Iterative techniques for mixed discretizations of Maxwells
Joseph E. Pasciak
Maxwell equations in lossless media leads to a second order differential
equation for the
electric field that is not elliptic, and is indefinite. This is
system involving an indefinite bilinear form in
discretization based on
Nedelec spaces has been show to provide accurate approximate solutions.
In this talk,
the issue of preconditioning the indefinite matrix arising from this
method will be discussed. Specifically, the overlapping Schwarz method
will be shown to give rise to an iterative scheme converging at a rate
of the the mesh size.