A parallelized point rowwise successive over-relaxation method on a multiprocessor (Q1079933)

A parallelized point successive over-relaxation (SOR) iterative algorithm is derived for the heterogeneous element processor (HEP). The solution of the two-dimensional Laplace equation with simple Dirichlet boundary conditions using central finite-difference approximations at mesh points is considered as a model problem to explain the parallelization technique. The parallel computer HEP consists of one or more pipelined MIMD process execution modules (PEMs), where multiple instruction streams act on multiple data items in parallel (MIMD). Sequential version of the SOR and various parallel versions of the SOR HEP implementations of the model problem with 102\(\times 102\) grid points are evaluated from the point of view of the execution time as a function of the number of parallel processors. The numerical results of the solution of the two- dimensional incompressible Navier-Stokes equations in a square cavity using the SOR are supplied.