A PARALLEL BOUNDARY VALUE ODE CODE FOR SHARED-MEMORY MACHINES

The software package COLNEW [G. Bader and U. Ascher, SIAM J. Sci. Statist. Comput., 8 (1987), pp. 483–500], which implements the method of spline collocation at Gauss points, has been widely used for the solution of mixed-order systems of boundary value problems in ordinary differential equations. Considerable attention has been given in recent years to the development of efficient algorithms for the solution of the almost block diagonal (ABD) linear systems of the type which arise in this method, and some of these algorithms have been designed to exploit parallelism. However, in COLNEW, the solution of the ABD systems contributes only a modest amount to the overall execution time, thus limiting the potential of these new solvers. In this paper, we examine the linear system setup, which is the primary bottleneck in COLNEW and has not been addressed previously. We describe PCOLNEW, a modified version of COLNEW which incorporates coarse-grained parallelism to minimize the cost of this bottleneck. Numerical results of tests conducted on a variety of shared-memory machines are presented which demonstrate the efficacy of this parallel implementation.