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An affirmative partial answer is provided to the question of whether it is possible to program parallel-processor computing systems to efficiently decrease execution time for useful problems. Parallel-processor systems ore multiprocessor systems in which several of the processors con simultaneously execute separate tasks of o single job, thus cooperating to decrease the solution time of a computational problem. The processors have independent instruction counters, meaning that each processor executes its own task program relatively independently of the other processors. Communication between cooperating processors is by means of data in storage shared by oil processors. A program for the determination of the distribution of current in an electrical network was written for a parallel-processor computing system, and execution of this program was simulated. The data gathered from simulation runs demonstrate the efficient solution of this problem, typical of a large class of important problems. It is shown that, with proper programming, solution time when Np processors are applied approaches 1/Np times the solution time for a single processor, while improper programming con actually lead to an increase of solution time with the number of processors. Storage interference and other measures of performance are discussed. Stability of the method of solution was also investigated. [ABSTRACT FROM AUTHOR]

We present a complete GPU implementation of a geometric multigrid solver for the numerical solution of the Navier–Stokes equations for incompressible flow. The approximate solution is constructed on a two-dimensional unstructured triangular mesh. The problem is discretized by means of the mixed finite element method with semi-implicit timestepping. The linear saddle-point problem arising from the scheme is solved by the geometric multigrid method with a Vanka-type smoother. The parallel solver is based on the red–black coloring of the mesh triangles. We achieved a speed-up of 11 compared to a parallel (4 threads) code based on OpenMP and 19 compared to a sequential code. [ABSTRACT FROM AUTHOR]