[Zurück]

M. Feischl, T. Führer, D. Praetorius, E. Stephan:
"Optimal additive Schwarz preconditioning for hypersingular integral equations on locally refined triangulations";
Calcolo, 54 (2017), S. 367 - 399.

For the non-preconditioned Galerkin matrix of the hypersingular integral operator, the
condition number grows with the number of elements as well as the quotient of the
maximal and the minimal mesh-size. Therefore, reliable and effective numerical
computations, in particular on adaptively refined meshes, require the development of
appropriate preconditioners. We propose and analyze a local multilevel preconditioner
which is optimal in the sense that the condition number of the corresponding
preconditioned system is independent of the number of elements, the local mesh-size,
and the number of refinement levels. The theory covers closed boundaries as well as
open screens in 2D and 3D. Numerical experiments underline the analytical results
and compare the proposed preconditioner to other multilevel schemes as well as
techniques based on operator preconditioning.

http://dx.doi.org/10.1007/s10092-016-0190-3