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.
|