PARALLELIZATION METHODS AND PARALLEL CODE FOR NUMERICAL CALCULATION OF 3-D HEAT CONDUCTION EQUATION ON DISTRIBUTED MEMORY SYSTEM. COMPUTATIONAL RESULTS OBTAINED ON MP-3 AND MEIKO SYSTEMS

I.D. Sofronov, B.L.Voronin, O.L. Butnev, A.N. Bykov, S.L. Skrypnik, D. Nielsen, Jr. D. Nowak, N. Medsen, R. Evans
VANT. Ser.: Mat. Mod. Fiz. Proc 1997. Вып.1. С. 64.

      Numerical calculation of 3-D problems requires the threshold computing resources provided by massively parallel distributed memory systems. A successful use of a high potential performance of such systems for the calculation of a single problem is only possible after the development of application programs supporting the parallel processing.
      The paper presents the results of the parallelization efforts for 3-D heat conduction equation. The basic method for numerical calculation of 3-D implicit finite-difference equations is the directional splitting. This method allows to reduce a complicated multidimensional problems to a collection of simpler problems that can be run on parallel processors.
      Two conceptually different approaches were developed for the organization of massively parallel computations. The first uses the decomposition of 3-D data matrix reconfigured at a timestep and is the development of the parallelization algorithms for the shared-memory multiprocessors. The second approach rests on nonreconfigurable decomposition of the 3-D data matrix.
      The resulting algorithms were implemented as a parallel code for massively parallel distributed-memory systems.
      The series of computations allowed the numerical studies of the parallelization efficiency for various techniques of the geometrical decomposition, for two modes of processor loading and depending on arithmetic execution/communications ratio.
      The quantitative estimates are given for the parallelization of the resulting algorithms obtained on MP-3 and Meiko systems.