A Fast Solver for Implicit Integration of the VlasovPoisson System in the Eulerian Framework
In this paper, we present a domain decomposition algorithm to accelerate the solution of Euleriantype discretizations of the linear, steadystate Vlasov equation. The steadystate solver then forms a key component in the implementation of fully implicit or nearly fully implicit temporal integrators for the nonlinear VlasovPoisson system. The solver relies on a particular decomposition of phase space that enables the use of sweeping techniques commonly used in radiation transport applications. The original linear system for the phase space unknowns is then replaced by a smaller linear system involving only unknowns on the boundary between subdomains, which can then be solved efficiently with Krylov methods such as GMRES. Steadystate solves are combined to form an implicit RungeKutta time integrator, and the Vlasov equation is coupled selfconsistently to the Poisson equation via a linearized procedure or a nonlinear fixedpoint method for the electric field. Finally, numerical results for standard test problems demonstrate the efficiency of the domain decomposition approach when compared to the direct application of an iterative solver to the original linear system.
 Authors:

^{[1]};
^{[2]}
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Publication Date:
 Report Number(s):
 LAUR1724638
Journal ID: ISSN 10648275
 Grant/Contract Number:
 AC5206NA25396; AC0500OR22725
 Type:
 Accepted Manuscript
 Journal Name:
 SIAM Journal on Scientific Computing
 Additional Journal Information:
 Journal Volume: 40; Journal Issue: 2; Journal ID: ISSN 10648275
 Publisher:
 SIAM
 Research Org:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC21); ORNL Laboratory Directed Research and Development (LDRD) Program
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; VlasovPoisson; implicit time integration; domain decomposition
 OSTI Identifier:
 1435515
Garrett, C. Kristopher, and Hauck, Cory D.. A Fast Solver for Implicit Integration of the VlasovPoisson System in the Eulerian Framework. United States: N. p.,
Web. doi:10.1137/17M1134184.
Garrett, C. Kristopher, & Hauck, Cory D.. A Fast Solver for Implicit Integration of the VlasovPoisson System in the Eulerian Framework. United States. doi:10.1137/17M1134184.
Garrett, C. Kristopher, and Hauck, Cory D.. 2018.
"A Fast Solver for Implicit Integration of the VlasovPoisson System in the Eulerian Framework". United States.
doi:10.1137/17M1134184.
@article{osti_1435515,
title = {A Fast Solver for Implicit Integration of the VlasovPoisson System in the Eulerian Framework},
author = {Garrett, C. Kristopher and Hauck, Cory D.},
abstractNote = {In this paper, we present a domain decomposition algorithm to accelerate the solution of Euleriantype discretizations of the linear, steadystate Vlasov equation. The steadystate solver then forms a key component in the implementation of fully implicit or nearly fully implicit temporal integrators for the nonlinear VlasovPoisson system. The solver relies on a particular decomposition of phase space that enables the use of sweeping techniques commonly used in radiation transport applications. The original linear system for the phase space unknowns is then replaced by a smaller linear system involving only unknowns on the boundary between subdomains, which can then be solved efficiently with Krylov methods such as GMRES. Steadystate solves are combined to form an implicit RungeKutta time integrator, and the Vlasov equation is coupled selfconsistently to the Poisson equation via a linearized procedure or a nonlinear fixedpoint method for the electric field. Finally, numerical results for standard test problems demonstrate the efficiency of the domain decomposition approach when compared to the direct application of an iterative solver to the original linear system.},
doi = {10.1137/17M1134184},
journal = {SIAM Journal on Scientific Computing},
number = 2,
volume = 40,
place = {United States},
year = {2018},
month = {4}
}