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.
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The work of R. E. Bank was supported in part by the Office of Naval Research under contract N00014-82K-0197. The work of T. F. Chan was supported in part by the National Science Foundation under grant NSF-DMS87-14612 and by the Army Research Office under contract DAAL03-88-K-0085.
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Bank, R.E., Chan, T.F., Coughran, W.M. et al. The alternate-block-factorization procedure for systems of partial differential equations. BIT 29, 938–954 (1989). https://doi.org/10.1007/BF01932753
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DOI: https://doi.org/10.1007/BF01932753