Efficient Computation of Sparse Higher Derivative Tensors

Abstract

The computation of higher derivatives tensors is expensive even for adjoint algorithmic differentiation methods. In this work we introduce methods to exploit the symmetry and the sparsity structure of higher derivatives to considerably improve the efficiency of their computation. The proposed methods apply coloring algorithms to two-dimensional compressed slices of the derivative tensors. The presented work is a step towards feasibility of higher-order methods which might benefit numerical simulations in numerous applications of computational science and engineering.