GPU-accelerated Mesh Adaptation for Structural Analysis

Today, engineering processes rely on structural analysis using computer-aided design (CAD). This typically involves discretizing the geometry to apply the finite element method (FEM) solving the partial differential equations (PDEs) of elasticity. The accuracy of the FEM depends on the resolution of the dis-cretization. However, a high resolution typically leads to slower runtime per-formance, because each element adds to the computational cost. Using a CAD geometry and specified load cases, computing the elasticity PDE requires multiple steps, each of which can become a bottleneck if executed on the CPU. For fast and automated computation, we suggest a GPU-accelerated adaptive simulation pipeline for structural analysis. Due to their capabilities in representing complex geometries and facilitating robust local adaptivity, unstructured tetra-hedral meshes are well-suited for mesh adaptation. Since previous work pre-sented fast simulation (Weber et al. [1]), massively parallel optimization and remeshing of unstructured tetrahedral meshes (Ströter et al. [2], [3]), and data structures for massively parallel matrix assembly algorithms (Mueller-Roemer [4]), this work focuses on a-posteriori adaptive mesh refinement of discretized models. This closes a remaining gap towards a fully automated GPU-accelerated adaptive structural analysis for CAD models. Our method achieves a speedup of 2× to 10× compared to the open-source mesh adaptor MMG [5] for tetrahedral meshes. By shifting the bottleneck away from mesh adaptation, the overall computation time of certain structural analysis tasks can be reduced by half. It utilizes the GPU for error estimation and sizing field processing. As a result, the proportion of these steps in the overall runtime is negligible. With heuristic adaptation and little data transfer between CPU and GPU, we achieved fast mesh adaptation to a sizing field. In combination with the fast structural analysis by Weber et al. [1], our pipeline quickly determines struc-tural analysis results close to the so-called mesh-independent solution without laborious manual intervention. References [1] D. Weber, T. Grasser, J. Mueller-Roemer and A. Stork, "Rapid Interactive Structural Analysis," 2020. [2] D. Ströter, J. S. Mueller-Roemer, D. Weber and D. W. Fellner, "Fast harmonic tetrahedral mesh optimization," The Visual Computer, vol. 38, p. 3419'“3433, June 2022. [3] D. Stroeter, A. Stork and D. Fellner, "Massively Parallel Adaptive Collapsing of Edges for Unstructured Tetrahedral Meshes," 2023. [4] J. S. Mueller-Roemer, "GPU Data Structures and Code Generation for Modeling, Simulation, and Visualization," TUprints, 2020. [5] C. Dobrzynski, "MMG3D: User Guide. [Technical Report] RT-0422, INRIA (hal-00681813)," 2012.