Multiscale preconditioning for the coupling of FEM–BEM

We apply multiscale methods to the coupling of finite and boundary element methods to solve an exterior two‐dimensional Laplacian. The matrices belonging to the boundary terms of the coupled FEM–BEM system are compressed by using biorthogonal wavelet bases developed from A. Cohen, I. Daubechies and J.‐C. Feauveau (Comm. Proc. Appl. Math. 1992; 45 :485). The coupling yields a linear equation system which corresponds to a saddle point problem. As favourable solver, the Bramble–Pasciak–CG (Math. Comp. 1988; 50 :1) is utilized. A suitable preconditioner is developed by combining the BPX (Math. Comp. 1990; 55 :1) with the wavelet preconditioning (Numer. Math. 1992; 63 :315). Through numerical experiments we provide results which corroborate the theory of the present paper. Copyright © 2002 John Wiley & Sons, Ltd.