AI 中文总结
研究针对三维压力容器分析中有限元方法的局限，提出FEVessel，通过编码点云、预训练算子及热启动求解器，实现跨材料等通用分析，降低误差，加速求解，能在不同网格转换且无需标签，消除手动网格修复。
AI 中文摘要
化学、核能和新能源行业中的压力容器分析需要在多种材料、几何形状和载荷下解决相同的弹性问题，网格质量和重复求解影响精度和成本。有限元方法（FEM）无法分摊重复成本且在退化网格上失效，而替代它的神经算子仍需FEM生成的标记数据。本文提出FEVessel，将预训练有限元方法（PFEM）应用于三维压力容器，并验证了针对上述两个局限性的四种能力。FEVessel将每个容器编码为具有坐标、材料和载荷通道的点云，在总势能上预训练Transolver算子而非FEM标签，并利用其预测热启动迭代求解器。一个模型在材料、几何形状和边界条件上具有通用性，相对位移误差为1.35%，应变误差为2.07%，比有监督的傅里叶神经算子低约4.7倍。其热启动将代数多重网格迭代从195次减少到18次，在10^-3工程公差下实现了9.2倍的端到端时钟加速。该模型无需重新训练即可在不同网格分辨率间转换，在仅30%训练点密度下误差保持在3%左右。在FEM失败的倒置和银纹网格上，误差仍低于3.66%。据我们所知，这是首次对具有退化网格的工业相关三维压力容器进行网格无关解的系统研究。由于训练无需标签，FEVessel在FEM无法提供的情况下也能工作，从分析流程中消除了手动网格修复。
英文摘要
Pressure vessel analysis in the chemical, nuclear, and new-energy industries requires solving the same elasticity problem across many materials, geometries, and loads, where mesh quality and repeated solving govern both accuracy and cost. The finite element method (FEM) cannot amortise this repeated cost and fails on degenerate meshes, while the neural operators meant to replace it still need labelled data that FEM must generate. This paper proposes FEVessel, an adaptation of the Pretrained Finite Element Method (PFEM) to three-dimensional (3D) pressure vessels, and validates four capabilities across the two limitations above. FEVessel i) encodes each vessel as a point cloud with coordinate, material, and load channels, ii) pretrains a Transolver operator on the total potential energy instead of FEM labels, and iii) warm-starts iterative solvers with its prediction. A single model generalises across material, geometry, and boundary conditions at a $1.35\%$ relative displacement error, and its $2.07\%$ strain error is about $4.7$ times lower than that of a supervised Fourier neural operator ($9.72\%$), whose structured grid cannot preserve the through-thickness strain. Its warm start cuts algebraic multigrid iterations from $195$ to $18$, a $9.2\times$ end-to-end wall-clock speedup at the $10^{-3}$ engineering tolerance. The model transfers across mesh resolutions without retraining, holding about $3\%$ error at only $30\%$ of the training point density. On inverted and sliver meshes where FEM fails, the error remains below $3.66\%$. To our knowledge, this is the first systematic study of mesh-independent solution on industrially relevant 3D pressure vessels with degenerate meshes. Because training needs no labels, FEVessel works exactly where FEM cannot supply any, removing manual mesh repair from the analysis pipeline.
