Parallel Triangular System Solving on a Mesh Network of Transputers

Abstract

A parallel algorithm is presented for triangular system solving on a distributed-memory MIMD computer with a square mesh topology. The algorithm is based on the square grid (scattered) distribution of matrix elements across the processors. The theoretical time complexity is $n^2/ p + O(n)$, for p processors and an $n \times n$ matrix. Experimental timings of an implementation in occam 2 on a square mesh of $p = 36$ transputers confirm the theoretical time model. The scaled speedup achieved for $n = 1200$ is 24 on a 36 transputer mesh. This corresponds to a computing rate of 11.7 Mflop/s.