Preconditioners for the p-Version of the Galerkin Method for a Coupled
Finite Element/Boundary Element System
Norbert Heuer, Ernst P. Stephan
Numer. Methods Partial Differential Eq., 14 (1), 47-61, 1998.
Abstract
We propose and analyse efficient preconditioners for solving systems
of equations arising from the p-version for the finite element/boundary
element coupling.
The first preconditioner amounts to a block Jacobi method whereas the second
one is partly given by diagonal scaling.
We use the generalised minimum residual method for the solution of the
linear system. For our first preconditioner the number of iterations
of the GMRES which are necessary to obtain a given accuracy grows like
$\log^2 p$ where $p$ is the polynomial degree of the ansatz functions.
The second preconditioner, which is more easily implemented, leads to a
number of iterations which behaves like $p\log^3 p$.
Computational results are presented which support this theory.