On storage, retrieval, and Gauss-Seidel iteration involving nonzero elements of a sparse stiffness matrix compacted as a vector

This paper presents a storing and retrieving algorithm developed for the Gauss-Seidel iterative solution of a large system of simultaneous linear algebraic equations when the non-zero elements of its sparse coefficient matrix is to be compacted into a one-dimensional array for the sake of saving computer space. Particular reference is made to the system of equations arising from the finite-element applications. Though at the expense of more computer time, the algorithm resolves the problem encountered by some computing facilities, at which such a large system of linear equations needs to be solved but under the handicap of limited available computer space. Examples are given to depict the problem involved as well as to illustrate the details of the developed algorithm.