Simple and efficient GPU accelerated topology optimisation: Codes and applications

Erik A. Träff, Anton Rydahl, Sven Karlsson, Ole Sigmund, Niels Aage
Department of Civil and Mechanical Engineering, Technical University of Denmark, Building 404, Koppels Alle, Kgs. Lyngby, 2800, Denmark
Computer Methods in Applied Mechanics and Engineering, Volume 410, 116043, 2023


   title={Simple and efficient GPU accelerated topology optimisation: Codes and applications},

   author={Tr{"a}ff, Erik A and Rydahl, Anton and Karlsson, Sven and Sigmund, Ole and Aage, Niels},

   journal={Computer Methods in Applied Mechanics and Engineering},






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This work presents topology optimisation implementations for linear elastic compliance minimisation in three dimensions, accelerated using Graphics Processing Units (GPUs). Three different open-source implementations are presented for linear problems. Two implementations use GPU acceleration, based on either OpenMP 4.5 or the Futhark language to implement the hardware acceleration. Both GPU implementations are based on high level GPU frameworks, and hence, avoid the need for expertise knowledge of e.g. CUDA or OpenCL. The third implementation is a vectorised and multi-threaded CPU code, which is included for reference purposes. It is shown that both GPU accelerated codes are able to solve large-scale topology optimisation problems with 65.5 million elements in approximately 2 h using a single GPU, while the reference implementation takes approximately 3 h and 10 min using 48 CPU cores. Furthermore, it is shown that it is possible to solve nonlinear topology optimisation problems using GPU acceleration, demonstrated by a nonlinear end-compliance optimisation with finite strains and a Neo-Hookean material model discretised by 1 million elements.
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