We apply multiscale methods to the coupling of finite and boundary element methods to solve an exterior Dirichlet boundary value problem for the two dimensional Poisson equation. Adopting biorthogonal wavelet matrix compression to the boundary terms with N degrees of freedom, we show that the resulting compression strategy fits the optimal convergence rate of the coupling Galerkin methods, while the number of nonzero entries in the corresponding stiffness matrices is considerably smaller than N 2 .

We present the control of continuous sedimentation in an ideal thickener as an initial and boundary value problem and construct the entropy solution. ,

SUMMARYWe apply multiscale methods to the coupling of ÿnite 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.

No abstract

No abstract

No abstract

No abstract