CONJUGATE GRADIENT METHOD FOR SOLVING LARGE SPARSE LINEAR SYSTEMS ON MULTI-CORE PROCESSORS

Abstract

In the mathematical modelling of the fluid flow and heat transfer processes it is frequent to find systems of second order linear or non linear partial differential equations. When solving such systems of partial differential equations through the use of numerical methods such as finite elements or finite differences it is necessary to do the discretization process that transforms the original systems of equations, defined over a continuum domain, into a linear or non linear algebraic system, defined over a discrete domain. Due to the char- acteristics of discretization methods for the partial differential equations domain as well for the equations themselves, generally the algebraic system that appears has the coefficient ma- trix with a very high sparsity. In this work we present the implementation in parallel pro- cessing of routines capable to solve large linear sparse systems with positive definite coeffi- cient matrix, exploiting and preserving the initial sparsity. It is analyzed the use of the conju- gate gradient method in the solution of large sparse linear systems running on multi-core processors.