Structure-exploiting automatic differentiation of finite element discretizations

Abstract

A common way to solve PDE constrained optimal control problems by automatic differentiation (AD) is the full black box approach. This technique may fail because of the large memory requirement. In this paper we present two alternative approaches. First, we exploit the structure in time yielding a reduced memory requirement. Second, we additionally exploit the structure in space by providing derivatives on a reference finite element. This approach reduces the memory requirement once again compared to the exploitation in time. We present numerical results for both approaches, where the derivatives are determined by the AD-enabled NAGWare Fortran compiler.