Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation
[1] A. M. Bruaset, H. P. Langtangen, and G. W. Zumbusch. Domain decomposition and multilevel methods in Diffpack. In P. E. Bjørstad, M. S. Espedal, and D. E. Keyes, editors, Proceedings of Domain Decomposition Methods 9, DD9, pages 655-662, Bergen, Norway, 1998. Domain Decomposition Press. also as report STF42 F96017, Sintef Applied Mathematics, Oslo, 1996.
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... Domain decomposition and multilevel methods contain a variety of more standard numerical building blocks (linear solvers, matrix assembly, interpolation of fields etc.). Successful software for complicated applications must offer the user a flexible run-time combination of all these different components. The purpose of the present paper is to describe how one can achieve such flexible software. In particular, we present a unified framework for domain decomposition and multilevel methods, and show how this framework can be efficiently implemented in existing software packages for PDEs.
The unified framework about to be presented is in part well known from the analysis of overlapping and non-overlapping methods [M. Dryja O.B. Widlund 1990 ], as well as from theory for overlapping and multilevel schemes [J. Xu 1992]. In this context, the goal of this paper is to extend the known framework to cover even more methods in common use, especially some Schur complement and nonlinear schemes. We will formulate the framework in a novel way that encourages systematic implementation of a wide class of domain decomposition and multilevel methods. Finally, we report on the experiences gathered from a particular implementation in the Diffpack software.