Block Elimination on Finite Element Systems of Equations

In this paper we consider the systematic use of block elimination in solving sparse symmetric positive definite systems of equations that arise in the application of finite element methods to two dimensional elliptic and parabolic problems. Given such an N by N system of equations, it has been shown by Rose* that applying block elimination to r < N of the unknowns is equivalent computationally to permuting the system so that the r unknowns appear first, and then performing the first r steps of the Cholesky or LDL^T factorization algorithms. Thus, our judicious application of block elimination can be interpreted as an efficient ordering of the equations for the ordinary step by step elimination procedure; indeed, it is convenient in the sequel to discuss orderings rather than successive applications of block elimination. However, in practice, storage management may make actual block elimination desirable.

Authors and Affiliations

1. Department of Applied Analysis and Computer Science, University of Waterloo, Waterloo, Ontario, Canada

   J. Alan George

Editors and Affiliations

1. Department of Mathematics, University of Denver, Denver, Colorado, USA

   Donald J. Rose

2. Mathematical Sciences Department, IBM Thomas J. Watson Research Center, Yorktown Heights, New York, USA

   Ralph A. Willoughby

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© 1972 Plenum Press, New York

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