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Efficient hybrid topology optimization using GPU and homogenization-based multigrid approach

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Abstract

We propose an efficient implementation of a new hybrid topology optimization algorithm based on multigrid approach that combines the parallelization strategy of CPU using OpenMP and heavily multithreading capabilities of modern Graphics Processing Units (GPU). In addition to that, significant computational efficiency in memory requirement has been achieved using homogenization strategy. The algorithm has been integrated with versatile computing platform of MATLAB for ease of use and customization. The bottlenecking repetitive solution of the state equation has been solved using an optimized geometric multigrid approach along with CUDA parallelization enabling an order of magnitude faster in computational time than current state of the art implementations. The main novelty lies in the efficient implementation wherein on the fly computation of auxiliary matrices in the multigrid scheme and modification in interpolation schemes using homogenization strategy removes memory limitation of GPUs. Memory hierarchy of GPU has also been exploited for further optimized implementations. All these enable solution of structures involving hundred millions of three dimensional brick elements to be accomplished in a standard desktop computer or a workstation. Performance of the proposed algorithm is illustrated using several examples including design dependent loads. Results obtained indicate the excellent performance and scalability of the proposed approach.

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Notes

  1. A is computed on the fly and hence only Q is actually stored.

  2. For numerical stability, we consider a very small stiffness of \(1/10^6\).

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Acknowledgements

APP acknowledge the financial support received from IIT Rookee in form of MHRD, Govt. Of India, fellowship. SC acknowledges the financial support received from Science and Engineering Research Board via Grant no. SRG/2021/000467.

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Authors and Affiliations

  1. Centre for Transportation Systems (CTRANS), Indian Institute of Technology Roorkee, Roorkee, UK, 247667, India

    Arya Prakash Padhi

  2. Department of Applied Mechanics, Indian Institute of Technology Delhi, Hauz Khas, 110016, India

    Souvik Chakraborty

  3. Yardi School of Artificial Intelligence (ScAI), Indian Institute of Technology Delhi, Hauz Khas, 110016, India

    Souvik Chakraborty

  4. Department of Civil Engineering, Indian Institute of Technology Roorkee, Roorkee, UK, 247667, India

    Anupam Chakrabarti & Rajib Chowdhury

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  1. Arya Prakash Padhi
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  2. Souvik Chakraborty
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  3. Anupam Chakrabarti
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  4. Rajib Chowdhury
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Correspondence to Souvik Chakraborty or Rajib Chowdhury.

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Replication of results

Matlab codes as well as the dependent CUDA C routines for the examples shown in this work are available at https://github.com/csccm-iitd/GPU-TO.

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Appendix 1: Three different system configurations used for testing

Appendix 1: Three different system configurations used for testing

See Table 11.

Table 11 Specification of systems used for testing
Full size table

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Padhi, A.P., Chakraborty, S., Chakrabarti, A. et al. Efficient hybrid topology optimization using GPU and homogenization-based multigrid approach. Engineering with Computers 39, 3593–3615 (2023). https://doi.org/10.1007/s00366-022-01771-x

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