Introduction

For a certain choice of the two scalings, our preconditioner results in a method that is identical to one recently tested successfully by Rixen and Farhat [22]; see also [1] in which the class of algorithms is extended and the methods further tested for very difficult and large problems. Our algorithms are also

defined for this class of problems, but in our analysis we have to impose certain restrictions on the coefficients and on the geometry of the subregions. We

note that, by now, many variants of the FETI algorithms have been designed and that a number of them have been tested extensively; see in particular the

discussion in [23]. Our results have also already been extended to Maxwell’s

equation in two dimensions by Toselli and Klawonn [27].