SOLUTION PROPERTIES OF THE VARIATIONAL STEP-BY-STEP OPTIMIZATION PROBLEM OF REDISTRIBUTION OF MESH POINTS ON A PROCESSOR LINE

Yu.A. Bondarenko
VANT. Ser.: Mat. Mod. Fiz. Proc 1996. Вып.4. С. 5-7.

      A numerical method of explicit-difference-scheme type with an ordered mesh point distribution between processors is considered as applied to a processor line. It is presumed that its parallelization involves a load balancing algorithm, when mesh points are transferred from one processor to its neighbor at each time step. Presuming that the computational time is different for different points and that it can vary with time, we set a variational problem of step-by-step computational time minimization with the account for processor load non-uniformity and time losses for both regular processor communication and exchange of mesh points between processors to balance their load. A complete mathematical analysis of this variational problem was carried out. Practical applicability of the results obtained is discussed.

      Parallelization techniques for an explicit and an implicit difference scheme are described. The explicit scheme was used for multidimensional gas dynamics equations, and the implicit scheme, for the 2D heat transfer equation. Computational results are reported.