This paper is concerned with asymptotically almost optimal preconditioning
techniques for the solution of coupled elliptic problems with piecewise con
tinuous coefficients: by domain decomposition methods. Spectrally equivalen
t, two- and multilevel interface preconditioners are proposed and analyzed.
They are applied to two basic formulations: strongly elliptic skew symmetr
ic problems and symmetric, positive definite variational problems: the form
er involves the classical boundary potentials from the Calderon projections
and the latter is based on the Steklov-Poincare operators associated with
subdomains of the decomposition. The preconditioners considered are shown t
o be robust with respect to both mesh-parameters and jumps in the coefficie
nts. (C) 2001 Elsevier Science Ltd. All rights reserved.