On accelerating transformations of programs for solving the generalized Dirichlet problem

Abstract

The chain of transformations in the program implementation of the Gauss–Seidel algorithm for solving the generalized two-dimensional Dirichlet problem of the Poisson equation is considered in this paper. It complements the previous chain of accelerating (in particular, parallelizing) transformations of this program. The previous chain of transformations contained “skewing”, “tiling”, “hyperplane method” and “parallelization”. In this work, it is supplemented with the transformations “removal of general subexpressions”, “removal of loop invariants”, “optimization of the loop header”, “optimization of the calculation of array pointers”. A series of numerical experiments were carried out with the resulting chain of transformations on a computer with an eight-core processor. Experiments were performed for different tile sizes. The greatest obtained acceleration is 24%. An analysis of the obtained accelerations was conducted.