Quantitative performance modeling of scientific computations and creating locality in numerical algorithms

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1995.Includes bibliographical references (p. 141-150) and index.by Sivan Avraham Toledo.Ph.D

Preconditioning with a Decoupled Rowwise Ordering on the CM-5

Decoupled rowwise ordering is an ordering scheme for 2-dimensional grids, which is tailored for preconditioning 5-point difference equations arising from discretizations of partial differential equations. This paper describes the ordering scheme and implementations of a conjugate gradient solver and SSOR preconditioners which use the decoupled rowwise and the red black ordering schemes on the CM-5 parallel supercomputer. The rowwise decoupled preconditioner leads to faster convergence than the red black preconditioner, and it reduces the solution time by a factor of 1:5 to 2:5 over a nonpreconditioned solver on a variety of test problems. 1 Introduction This paper describes the implementation and performance of a preconditioned conjugate gradient solver for discretized Poisson problems in 2 dimensions, which we have implemented on the Connection Machine CM-5 parallel supercomputer [5]. The preconditioner is an SSOR preconditioner with a novel ordering scheme for the variables, which w..