Extending the functionality of the general-purpose finite element package SEPRAN by automatic differentiation

From an abstract point of view, a numerical simulation implements a mathematical function that produces some output from some given input. Derivatives (or sensitivities) of the function’s output with respect to its input can be obtained—free from truncation error—by using a technique called automatic di erentiation. Given a computer code in a high-level programming language like Fortran, C, or C++, automatic di erentiation generates another code capable of computing not only the original function but also its derivatives. Thus, the application of automatic di erentiation signi cantly extends the functionality of a simulation package. For instance, automatic di erentiation enables, in a completely mechanical fashion, the usage of derivative-based optimization algorithms where the evaluation of the objective function comprises some given large-scale engineering simulation. In this paper, the automatic di erentiation tool ADIFOR is used to transform the general-purpose nite element package SEPRAN. In doing so, we automatically transform the given 400 000 lines of Fortran 77 into a new program consisting of 600 000 lines of Fortran 77. We compare our approach with a traditional approach based on numerical di erentiation and quantify its advantages in terms of accuracy and computational e ciency for a standard uid ow problem