Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation

  author = {A. M. Bruaset and H. P. Langtangen and G. W. Zumbusch},
  title = {Domain Decomposition and Multilevel Methods in
  booktitle = {Proceedings of Domain Decomposition Methods 9, DD9},
  pages = {655--662},
  year = {1998},
  editor = {P. E. Bj{\o}rstad and M. S. Espedal and D. E. Keyes},
  publisher = {Domain Decomposition Press},
  address = {Bergen, Norway},
  note = {also as report STF42 F96017, Sintef Applied Mathematics,
		  Oslo, 1996 },
  ps = { 1},
  pdf = { 1},
  annote = {refereed},
  abstract = {... 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