An implicit energy-conservative 2D Fokker-Planck algorithm. II: Jacobian-free Newton-Krylov solver
type: Item
instance of: scholarly article
title: An implicit energy-conservative 2D Fokker-Planck algorithm. II: Jacobian-free Newton-Krylov solver
zbMATH Open document ID: 0961.76058
author: D. C. Barnes
author: Luis Chacón
author: D. A. Knoll
author: G. H. Miley
published in: Journal of Computational Physics
publication date: 2001-06-10T00:00:00Z
review text: [For part I, see the foregoing entry.] From the summary: We discuss efficient numerical implementation of an implicit energy-conservative scheme for multidimensional Fokker-Planck problems using multigrid-preconditioned Krylov methods. Results show that multigrid preconditioning is effective in speeding convergence and decreasing CPU requirements, particularly on fine meshes. The solver is demonstrated on grids up to \(128\times 128\) points in two-dimensional cylindrical velocity space \((v_r,v_p)\) with implicit time steps of the order of collisional time scale of the problem, \(\tau\). The method preserves particles exactly, and energy conservation is improved over alternative approaches, particularly in coarse meshes. Typical errors in the total energy over a time period of \(10\tau\) remain below a percent.
Mathematics Subject Classification ID: 76M20
Mathematics Subject Classification ID: 76X05
zbMATH DE Number: 1422653
zbMATH Keywords: implicit plasma simulation
zbMATH Keywords: non-symmetric systems
zbMATH Keywords: multigrid methods
zbMATH Keywords: implicit energy-conservative scheme
zbMATH Keywords: multidimensional Fokker-Planck problems
zbMATH Keywords: multigrid-preconditioned Krylov methods
zbMATH Keywords: cylindrical velocity space
MaRDI profile type: Publication
full work available at URL: jcph.1999.6395
OpenAlex ID: W2797417811
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DOI: 10.1006/JCPH.1999.6395
description: scientific article; zbMATH DE number 1422653