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Computational Science, Engineering & Technology Series
ISSN 1759-3158
Edited by: B.H.V. Topping
Chapter 12

A New Parallel Domain Decomposition Preconditioner II: Generalization to a Mesh-Free Parallel Solver

R.E. Bank+ and P.K. Jimack*

+Department of Mathematics, University of California at San Diego, United States of America
*School of Computer Studies, University of Leeds, Leeds, United Kingdom

Full Bibliographic Reference for this chapter
R.E. Bank, P.K. Jimack, "A New Parallel Domain Decomposition Preconditioner II: Generalization to a Mesh-Free Parallel Solver", in B.H.V. Topping, (Editor), "Computational Mechanics using High Performance Computing", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 12, pp 243-259, 2002. doi:10.4203/csets.9.12
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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