M. Feischl, T. Führer, D. Praetorius, E. Stephan:

"Optimal additive Schwarz preconditioning for hypersingular integral equations on locally refined triangulations";

in: "ASC Report 25/2013", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2013, ISBN: 978-3-902627-06-3, 1 - 28.

For non-preconditioned Galerkin systems, the condition number grows with the number of elements as well as the quotient of the maximal and the minimal meshsize.

Therefore, reliable and effective numerical computations, in particular on adaptively refined meshes, require the development of appropriate preconditioners. We analyze and numerically compare multilevel additive Schwarz preconditioners for hypersingular integral

equations, where 2D and 3D as well as closed boundaries and open screens are covered. The focus is on a new 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.

preconditioner, multilevel additive Schwarz, hypersingular integral equation

http://www.asc.tuwien.ac.at/preprint/2013/asc25x2013.pdf

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