COMPUTER SOLUTION OF LARGE SPARSE SYMMETRIC SYSTEM OF EQUATIONS

Abstract

Large sparse symmetric system of equations generally arise in practice as a result of numerical discretization of engineering systems by finite difference or finite element methods. At present the finite element models for automobiles, aircraft, etc., have around 3 million degrees of freedom. This number is about a hundred times larger than the largest problem of about 15 years ago. Hence, the study seeks to address the most important part of finite element solutions. The present study deals with the solution of large sparse system of equations by direct methods. A number of algorithms (Cholesky, Crout's, etc.) and their various computer implementation are reviewed and discussed. The storage considerations and the different methods of storing the sparse matrices have been explained. Toward this end, an effort has been made to develop the routine in FORTRAN 77 coding. This routine is developed to solve the system of equations for the skyline stored coefficient matrix. The Crout's factorizations is used in the routine. The routine can be used for processing constrained systems without the need for prearranging the equations.