Numerische Simulation Auf Massiv Parallelen Rechnern Least Squares Methods for the Coupling of Fem and Bem Preprint-reihe Des Chemnitzer Sfb 393

In the present paper we propose least squares formulations for the numerical solution of exterior boundary value problems. The partial di erential equation is a rst order system in a bounded subdomain, and the unbounded subdomain is treated by means of boundary integral equations. The rst order system is derived from a strongly elliptic second order system. The analysis of the present least squares formulations is reduced to the analysis of the Galerkin method for the coupling of nite element and boundary element methods (FEM and BEM) of the second order problem. The least squares approach requires no stability condition. But it requires the computation of negative as well as of half integer Sobolev norms. The arising linear systems can be preconditioned to have condition numbers 1. The present methods bene t strongly from the use of biorthogonal wavelets on the coupling boundary and the computation of corresponding equivalent norms in Sobolev spaces. Our approach leads to a very e cient discretization of the least squares formulations. Mathematics Subject Classi cations (1991): 65J15, 65N30, 65N38, 65R20