Solving banded systems using a parallel programming language with hierarchically data descriptive features

This paper presents a parallel code for solving banded systems by using the PARAGRAM language. First, the banded area is hierarchically partitioned, and then a parallel solving method based on S.L. Johnsson’s work (1985) is applied. Seveml descriptive features are effectively used to express the algorithm including hierarchical data definition provided by PARAGRAM. Only half the program lines are necessary for PARAGRAM description as compared with the macro task level parallel FORTRAN. A lower level parallel code generated by the PARAGRAM translator was executed on the Japanese National Research Project machine. For a solution of a banded matrix with 8192 equations, a speedup time of 2.83 is measured on 4 processing elements. This performance coincides well with a prediction resulting from the analysis of operations count and the amount of data transferred.

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