Abstract
We present a domain decomposition algorithm to accelerate the solution of Eulerian-type discretizations of the linear, steady-state Vlasov equation. The steady-state solver then forms a key component in the implementation of fully implicit or nearly fully implicit temporal integrators for the nonlinear Vlasov–Poisson 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. Steady-state solves are combined to form an implicit Runge–Kutta time integrator, and the Vlasov equation is coupled self-consistently to the Poisson equation via a linearized procedure or a nonlinear fixed-point method for the electric field. 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.
| Original language | English |
|---|---|
| Pages (from-to) | B483-B506 |
| Journal | SIAM Journal on Scientific Computing |
| Volume | 40 |
| Issue number | 2 |
| DOIs | |
| State | Published - 2018 |
Funding
∗Submitted to the journal’s Computational Methods in Science and Engineering section June 12, 2017; accepted for publication (in revised form) January 16, 2018; published electronically April 5, 2018. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan). http://www.siam.org/journals/sisc/40-2/M113418.html Funding: The first author’s work was supported by Los Alamos National Security, operator of LANL, under contract DE-AC52-06NA25396 with the U.S. Department of Energy. The second author’s work is based, in part, upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing, and by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory (ORNL), managed by UT-Battelle, LLC, for the U.S. Department of Energy under contract De-AC05-00OR22725. †Los Alamos National Laboratory, Los Alamos, NM 87545 ([email protected]). ‡Oak Ridge National Laboratory, Oak Ridge, TN 37831 ([email protected]). The first author’s work was supported by Los Alamos National Security, operator of LANL, under contract DE-AC52-06NA25396 with the U.S. Department of Energy. The second author’s work is based, in part, upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing, and by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory (ORNL), managed by UT-Battelle, LLC, for the U.S. Department of Energy under contract De-AC05-00OR22725.
| Funders | Funder number |
|---|---|
| UT-Battelle | |
| U.S. Department of Energy | De-AC05-00OR22725 |
| Office of Science | |
| Advanced Scientific Computing Research | |
| Oak Ridge National Laboratory | |
| Laboratory Directed Research and Development | |
| Los Alamos National Laboratory | DE-AC52-06NA25396 |
Keywords
- Domain decomposition
- Implicit time integration
- Vlasov–Poisson