Evidences that Software Based on Non-overlapping Discretization Is Most Efficient for Applying Highly Parallelized Supercomputers to Solving Partial Differential Equations

摘要

One of the main problems for applying the highly parallelized supercomputers available today to computational physico-mathematical modeling of science and engineering is to develop software capable of effectively solving in parallel partial differential equations or systems of such equations. For this purpose much work on domain decomposition methods has been done. Recently, I. Herrera introduced a new 'non-overlapping discretization method' that for the application of domain decomposition methods has many advantages over standard methods of discretization. Based on theoretical grounds, some of these advantages have been indicated in previous publications. This paper, however, is devoted to present numerical evidences of such advantages and some of the outstanding parallelization-efficiencies that are feasible when domain decomposition methods are applied to the discrete system derived using non-overlapping discretization methods.