Level set topology optimization with sparse automatic differentiation.

Analytical differentiation for a smooth and accurate sensitivity field is typically used for efficient structural and multidisciplinary optimization. However, it can be challenging for multiphysics and non-linear problems. An alternative approach is automatic differentiation (AD). For large problems with many design variables AD can be computationally expensive and memory demanding and thus its use is still limited. To address some of these challenges, we propose to exploit the sparsity of the level set topology optimization (LSTO) in combination with a hybrid mode when using AD. The modularized LSTO used here enables the use of AD in combination with the classical level set method. In our method, we utilize the operator overloading (OO) approach, and we start our development by comparing different OO libraries. Next, a sparse AD implementation is proposed to take advantage of the sparsity of the level set method, in which sensitivities are only required within a narrow band close to the level set boundary. The obtained results indicate that this sparsity can improve the efficiency of the implementation. However, the reduction in memory requirements is not as significant. To improve the memory consumption as well, we introduce a hybrid mode, where instead of computing the total sensitivity directly with OO, the expression is first derived analytically and then OO is used to obtain the partial derivatives. Our studies show that combining the hybrid mode with the sparsity of the LSTO results in improvements in efficiency, with almost an order of magnitude less computational time for the biggest mesh size studied. Finally, the combination of the forward and reverse modes depending on the partial derivatives at hand is exploited to further improve memory requirements and computational cost. [ABSTRACT FROM AUTHOR]