Time harmonic Maxwell equations in a lossless cavity lead to a second
order partial differential equation for electric field involving a
differential operator that is neither elliptic nor definite. A Galerkin
method using Nedelec spaces can be employed to get approximate solutions
numerically. In this talk, we will discuss the problem of efficient
solution of the indefinite linear system arising from this method. Not all
standard techniques work well for this application due to complications
arising from the non-ellipticity and indefiniteness of the underlying
differential operator. The suitability of some Schwarz methods and
multigrid methods for the Maxwell application will be shown. Motivated by
certain analytical techniques developed in this analysis of iterative
techniques, some recent efforts have been made in simplifying the
convergence analysis of finite element methods for time harmonic Maxwell
equations. These will be briefly discussed.
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