Open Access
Issue
ESAIM: M2AN
Volume 56, Number 5, September-October 2022
Page(s) 1521 - 1544
DOI https://doi.org/10.1051/m2an/2022049
Published online 20 July 2022
  1. B. Afkham and J. Hesthaven, Structure preserving model reduction of parametric hamiltonian systems. SIAM J. Sci. Comput. 39 (2017) A2616–A2644. [Google Scholar]
  2. G. Ben Arous and H. Owhadi, Multiscale homogenization with bounded ratios and anomalous slow diffusion. Commun. Pure Appl. Math. 56 (2003) 80–113. [CrossRef] [Google Scholar]
  3. A. Bensoussan, J.L. Lions and G. Papanicolaou, Asymptotic Analysis for Periodic Structures. Vol. 374. American Mathematical Soc. (2011). [Google Scholar]
  4. L. Biferale, A. Crisanti, M. Vergassola and A. Vulpiani, Eddy diffusivities in scalar transport. Phys. Fluids 7 (1995) 2725–2734. [CrossRef] [MathSciNet] [Google Scholar]
  5. N. Brummell, F. Cattaneo and S. Tobias, Linear and nonlinear dynamo properties of time-dependent ABC flows. Fluid Dyn. Res. 28 (2001) 237. [CrossRef] [Google Scholar]
  6. S. Childress and A.D. Gilbert, Stretch, Twist, Fold: the Fast Dynamo. Vol. 37. Springer Science & Business Media (1995). [Google Scholar]
  7. A. Debussche and E. Faou, Weak backward error analysis for SDEs. SIAM J. Numer. Anal. 50 (2012) 1735–1752. [Google Scholar]
  8. T. Dombre, U. Frisch, J. Greene, M. Hénon, A. Mehr and A. Soward, Chaotic streamlines in the ABC flows. J. Fluid Mech. 167 (1986) 353–391. [CrossRef] [MathSciNet] [Google Scholar]
  9. A. Fannjiang and G. Papanicolaou, Convection-enhanced diffusion for periodic flows. SIAM J. Appl. Math. 54 (1994) 333–408. [Google Scholar]
  10. K. Feng and Z. Shang, Volume-preserving algorithms for source-free dynamical systems. Numer. Math. 71 (1995) 451–463. [CrossRef] [MathSciNet] [Google Scholar]
  11. D. Galloway and M. Proctor, Numerical calculations of fast dynamos in smooth velocity fields with realistic diffusion. Nature 356 (1992) 691. [CrossRef] [Google Scholar]
  12. J. Garnier, Homogenization in a periodic and time-dependent potential. SIAM J. Appl. Math. 57 (1997) 95–111. [Google Scholar]
  13. R. Gilmore, Baker-Campbell-Hausdorff formulas. J. Math. Phys. 15 (1974) 2090–2092. [CrossRef] [Google Scholar]
  14. E. Hairer, C. Lubich and G. Wanner, Geometric Numerical Integration: Structure-preserving Algorithms for Ordinary Differential Equations. Springer Science and Business Media (2006). [Google Scholar]
  15. J. Hong, H. Liu and G. Sun, The multi-symplecticity of partitioned Runge-Kutta methods for Hamiltonian PDEs. Math. Comput. 75 (2006) 167–181. [Google Scholar]
  16. V.V. Jikov, S. Kozlov and O.A. Oleinik, Homogenization of Differential Operators and Integral Functionals. Springer, Berlin (1994). [CrossRef] [Google Scholar]
  17. C. Kao, Y.-Y. Liu and J. Xin, A Semi-Lagrangian Computation of Front Speeds of G-equation in ABC and Kolmogorov Flows with Estimation via Ballistic Orbits. SIAM J. Multiscale Model. Simul. 20 (2022) 107–117. [CrossRef] [Google Scholar]
  18. T. Kato, Perturbation Theory for Linear Operators. Vol. 132. Springer Science & Business Media (2013). [Google Scholar]
  19. N.V. Krylov, Lectures on elliptic and parabolic equations in Hölder spaces, In Vol. 12 of Graduate Studies in Mathematics. American Mathematical Soc. (1996). [CrossRef] [Google Scholar]
  20. C. Landim, S. Olla and H.T. Yau, Convection–diffusion equation with space–time ergodic random flow. Probab. Theory Relat. Fields. 112 (1998) 203–220. [Google Scholar]
  21. T. Lelièvre and G. Stoltz, Partial differential equations and stochastic methods in molecular dynamics. Acta Numer. 25 (2016) 681–880. [CrossRef] [MathSciNet] [Google Scholar]
  22. J. Lyu, J. Xin and Y. Yu, Computing residual diffusivity by adaptive basis learning via spectral method. Numer. Math.: Theory Methods Appl. 10 (2017) 351–372. [CrossRef] [MathSciNet] [Google Scholar]
  23. A.J. Majda and P.R. Kramer, Simplified models for turbulent diffusion: theory, numerical modelling, and physical phenomena. Phys. Rep. 314 (1999) 237–574. [CrossRef] [MathSciNet] [Google Scholar]
  24. T. McMillen, J. Xin, Y. Yu and A. Zlatos, Ballistic orbits and front speed enhancement for ABC flows. SIAM J. Appl. Dyn. Syst. 15 (2016) 1753–1782. [CrossRef] [MathSciNet] [Google Scholar]
  25. I. Mezić, J.F. Brady and S. Wiggins, Maximal effective diffusivity for time-periodic incompressible fluid flows. SIAM J. Appl. Math. 56 (1996) 40–56. [Google Scholar]
  26. G. Milstein, Y. Repin and M. Tretyakov, Symplectic integration of Hamiltonian systems with additive noise. SIAM J. Numer. Anal. 39 (2002) 2066–2088. [Google Scholar]
  27. B. Oksendal, Stochastic Differential Equations: an Introduction with Applications. Springer Science and Business Media (2013). [Google Scholar]
  28. G. Pavliotis and A. Stuart, Multiscale Methods: Averaging and Homogenization. Springer Science and Business Media (2008). [Google Scholar]
  29. G. Pavliotis, A. Stuart and K. Zygalakis, Calculating effective diffusivities in the limit of vanishing molecular diffusion. J. Comput. Phys. 228 (2009) 1030–1055. [CrossRef] [MathSciNet] [Google Scholar]
  30. S. Reich, Backward error analysis for numerical integrators. SIAM J. Numer. Anal. 36 (1999) 1549–1570. [Google Scholar]
  31. M. Tao, H. Owhadi and J. Marsden, Nonintrusive and structure preserving multiscale integration of stiff ODEs, SDEs, and Hamiltonian systems with hidden slow dynamics via flow averaging. Multiscale Model. Simul. 8 (2010) 1269–1324. [CrossRef] [MathSciNet] [Google Scholar]
  32. Z. Wang, J. Xin and Z. Zhang, Computing effective diffusivity of chaotic and stochastic flows using structure-preserving schemes. SIAM J. Numer. Anal. 56 (2018) 2322–2344. [Google Scholar]
  33. Z. Wang, J. Xin and Z. Zhang, Sharp error estimates on a stochastic structure-preserving scheme in computing effective diffusivity of 3D chaotic flows. SIAM Multiscale Model. Simul. 19 (2021) 1167–1189. [Google Scholar]
  34. J. Xin, Y. Yu and A. Zlatos, Periodic orbits of the ABC flow with A = B = C = 1. SIAM J. Math. Anal. 48 (2016) 4087–4093. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you