An Efficient GPU Solver for Maximizing Fundamental Eigenfrequency in Large-Scale Three-Dimensional Topology Optimization

A major bottleneck in large-scale eigenfrequency topology optimization is the repeated solution of the generalized eigenvalue problem. This work presents an efficient graphics processing unit (GPU) solver for three-dimensional (3D) topology optimization that maximizes the fundamental eigenfrequency. The Successive Iteration of Analysis and Design (SIAD) framework is employed to avoid solving a full eigenproblem at every iteration. The sequential approximation of the eigenpairs is solved by the GPU-accelerated multigrid-preconditioned conjugate gradient (MGPCG) method to efficiently improve the eigenvectors along with the topological evolution. The cluster-mean approach is adopted to address the non-differentiability issue caused by repeated eigenfrequencies. The corresponding sensitivity analysis method is provided. The parallelized gradient-based Zhang-Paulino-Ramos Jr. (ZPR) algorithm is employed to update the design variables. The effectiveness of the proposed solver is demonstrated through two large-scale numerical examples. The first example demonstrates the accuracy, efficiency, and scalability of the proposed solver by solving a 3D optimization problem of 50.33 million elements being solved in approximately 15.2 h over 300 iterations on a single NVIDIA Tesla V100 GPU. The second example validates the effectiveness of the proposed solver in the presence of repeated eigenfrequencies. Our findings also highlight that higher-resolution models produce distinct optimized structures with higher fundamental frequencies, underscoring the necessity of large-scale topology optimization.