No. 10 (00078)

Family name : Moiseenko
Given name : Vladimir
Affiliation : Institute of Plasma Physics, National Science Center
              "Kharkov Institute of Physics and Technology", 
              61108 Kharkov, Ukraine
Abbreviation : IPP NSC KhIPT
E-mail address : moiseenk@ipp.kharkov.ua
Title : Numerical Modeling of Radio Frequency Fields in Plasma
Authors : V.E.Moiseenko
Abstract : 
The problem of numerically solving of Maxwell's equations written in
terms of electric field in plasma is reviewed. The measures for
providing the numerical stability are discussed. 
The problems arising from the stiffness of Maxwell's equations in plasma
are analyzed. In this respect a newly proposed weighted residuals scheme
with identical trial functions is compared with the standard numerically
stable Galerkin scheme. The comparison shows the advantage of the first
scheme that becomes prominent in the case of stiffness. 
The numerical stability of the finite difference scheme on
two-dimensional mesh is addressed briefly. A specific version of
staggered mesh method that is stable on non-orthogonal mesh is
discussed. 
Among other approaches a method consisting in discretization of
Maxwell's equations written in other equivalent form and recently
proposed local solution method are considered. 
For solving the discretized equations the Gauss elimination is normally
used. For 3D problems this approach leads to enormous number of
calculations. Usage of modern iterative algorithms, i.e. GMRes for
problem with right-hand side and Jacobi-Davidson for eigenvalue problem,
substantially reduces both the number of calculations and memory
requirements.