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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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The construction of preconditioners for elliptic problems by substructuring. II
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by J. H. Bramble, J. E. Pasciak and A. H. Schatz PDF
Math. Comp. 49 (1987), 1-16 Request permission


We give a method for constructing preconditioners for the discrete systems arising in the approximation of solutions of elliptic boundary value problems. These preconditioners are based on domain decomposition techniques and lead to algorithms which are well suited for parallel computing environments. The method presented in this paper leads to a preconditioned system with condition number proportional to $d/h$ where d is the subdomain size and h is the mesh size. These techniques are applied to singularly perturbed problems and problems in three dimensions. The results of numerical experiments illustrating the performance of the method on problems in two and three dimensions are given.
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Math. Comp. 49 (1987), 1-16
  • MSC: Primary 65N30; Secondary 65F10
  • DOI:
  • MathSciNet review: 890250