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Computational Science, Engineering & Technology Series
ISSN 17593158 CSETS: 9
COMPUTATIONAL MECHANICS USING HIGH PERFORMANCE COMPUTING Edited by: B.H.V. Topping
Chapter 12
A New Parallel Domain Decomposition Preconditioner II: Generalization to a MeshFree Parallel Solver R.E. Bank+ and P.K. Jimack*
+Department of Mathematics, University of California at San Diego, United States of America R.E. Bank, P.K. Jimack, "A New Parallel Domain Decomposition Preconditioner II: Generalization to a MeshFree Parallel Solver", in B.H.V. Topping, (Editor), "Computational Mechanics using High Performance Computing", SaxeCoburg Publications, Stirlingshire, UK, Chapter 12, pp 243259, 2002. doi:10.4203/csets.9.12
Abstract
This chapter continues and further develops some of the ideas
previously introduced in Chapter 11. In particular, it is shown that
the main parallel solution technique developed in Chapter 11 may be
generalized to allow the parallel solution of an arbitrary sparse matrix.
This generalization requires the matrix to be partitioned into p blocks
and then coarsened (preferably in parallel) so that each of p different
processors stores an entire submatrix plus a coarsening of the rest of the
matrix. The linear problems with these new matrices may then be solved
concurrently in order to obtain approximations to the solution of the
full problem which may then be combined together in an appropriate way to
define a general parallel preconditioner. As well as providing an overview
of this new algorithm the paper also addresses the issues associated with
partitioning the sparse matrix and coarsening certain blocks of its rows
and columns. The paper concludes with the presentation and discussion of
some preliminary numerical results.
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