NDLI: Enhanced Nonlinear Iterative Techniques Applied to a Nonequilibrium Plasma Flow

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Knoll, D. A. McHugh, P. R.
Copyright Year	1998
Abstract	We study the application of enhanced nonlinear iterative methods to the steady-state solution of a system of two-dimensional convection-diffusion-reaction partial differential equations that describe the partially ionized plasma flow in the boundary layer of a tokamak fusion reactor. This system of equations is characterized by multiple time and spatial scales and contains highly anisotropic transport coefficients due to a strong imposed magnetic field. We use Newton's method to linearize the nonlinear system of equations resulting from an implicit, finite volume discretization of the governing partial differential equations, on a staggered Cartesian mesh. The resulting linear systems are neither symmetric nor positive definite, and are poorly conditioned. Preconditioned Krylov iterative techniques are employed to solve these linear systems. We investigate both a modified and a matrix-free Newton--Krylov implementation, with the goal of reducing CPU cost associated with the numerical formation of the Jacobian. A combination of a damped iteration, mesh sequencing, and a pseudotransient continuation technique is used to enhance global nonlinear convergence and CPU efficiency. GMRES is employed as the Krylov method with incomplete lower-upper (ILU) factorization preconditioning. The goal is to construct a combination of nonlinear and linear iterative techniques for this complex physical problem that optimizes trade-offs between robustness, CPU time, memory requirements, and code complexity. It is shown that a mesh sequencing implementation provides significant CPU savings for fine grid calculations. Performance comparisons of modified Newton--Krylov and matrix-free Newton--Krylov algorithms will be presented.
Starting Page	291
Ending Page	301
Page Count	11
File Format	PDF
ISSN	10648275
DOI	10.1137/S1064827596304034
e-ISSN	10957197
Issue Number	1
Volume Number	19
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-25
Access Restriction	Subscribed
Subject Keyword	Systems of equations preconditioned Krylov algorithms plasma flow Solution of discretized equations Iterative methods for linear systems Ionized gas flow in electromagnetic fields; plasmic flow Newton--Krylov methods nonlinear iterative methods
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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