Solution of linear equations for small computer systems

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Abstract
A solution technique, based on Gauss elimination, is described which can solve symmetric or unsymmetric matrices on computers with small core and disk requirement capabilities. The method is related to frontal techniques in that renumbering of the nodes, such as in a finite element mesh, is not required, and the elimination is performed immediately after the equations for a particular node have been fully summed. Only two rows of the matrix need be on core at any step of the solution, but for more efficiency, the program presented here requires all the equations associated with two nodes to be on core. Minimum disk storage is achieved by storing only nonzero entries of the matrix, a single pointing vector for each node, regardless of the number of degrees‐of‐freedom, and the use of a single sequential file. Special care is taken of the boundary nodes where only the diagonal and the right‐hand‐side vector are stored. Assembly and elimination for these nodes are avoided completely. The performance of the program is compared with both symmetric and nonsymmetric frontal routines and is shown to be acceptable. The major merit of the method lies in the fact that it can be implemented on small minicomputers. The reduction of core and disk storage inevitably increases the solution time, but the decrease in the output file size also makes the back‐substitution and resolution processes more efficient. In some cases, the total solution time can be shorter than for the frontal method due to this property.

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