USE OF NORMA LANGUAGE FOR THE INTEGRATION OF POISSON EQUATION WITH VARIABLE COEFFICIENTS ON PARALLEL COMPUTERS

A.N. Andrianov, K.N. Efimkin, S.V. Zybin
VANT. Ser.: Mat. Mod. Fiz. Proc 1997. Вып.1. С. 39.

      The issues are considered for the use of declarative (nonprocedural) NORMA language to solve 2-D Poisson: equation in cylindrical coordinates on nonuniform grids in the problem of streamer propagation through the cathode layer.
      NORMA language is a tool designed for the specification of numerical methods for the calculations in computational physics on parallel computer systems. It actually allows to automate the programming phase needed to convert from the computational formulas specified by the applications specialists to the computer-specific code.
      There is no considerable difference between the computational formulas and NORMA, representation (of the algorithm; these formulas are the source information for the translation system. This description retains the natural parallelism of the problem without containing any restrictions related with the, wish to adapt the program to a parallel architecture or programming language features. NORMA representation does not require any information about the computational procedure, organization techniques for the computational (cyclic) processes. The order of language clauses can be arbitrary: the informational relations are identified and taken into account by the translator during the computational process organization. This resulted in the following high-level automatization of applications program development (the programmer operates primarily in terms of computational formulas from the application domain):
      — development of reliable applications programs (if the computational formulas are written, correctly, then the correct target program is guaranteed);
      — portability of NORMA programs (the synthesis NORMA translator takes into account the architecture features).
      In this paper NORMA language is used for the representation of the parallel.-algorithm for the calculation of 2-D Poisson equation in cylindrical coordinates using SOR method. The use of NQRMA allowed to obtain automatically the target Fortran program for IBM PG for a single (shared memory) node of the parallel Convex SPP-1000, and Fortran GNS program for. the distributed- memory i860XP parallel system with message passing. The source NORMA program was not actually changed; in the last case it is sufficient to add the specification of the number of processors to the, program that would be desirable for the execution., NORMA programming does not require the knowledge of complicated message passing mechanism; NORMA translator automatically organizes the computations and the communications between parallel tasks.
      The results obtained allow to suggest that the use of NORMA language for the calculations in computational, physics would considerably reduce the development cost of high-performance algorithms especially on parallel architectures.