Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation
[1] G. W. Zumbusch. Schur complement domain decomposition methods in Diffpack. Technical report, Sintef Applied Mathematics, Oslo, Norway, 1996.
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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 [?] and on multigrid [?] methods in Diffpack.