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IBM Journal of Research and Development  
Volume 30, Number 2, Page 184 (1986)
Vector Processing
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Parallel iterative linear solvers for oil reservoir models

by I. Efrat, M. Tismenetsky
This paper suggests a new algorithm for solving sparse linear systems which is readily parallelized and is very efficient for matrices arising in such domains as reservoir modeling. The algorithm is, in fact, a variant of the incomplete block factorization technique, accelerated by Biconjugate Gradient iterations or by another acceleration method. Implementation on a vector computer such as the IBM 3090 Vector Facility is described. We also suggest some refinements of known preconditioning methods enabling their parallel computation. Numerical experiments are presented to display the performance of the suggested methods. Special attention is given to fully implicit, multiphase models which yield asymmetrical systems.
Related Subjects: Algorithms; Computational methods; Geophysics; Large-scale computing; Mathematical functions and techniques; Vector processing