Wavelet boundary element methods for 3D boundary value problems

Prof. Tobias von Petersdorff

Department of Mathematics, University of Maryland, College Park

Boundary Element Methods require only a mesh on the boundary of the domain, but they lead to a full stiffness matrix. Wavelet methods introduce new basis functions which give an optimal preconditioning and allow to use a sparse matrix. Therefore the solution requires only O(N log(N)^a) operations for N degrees of freedom on the boundary. The theory for 2D domains is by now fairly complete, but for 3D domains new problems occur: construction of wavelets on polyhedra, quadrature, efficient implementation, handling of singularities.