Additive Schwarz Methods for Indefinite Hypersingular
Integral Equations in R³ - the p-Version
Norbert Heuer
Appl. Anal., 72 (3-4), 411-437, 1999.
Abstract
We propose and analyze preconditioners for the p-version of the boundary
element method in three dimensions. We consider indefinite
hypersingular integral equations on surfaces and use quadrilateral elements
for the boundary discretization.
We use the GMRES method as iterative
solver for the linear systems and prove for an overlapping additive
Schwarz method that the number of iterations is bounded. This bound is
independent of the polynomial degree of the ansatz functions and
of the size of the underlying mesh.
For a modified diagonal scaling, which uses special basis functions,
we prove that the number of iterations grows only polylogarithmically
in the polynomial degree. Here, a sufficiently fine mesh is required.
Numerical results supporting the theory are presented.