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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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The construction of preconditioners for elliptic problems by substructuring. I
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by J. H. Bramble, J. E. Pasciak and A. H. Schatz PDF
Math. Comp. 47 (1986), 103-134 Request permission

Abstract:

We consider the problem of solving the algebraic system of equations which arise from the discretization of symmetric elliptic boundary value problems via finite element methods. A new class of preconditioners for these discrete systems is developed based on substructuring (also known as domain decomposition). The resulting preconditioned algorithms are well suited to emerging parallel computing architectures. The proposed methods are applicable to problems on general domains involving differential operators with rather general coefficients. A basic theory for the analysis of the condition number of the preconditioned system (which determines the iterative convergence rate of the algorithm) is given. Techniques for applying the theory and algorithms to problems with irregular geometry are discussed and the results of extensive numerical experiments are reported.
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Math. Comp. 47 (1986), 103-134
  • MSC: Primary 65N30; Secondary 65F10, 65W05
  • DOI: https://doi.org/10.1090/S0025-5718-1986-0842125-3
  • MathSciNet review: 842125