer Verlag. https://doi.org/10.1007/3-540-45492-6_11
van Liere, R., Mulder, J., Frank, J., & de Swart, J. (2000). Virtual Fekete point configurations: A case study in perturbing complex systems. 189-195. Paper presented at IEEE Virtual Reality 2000, New Brunswick, NJ, USA.
Frank, J. E., & Van Der Houwen, P. J. (2000). Diagonalizable extended backward differentiation formulas. BIT Numerical Mathematics, 40(3), 497-512. https://doi.org/10.1023/A:1022367713296
1999
Wetenschappelijke publicaties
Vuik, C., & Frank, J. (1999). A parallel implementation of the block preconditioned GCR method. In P. Sloot, A. Hoekstra, B. Hertzberger, & M. Bubak (Eds.), High-Performance Computing and Networking - 7th International Conference, HPCN Europe 1999, Proceedings (pp. 1052-1060). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1593). Springer Verlag. https://doi.org/10.1007/bfb0100666
Frank, J., & Vuik, C. (1999). Parallel implementation of a multiblock method with approximate subdomain solution. Applied Numerical Mathematics, 30(4), 403-423. https://doi.org/10.1016/S0168-9274(98)00095-6
1997
Wetenschappelijke publicaties
Frank, J., Hundsdorfer, W., & Verwer, J. G. (1997). On the stability of implicit-explicit linear multistep methods. Applied Numerical Mathematics, 25(2-3), 193-205. https://doi.org/10.1016/S0168-9274(97)00059-7
Frank, J., Huang, W., & Leimkuhler, B. (1997). Geometric integrators for classical spin systems. Journal of Computational Physics, 133(1), 160-172. https://doi.org/10.1006/jcph.1997.5672
1995
Wetenschappelijke publicaties
Frank, J. E., & Taghavi, R. R. (1995). Supersonic rectangular jets with swirling shear layers. 77-82. Paper presented at Proceedings of the 1995 ASME/JSME Fluids Engineering and Laser Anemometry Conference and Exhibition, Hilton Head, SC, USA.