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April 27, 9:30 am in room MTH 3206, University of Maryland, College Park

Wavelet Boundary Element Methods with Mesh Refinement

Prof. Tobias von Petersdorff

Department of Mathematics
University of Maryland
College Park, MD 20742

tvp@math.umd.edu

Boundary element methods for elliptic boundary value problems (e.g., Laplacian or linear elasticity) require only the discretization of the boundary of the domain, and they give (especially for Galerkin methods) high accuracy in interior points due to superconvergence. The main drawback is the fully occupied stiffness matrix which requires at least O(N^2) operations. By using wavelet basis functions we can replace the full matrix by a sparse matrix, reducing the operation count to O(N log(N)^k).

In the case of polygonal domains the solution is singular at the vertices. This reduces the convergence rates for uniform grids. We use a mesh refinement strategy with wavelets to obtain optimal convergence rates (also for superconvergence in interior points) without increasing the complexity.