ON THE PERFORMANCE OF A DIRECT PARALLEL METHOD FOR SOLVING SEPARABLE ELLIPTIC-EQUATIONS BASED ON BLOCK CYCLIC REDUCTION

A comparison of the performance of the Buneman's version of the block cyclic reduction (BCR) algorithm based on a) polynomial factorization and b) partial fraction expansion for separable elliptic equations wit h Dirichlet boundary conditions is presented. This study was initiated by an interest in mesoscale atmospheric modeling and the parallel com puting techniques that can be used to increase the computational effic iency of these models. Examples cited are taken from the field of mete orology. Varying the numbering scheme during the discretization proces s of separable elliptic equations changes the form of the coefficient matrix. It was determined serendipitously that for certain classes of separable problems found in meteorology, choosing a particular numberi ng scheme can save computational time by allowing a Poisson solver to be used in place of a more computationally demanding separable solver. Timings are based on the University of Oklahoma's eight processor All iant FX/80 computer.