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Manuscript Title: An approximate factorization procedure for solving nine-point elliptic difference equations. Application for a fast 2-D relativistic Fokker-Planck solver.
Authors: Y. Peysson, M. Shoucri
Program title: FP2DLHEC
Catalogue identifier: ADHO_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 109(1998)55
Programming language: Fortran.
Computer: Alpha server 4000.
RAM: 4M words
Word size: 32
Keywords: General purpose, Differential equations, Plasma physics, Kinetic model, Factorization matrix, Nine-point elliptic, Difference equation, Strongly implicit, Procedure, Fokker-planck, Lower hybrid current, Drive, Electron cyclotron, Heating, Synergetic effects.
Classification: 4.3, 19.8.

Nature of problem:
A new fast solver of the 2-D linearized relativistic Fokker-Planck equation based on the use of a full implicit numerical scheme is presented for the current drive problem and synergetic effects between the lower hybrid and electron cyclotron waves. The code makes use of the accurate relativistic collision operators presented in Ref. [1]. Convergence rate for the steady state current drive solution may be strongly enhanced as compared to partial implicit procedures used in Ref. [2], without loss of accuracy for the electron distribution function.

Solution method:
The linearized relativistic Fokker-Planck equation is solved on a 2-D domain. The 2-D equation is discretized using a nine-point stencil, and solved with a strongly implicit procedure based on an approximate matrix factorization technique.

Running time:
An execution on an Alpha server 4000 from Digital requires 28.5 ms per iteration for a typical problem with 200 x 100 grid points. The typical number of iterations ranges between 100 and 1000.

References:
[1] B. Braams and C.F. Karney, Phys. Fluids B1, (1989) 1355.
[2] M. Shoucri, I. Shkarofsky, Comput. Phys. Comm. 82 (1994) 287.