A Method of Solving Very Large Physical Systems in Easy Stages

Abstract

Physical systems with a very large number of variables (say with tens of thousands) may be solved with available digital computers by tearing the system apart into a large number of small subdivisions. After solving each subdivision separately, the partial solutions are interconnected by a set of transformations so as to obtain the exact solution of the original system. Among the many advantages of the tearing method is the reduction of the amount of original calculations to a small fraction of about 2/n², where n is the number of subdivisions. Another advantage is the reduction of the number of nonzero elements in inverse matrices to a fraction smaller than 1/√n. The same labor saving appears also in smaller systems using slide-rule calculations. This paper illustrates the solution of Maxwell two-dimensional field-equations by tearing their electriccircuit models apart into a convenient number of subdivisions.