Element‐by‐Element Implicit Algorithms for Heat Conduction

Abstract

A new type of element‐by‐element implicit algorithm is proposed for heat conduction analysis. The algorithm is shown to be unconditionally stable, but does not involve a global coefficient matrix. Consequently, there are considerable operation count advantages over typical implicit schemes. Numerical test examples indicate the good behavior of the method. It is believed that the new approach will enable large heat conduction calculations to be performed much more economically than heretofore and is suggestive of related developments in other areas of engineering and the physical sciences.