Parameter Choices for ADI-like Methods on Parallel Computers

                                 S. Malhotra

                       Scientific Computing Associates
                              One Century Tower
                              265 Church Street
                        New Haven, CT 06510-7010, USA

                                C. C. Douglas

                          Department of Mathematics
                            University of Kentucky
                          715 Patterson Office Tower
                        Lexington, KY 40506-0027, USA

                                M. H. Schultz

               Department of Computer Science, Yale University
                               P.O. Box 20-8285
                        New Haven, CT 06520-8285, USA

                                   Abstract

Alternating direction iterative (ADI) methods do not usually work well on
parallel computers due to having to do parallel rather than serial tridiagonal
solves in all but one dimension.  An ADI-like iteration is developed and
analyzed which does not require parallel tridiagonal solves in any direction,
has at least as good of a convergence rate as ADI, and has almost no
communication when a small number of iterations are used.  Acceleration
parameters are investigated in order to reduce the number of of iterations to
a small number.  Numerical experiments on a network of workstations and a
parallel computer are also included.

Key words:  alternating direction implicit methods, ADI, partial differential
equations, iterative methods, parallel computing