GPU-accelerated parallel strategies for multiscale isogeometric topology optimization

In multiscale isogeometric topology optimization (ITO), the highly coupled cross-scale sensitivity analysis and the wide support of NURBS basis functions constitute the dominant computational bottleneck. To address these computational bottlenecks, this paper proposes a Decoupled GPU-accelerated Multiscale ITO framework that integrates sensitivity reformulation with GPU parallel computing. First, a decoupled sensitivity analysis is introduced to transform the conventional coupled evaluation into independent macro and microscale tensor operations, fundamentally eliminating serial dependencies. Second, GPU acceleration strategies are developed for the homogenization and sensitivity analysis stages. Persistent geometry caching reduces repeated NURBS-related computations, while warp-level thread scheduling and hierarchical memory organization improve parallel execution and memory-access efficiency; asynchronous multi-stream execution further exploits the independence of the macroscale and microscale computations. Three benchmark examples are used to assess numerical consistency, computational efficiency, and scalability. For the largest Michell-type case, DG-MITO achieves a 2162.35 × sensitivity-analysis speedup over Decoupled-CPU, while the combined effect of sensitivity decoupling and GPU acceleration yields a 39,576.22 × speedup over Baseline-CPU under the specified hardware and software configurations. Moreover, the achieved speedup increases with problem size, demonstrating favorable scalability for large-scale multiscale ITO.