Efficient hybrid topology optimization using GPU and homogenization based multigrid approach

TL;DR

This paper introduces a hybrid topology optimization method leveraging GPU multithreading, homogenization, and multigrid techniques to significantly accelerate computations and handle large-scale 3D structures efficiently.

Contribution

The paper presents a novel hybrid algorithm combining GPU parallelization, homogenization, and multigrid methods for efficient large-scale topology optimization.

Findings

Achieves an order of magnitude faster computation than existing methods.

Enables solving structures with hundreds of millions of elements on standard hardware.

Demonstrates excellent scalability and performance across various examples.

Abstract

We propose 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 versitile 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. 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 and multimaterial.Results obtained indicate the excellent performance and scalability of the proposed approach.