Numerical Analysis/Mathematical Problems in Mechanics Q-superlinear convergence of the GMRES algorithm for multi-materials with strong interface

We consider a model non-classical transmission problem corresponding to a multistructure composed of two bodies bonded by a thin strong layer. By using a domain decomposition, the problem is reduced to an equation defined on the interface of the form (I − G)g = F. We prove that G is compact of Carleman class Cs, and hence the q-superlinearly convergence of the GMRE