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

  author = {G. W. Zumbusch},
  title = {Schur Complement Domain Decomposition Methods in
  institution = {Sintef Applied Mathematics},
  year = {1996},
  address = {Oslo, Norway},
  ps = { 1},
  pdf = { 1},
  annote = {unrefereed},
  abstract = {The report gives an introduction to the Schur complement
		  domain decomposition solvers in Diffpack. It is meant as a
		  tutorial for the use of iterative solution methods of
		  equation systems arising in the discretization of partial
		  differential equations. Schur complement iterative solvers
		  are discussed, without and with preconditioners. They are
		  also referred to as iterative sub-structuring methods or
		  non-overlapping domain decomposition methods. Domain
		  decomposition methods are well suited and efficient
		  equation solvers on parallel computers. Schur complement
		  methods are also advantageous if there are abrupt changes
		  in the coefficients of the differential operator due to
		  abrupt changes in material properties. We provide an
		  introduction to the implementation and use of such methods
		  in Diffpack. We cover the basic Schur complement method
		  along with preconditioners of eigen-decomposition, BPS,
		  wire-basket and Neumann-Neumann type (with coarse grid).
		  The first steps are guided by a couple of examples and
		  exercises. We also want to refer to the related tutorials
		  on overlapping domain decomposition \cite{GWZumbusch:1996b}
		  and on multigrid \cite{GWZumbusch:1996a} methods in