Minimum residual iteration for a dual-dual mixed formulation of exterior
transmission problems
Gabriel N. Gatica, Norbert Heuer
Numer. Linear Algebra Appl. 8 (3), 147-164, 2001.
We investigate the minimum residual method for symmetric, indefinite
linear systems of a so-called dual-dual structure.
These systems arise when using
a combined dual-mixed finite element method with a
Dirichlet-to-Neumann mapping to solve a class of exterior transmission
problems. As a model problem we consider an elliptic equation
of divergence form coupled with the Laplace equation in an unbounded
region of the plane.
We give abstract convergence results for the preconditioned
minimum residual method for the solution of linear systems of
the special dual-dual structure.
For our model problem, we show that this iterative method
provides an efficient solution procedure where
standard preconditioners can directly be used.