Performance optimization of parallel algorithms

TL;DR: Finite algorithms for solving systems of linear equations, namely the matrix manipulation (Gauss elimination method, GEM) are designed for architectures with shared memory, distributed-memory and for their combination.

Abstract: The high intensity of research and modeling in fields of mathematics, physics, biology and chemistry requires new com- puting resources. For the big computational complexity of such tasks computing time is large and costly. The most efficient w ay to increase efficiency is to adopt parallel principles. Purp ose of this paper is to present the issue of parallel computing with em- phasis on the analysis of parallel systems, the impact of commu- nication delays on their efficiency and on overall execution time. Paper focuses is on finite algorithms for solving systems of l in- ear equations, namely the matrix manipulation (Gauss elimina- tion method, GEM). Algorithms are designed for architectures with shared memory (open multiprocessing, openMP), distributed- memory (message passing interface, MPI) and for their combina- tion (MPI + openMP). The properties of the algorithms were an- alytically determined and they were experimentally verifie d. The conclusions are drawn for theory and practice.