Higherorder time integration of Coulomb collisions in a plasma using Langevin equations
Abstract
The extension of Langevinequation MonteCarlo algorithms for Coulomb collisions from the conventional EulerMaruyama time integration to the next higher order of accuracy, the Milstein scheme, has been developed, implemented, and tested. This extension proceeds via a formulation of the angular scattering directly as stochastic differential equations in the two fixedframe sphericalcoordinate velocity variables. Results from the numerical implementation show the expected improvement [O(Δt) vs. O(Δt^{1/2})] in the strong convergence rate both for the speed v and angular components of the scattering. An important result is that this improved convergence is achieved for the angular component of the scattering if and only if the “areaintegral” terms in the Milstein scheme are included. The resulting Milstein scheme is of value as a step towards algorithms with both improved accuracy and efficiency. These include both algorithms with improved convergence in the averages (weak convergence) and multitimelevel schemes. The latter have been shown to give a greatly reduced cost for a given overall error level when compared with conventional MonteCarlo schemes, and their performance is improved considerably when the Milstein algorithm is used for the underlying time advance versus the EulerMaruyama algorithm. A new method for sampling the area integrals is given which ismore »
 Authors:

 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Univ. of California, Los Angeles, CA (United States). Dept. of Mathematics
 Publication Date:
 Research Org.:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1227022
 Report Number(s):
 LLNLJRNL577312
Journal ID: ISSN 00219991
 Grant/Contract Number:
 AC5207NA27344; FG0205ER25710
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 242; Journal Issue: C; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; 70 PLASMA PHYSICS AND FUSION; MonteCarlo methods; Milstein method; Collision processes; Plasmas; Collisions; Computer applications
Citation Formats
Dimits, A. M., Cohen, B. I., Caflisch, R. E., Rosin, M. S., and Ricketson, L. F. Higherorder time integration of Coulomb collisions in a plasma using Langevin equations. United States: N. p., 2013.
Web. doi:10.1016/j.jcp.2013.01.038.
Dimits, A. M., Cohen, B. I., Caflisch, R. E., Rosin, M. S., & Ricketson, L. F. Higherorder time integration of Coulomb collisions in a plasma using Langevin equations. United States. doi:10.1016/j.jcp.2013.01.038.
Dimits, A. M., Cohen, B. I., Caflisch, R. E., Rosin, M. S., and Ricketson, L. F. Fri .
"Higherorder time integration of Coulomb collisions in a plasma using Langevin equations". United States. doi:10.1016/j.jcp.2013.01.038. https://www.osti.gov/servlets/purl/1227022.
@article{osti_1227022,
title = {Higherorder time integration of Coulomb collisions in a plasma using Langevin equations},
author = {Dimits, A. M. and Cohen, B. I. and Caflisch, R. E. and Rosin, M. S. and Ricketson, L. F.},
abstractNote = {The extension of Langevinequation MonteCarlo algorithms for Coulomb collisions from the conventional EulerMaruyama time integration to the next higher order of accuracy, the Milstein scheme, has been developed, implemented, and tested. This extension proceeds via a formulation of the angular scattering directly as stochastic differential equations in the two fixedframe sphericalcoordinate velocity variables. Results from the numerical implementation show the expected improvement [O(Δt) vs. O(Δt1/2)] in the strong convergence rate both for the speed v and angular components of the scattering. An important result is that this improved convergence is achieved for the angular component of the scattering if and only if the “areaintegral” terms in the Milstein scheme are included. The resulting Milstein scheme is of value as a step towards algorithms with both improved accuracy and efficiency. These include both algorithms with improved convergence in the averages (weak convergence) and multitimelevel schemes. The latter have been shown to give a greatly reduced cost for a given overall error level when compared with conventional MonteCarlo schemes, and their performance is improved considerably when the Milstein algorithm is used for the underlying time advance versus the EulerMaruyama algorithm. A new method for sampling the area integrals is given which is a simplification of an earlier direct method and which retains high accuracy. Lastly, this method, while being useful in its own right because of its relative simplicity, is also expected to considerably reduce the computational requirements for the direct conditional sampling of the area integrals that is needed for adaptive strong integration.},
doi = {10.1016/j.jcp.2013.01.038},
journal = {Journal of Computational Physics},
number = C,
volume = 242,
place = {United States},
year = {2013},
month = {2}
}
Web of Science
Works referencing / citing this record:
A Langevin approach to multiscale modeling
journal, April 2018
 Hirvijoki, Eero
 Physics of Plasmas, Vol. 25, Issue 4