Level-set topology optimisation with GridapTopOpt.jl: a memory-distributed Julia package with automatic differentiation capabilities

Prof Vivien Challis

Queensland University of Technology

Abstract: Topology optimisation is a powerful computational tool for solving PDE-constrained engineering design problems for a range of applications, including those related to solid mechanics, fluid mechanics, acoustics, and more. When using a level-set approach, the material boundary is implicitly defined using a level-set function, which is evolved during the optimisation process to update the design. An appropriate boundary evolution can be determined using shape derivatives of the optimisation objective and of any constraints. Benefits of a level-set approach include a well-defined material boundary, which avoids the need for large regions of intermediate densities that can be problematic for some design problems. 

In this talk, I’ll present our open-source Julia package for level-set topology optimisation, GridapTopOpt.jl, and outline its features as well as recent extensions and applications. The package allows solution of large-scale topology optimisation problems by distributing computations over a high-performance computing cluster. The syntax is near one-to-one with mathematical notation, facilitating implementation of new topology optimisation problems. Furthermore, the package implements automatic differentiation, circumventing the need for analytical calculation of shape derivatives. I’ll talk about our work designing periodic piezoelectric materials as well as our recent extension of GridapTopOpt.jl to unfitted finite element discretisations.

Bio: Associate Professor Vivien Challis completed her undergraduate degree at the University of Otago, New Zealand, before completing her PhD in Mathematics at The University of Queensland. She moved to Queensland University of Technology in 2019 as a Lecturer in Applied and Computational Mathematics, and has since been promoted to Associate Professor. 

Associate Professor Challis's research interests lie in material modelling, structural topology optimisation, computational mechanics, level-set methods, and high-performance computing. As well as working on theoretical and computational developments, she collaborates with experimentalists. Her research contributions were recognised with the award of the 2024 JH Michell Medal from ANZIAM.