An overlapping domain decomposition preconditioner for
high order BEM with anisotropic elements
Norbert Heuer, Ernst P. Stephan
Adv. Comput. Math. 19 (1-3), 211-230, 2003.
We study a preconditioner for the boundary element
method with high order piecewise polynomials for hypersingular integral
equations in three dimensions.
The meshes may consist of anisotropic quadrilateral and triangular
elements.
Our preconditioner is based on an overlapping domain decomposition
which is assumed to be locally quasi-uniform. Denoting the subdomain
sizes by Hj and the overlaps by dj,
we prove that the condition number of the preconditioned system is bounded
essentially by
maxj O(1+log Hj/dj)2.
The appearing constant depends linearly on the maximum ratio
Hi/Hj for neighboring subdomains, but is independent
of the elements' aspect ratios.
Numerical results supporting our theory are reported.