Parallel computing on GPU with CuPy and vectorized SpMV for large-scale topology optimization

This paper presents a vectorized programming approach to Sparse Matrix-Vector multiplication (SpMV) based on a novel decomposition of the finite element matrix for GPU. The approach is employed for large-scale topology optimization. Unlike the existing matrix-free SpMV strategies (e.g., EbE, NbN, and DbD), our framework transforms SpMV into vector operations. This improvement enhances accessibility for non-expert users in Python environment (e.g., CuPy) while maintaining computational efficiency. Numerical examples of topology optimization on GPU, such as heat transfer and structural design, in both 2D and 3D with up to 63 million elements illustrate the effectiveness and efficiency of the proposed approach. Codes could be seen at https://github.com/HouJiangnan81/CuPy-for-TO.