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


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



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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