STABLE SCHEMES FOR PARALLEL REGION-BY-REGION CALCULATION OF HEAT CONDUCTION EQUATION

B.L.Voronin, A.M. Erofeev
VANT. Ser.: Mat. Mod. Fiz. Proc 1997. Вып.1. С. 65.

      Currently the highest performance is demonstrated by massively parallel computer systems with a large number of processors. The efficient use of high potential performance of these machines requires the development of parallel methods for the calculation of complicated multidimensional applications. An example is represented by 3-D heat conduction equation. One of the ways to calculate the multidimensional heat conduction equation is the directional splitting combined method with the implicit scheme. The resulting equations are solved by funning.
      The most natural approach to the parallelization of numerical solution in this case is a geometrical technique where each computational domain is split into subdomains each being computed by a designated processor. Multiple papers are devoted to the organization of region-by-region computations. At this point, there are many schemes for sequential region-by-region computations. The first one was that of Zaguskin-Kondrashoy. Later some authors developed the schemes with re redundant stability. This work considers some parallel schemes for region-by-region; calculations including the scheme that uses the running parallelization algorithm proposed in a paper by Yanenko. The studies were performed for the computational stability and accuracy, the conclusions are made relative to .the potential use of the schemes for the organization of massively parallel computations.