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 using biorthogonal wavelet bases developed from A. Cohen, I. Daubechies and J.-C. Feauveau [5]. We describe different solving and preconditioning techniques. Through numerical experiments we provide results which corroborate the theory of [19] and the present paper