Matrix-Free Jacobian Chaining

Society for Industrial and Applied Mathematics eBooks, pp. 13–27

Abstract

The efficient computation of Jacobians represents a fundamental challenge in computational science and engineering. Large-scale modular numerical simulation programs can be regarded as sequences of evaluations of in our case differentiable subprograms with corresponding elemental Jacobians. The latter are typically not available. Tangent and adjoint versions of the individual subprograms are assumed to be given as results of algorithmic differentiation instead. We reformulate the classical (Jacobian) Matrix Chain Product problem in terms of matrix-free Jacobian-matrix (tangents) and matrix-Jacobian products (adjoints), subject to limited memory for storing information required by latter. A corresponding new dynamic programming algorithm is developed. All numerical results can be reproduced using our open-source reference implementation.

Authors 1

1. Uwe Naumann corresponding Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University

   Software and Tools for Computational Engineering