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

R. E. Bank*, T. F. Chan, W. M. Coughran, R. K. Smith

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

41 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)938-954
Number of pages17
JournalBIT Numerical Mathematics
Issue number4
StatePublished - Dec 1989
Externally publishedYes


  • AMS subject classification: 65F10
  • Semiconductors
  • partial differential equations
  • simulation

ASJC Scopus subject areas

  • Software
  • Computational Mathematics
  • Applied Mathematics
  • Computer Networks and Communications


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