Author(s) :
Matthias Bollhöfer
Preprint series :
PhD Thesis of the Department of Mathematics, Chemnitz University of Technology
MSC 2000
- 65Y05 Parallel computation
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65F50 Sparse matrices
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65F05 Direct methods for linear systems and matrix inversion
-
65F10 Iterative methods for linear systems
Abstract :
We discuss algebraic domain decomposition strategies for large sparse linear systems. This is done by use of
the low rank modification formula due to Sherman, Morrison and Woodbury. Most part of this paper concentrates on the
properties and treatment of the so-called coupling system, which arises from the application of the low rank modification
formula. A strategy to improve the properties is presented and the close relations to algebraic multigrid methods are shown.
Several splittings for large sparse linear systems are discussed, especially modified block diagonal splittings. An approach
to improve the properties of the coupling system by the use of suitably modified block diagonal matrices is done and finally
parallel aspects of implementation are pointed out. The results are illustrated by several examples.
Keywords :
Domain decomposition, parallel computations, large sparse linear systems, iterative methods, direct methods