Fast quadrature techniques for high order boundary element methods

Abstract

In this thesis, we developed a new fast quadrature algorithm to set up e±ciently the sti®ness matrices in hp-BEM. The key ingredient of this algorithm is the sum factorization technique, which is an established tool in the related high-order FEM (or spectral method). A complete implementation for the 2D Dirichlet problem was done. It was shown that the complexity of the new quadrature algorithm is one order (in p) better than the standard algorithm, leading to signi¯cant speed-up. Additionally, numerical examples show that the exponential convergence of the p-BEM for problems with analytic solution is retained. Studies for the 3D case show that the speed-up obtainable with sum factorization techniques is much more pronounced in 3D than in 2D.