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BIT Numerical Mathematics

, Volume 29, Issue 4, pp 938–954 | Cite as

The alternate-block-factorization procedure for systems of partial differential equations

  • R. E. Bank
  • T. F. Chan
  • W. M. CoughranJr.
  • R. K. Smith
Preconditioned Conjugate Gradient Methods

Abstract

The alternate-block-factorization (ABF) method is a procedure for partially decoupling systems of elliptic partial differential equations by means of a carefully chosen change of variables. By decoupling we mean that the ABF strategy attempts to reduce intra-equation coupling in the system rather than intra-grid coupling for a single elliptic equation in the system. This has the effect of speeding convergence of commonly used iteration schemes, which use the solution of a sequence of linear elliptic PDEs as their main computational step. Algebraically, the change of variables is equivalent to a postconditioning of the original system. The results of using ABF postconditioning on some problems arising from semiconductor device simulation are discussed.

AMS subject classification

65F10 

Keywords

Semiconductors simulation partial differential equations 

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Copyright information

© BIT Foundations 1989

Authors and Affiliations

  • R. E. Bank
    • 1
  • T. F. Chan
    • 2
  • W. M. CoughranJr.
    • 3
  • R. K. Smith
    • 3
  1. 1.Dept. of MathematicsUniv. of CaliforniaSan Diego, La JollaUSA
  2. 2.Dept. of MathematicsUniv. of California, Los AngelesLos AngelesUSA
  3. 3.AT&T Bell LaboratoriesMurray HillUSA

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