Desarrollo de un Conjunto de Rutinas para la Resolución de Sistemas con Matrices Ralas no Simétricas. Comparación de Varios Métodos Iterativos Basados en el de Gradientes Conjugados

Abstract

Frequently the matrix sustems resulting from the discretization equations arising from Finite Element Method are non symmetric. The direct solvers use a complete factorization of the matrix with a number of operations known in advance for a given matrix size. The iterative methods tend to the solution from an initial guess using a number of operations not known a priori. The performance of these methods is greatly impreved when preconditioners are used.
In this work the behaviour of direct and iterative solvers for non symmetric matrices with Gustaffson [1] sparse storage is analysed. The results obtained by means of the iterative methods MCG, BCG, CGS and GMRES, the preconditioner ILE and the pre-preconditioners Blck Diagonal and Diagonal Scaling are shown. The different methods are compared and it is concluded that the CGS method performed best, but GMRES is recommended for very ill-conditioned problems.