Implementation of Dual Number Automatic Differentiation with John Newman's BAND Algorithm

Abstract

This paper asserts that the development of continuum-scale mathematical models utilizing John Newman's BAND subroutine can be simplified through the use of dual number automatic differentiation. This paper covers the salient features of the BAND algorithm as well as dual numbers and how they can be leveraged to algorithmically linearize systems of partial differential equations; these two concepts can be combined to produce accurate and computationally efficient models while significantly reducing the amount of personnel time necessary by eliminating the time-consuming process of equation linearization. As a result, this methodology facilitates more rapid model prototyping and establishes a more intuitive relationship between the numerical model and the differential equations. By utilizing an existing and validated programming module, dnadmod, these advantages are achieved without burdening the general user with significant additional programming overhead.