Accelerated convergence of the steepest-descent method for magnetohydrodynamic equilibria

Technical Report · Fri Jun 01 04:00:00 EDT 1984

DOI:https://doi.org/10.2172/7045611· OSTI ID:7045611

Handy, C. R.; Hirshman, S. P.

Iterative schemes based on the method of steepest descent have recently been used to obtain magnetohydrodynamic (MHD) equilibria. Such schemes generate asymptotic geometric vector sequences whose convergence rate can be improved through the use of the epsilon-algorithm. The application of this nonlinear recursive technique to stiff systems is discussed. In principle, the epsilon-algorithm is capable of yielding quadratic convergence and therefore represents an attractive alternative to other quadratic convergence schemes requiring Jacobian matrix inversion. Because the damped MHD equations have eigenvalues with negative real parts (in the neighborhood of a stable equilibrium), the epsilon-algorithm will generally be stable. Concern for residual monotonic sequences leads to consideration of alternative methods for implementing the algorithm.

• Research Organization: Oak Ridge National Lab., TN (USA)
• DOE Contract Number: AC05-84OR21400
• OSTI ID: 7045611
• Report Number(s): ORNL/TM-9133; ON: DE84013602
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700105* -- Fusion Energy-- Plasma Research-- Plasma Kinetics-Theoretical-- (-1987)
ALGORITHMS
ANALYTICAL SOLUTION
EIGENVALUES
EQUILIBRIUM PLASMA
FLUID MECHANICS
HYDRODYNAMICS
ITERATIVE METHODS
MAGNETOHYDRODYNAMICS
MATHEMATICAL LOGIC
MECHANICS
NONLINEAR PROBLEMS
PLASMA