Open Access

High-Order Variational Time Integrators for Particle Dynamics

Communications in Applied and Industrial Mathematics's Cover Image
Communications in Applied and Industrial Mathematics
Special Issue on Mathematical modelling for complex systems: multi-agents methods. Guest Editor: Elena De Angelis

Cite

1. J. E. Marsden and M. West, Discrete mechanics and variational integrators, Acta Numer., vol. 10, pp. 357{514, 2001.10.1017/S096249290100006XSearch in Google Scholar

2. C. Kane, J. E. Marsden, M. Ortiz, and M. West, Variational integrators and the Newmark algorithmfor conservative and dissipative mechanical systems, Internat. J. Numer. Methods Engrg., vol. 49, no. 10, pp. 1295{1325, 2000.10.1002/1097-0207(20001210)49:10<1295::AID-NME993>3.0.CO;2-WSearch in Google Scholar

3. E. Hairer, C. Lubich, and G. Wanner, Geometric numerical integration, vol. 31 of Springer Series in Computational Mathematics. Springer, Heidelberg, 2010.Search in Google Scholar

4. J. Hall and M. Leok, Spectral variational integrators, Numer. Math., vol. 130, no. 4, pp. 681{740, 2015.10.1007/s00211-014-0679-0Search in Google Scholar

5. S. Ober-Blobaum and N. Saake, Construction and analysis of higher order Galerkin variational integrators, Adv. Comput. Math., vol. 41, no. 6, pp. 955{986, 2015.10.1007/s10444-014-9394-8Search in Google Scholar

6. S. Ober-Blobaum, Galerkin variational integrators and modi_ed symplectic Runge-Kutta methods, IMA J. Numer. Anal., vol. 37, no. 1, pp. 375{406, 2017.10.1093/imanum/drv062Search in Google Scholar

7. R. Porc_u, Metodi numerici e tecniche di programmazione per l'accelerazione di un modello di dinamicadi particelle non interagenti, Master's thesis, Politecnico di Milano, 2013.Search in Google Scholar

8. L. D. Landau and E. M. Lifshitz, Mechanics. Course of Theoretical Physics, Vol. 1. Translatedfrom the Russian by J. B. Bell, Pergamon Press, Oxford-London-New York-Paris; Addison-WesleyPublishing Co., Inc., Reading, Mass., 1960.Search in Google Scholar

9. V. I. Arnol'd, Mathematical methods of classical mechanics, vol. 60 of Graduate Texts in Mathematics. Springer-Verlag, New York, second ed., 1989. Translated from the Russian by K. Vogtmann and A. Weinstein.10.1007/978-1-4757-2063-1Search in Google Scholar

10. G. Auchmuty, Optimal coercivity inequalities in W1;p(), Proc. Roy. Soc. Edinburgh Sect. A, vol. 135, no. 5, pp. 915{933, 2005.10.1017/S0308210500004182Search in Google Scholar

11. C. Bernardi, C. Canuto, and Y. Maday, Generalized inf-sup conditions for Chebyshev spectral approximationof the Stokes problem, SIAM J. Numer. Anal., vol. 25, no. 6, pp. 1237{1271, 1988.10.1137/0725070Search in Google Scholar

12. R. A. Nicolaides, Existence, uniqueness and approximation for generalized saddle point problems, SIAM J. Numer. Anal., vol. 19, no. 2, pp. 349{357, 1982.10.1137/0719021Search in Google Scholar

13. C. Canuto and A. Quarteroni, Approximation results for orthogonal polynomials in Sobolev spaces, Math. Comp., vol. 38, no. 157, pp. 67{86, 1982.10.1090/S0025-5718-1982-0637287-3Search in Google Scholar

14. C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. A. Zang, Spectral methods. Scientific Computation, Berlin: Springer-Verlag, 2006. Fundamentals in single domains.10.1007/978-3-540-30726-6Search in Google Scholar

15. C. Phillips and R. E. Brown, The effect of helicopter configuration on the fluid dynamics of brouwnout, in 34th European Rotorcraft Forum, 16-19 September 2008.Search in Google Scholar

16. E. Miglio, N. Parolini, M. Penati, and R. Porcu, GPU parallelization of brownout simulations with a non-interacting particles dynamic model, MOX Report 29/2016, Politecnico di Milano, 2016.Search in Google Scholar

eISSN:
2038-0909
Language:
English
Publication timeframe:
Volume Open
Journal Subjects:
Mathematics, Numerical and Computational Mathematics, Applied Mathematics