Thesis Summary:

In this thesis we consider the application of wavelet methods to the coupling of finite element and boundary element methods into two dimensions. By means of compression techniques of matrices by means of bases of biortogonal partitions for the boundary terms with N degrees of freedom, it is proved that the convergence of the compressed scheme is not deteriorated, whereas the number of coefficients in the corresponding stiffness matrices is Considerably smaller than N ^ 2 N⁲. Since the coupling method deals with the Dirichlet and Neumann data, it is necessary to consider integral boundary operators of nonzero orders and Sobolev spaces of fractional orders. In this context, the bases of wavelets can be normalized to be stable in these spaces. This property, combined with the known BPX preconditioner, is used to construct a preconditioner for the complete matrix system resulting from the coupling method.

ISI Publications from the Thesis

Helmut HARBRECHT, Freddy PAIVA, Cristian PEREZ, Reinhold SCHNEIDER: Multiscale preconditioning for the coupling of FEM-BEM. Numerical Linear Algebra with Applications, vol. 10, 3, pp. 197-222, (2003)

Helmut HARBRECHT, Freddy PAIVA, Cristian PEREZ, Reinhold SCHNEIDER: Biorthogonal wavelet approximation for the coupling of FEM-BEM. Numerische Mathematik, vol. 92, 2, pp. 325-356, (2002)