High-quality anisotropic boundary-layer meshes are crucial for numerical simulations, yet their automated generation for complex geometries remains a significant challenge. This paper presents AnisoMeshNet, a novel deep learning framework that automates the generation of hybrid semi-structured meshes. At its core, AnisoMeshNet learns a smooth guiding vector field for anisotropic meshing by adopting a boundary-informed neural network (BINN) philosophy. Instead of learning the field from scratch, our method first constructs a robust geometric prior-a boundary condition extension (BCE) field-using a K-nearest neighbors (KNN) algorithm. The neural network is then trained to learn a smooth correction field that refines this prior, ensuring strict adherence to BCs through a weighted cosine similarity loss. The resulting composite vector field smoothly guides an advancing layer method (ALM) to generate orthogonality-favored, quad-dominant boundary-layer meshes for complex 2D geometries, demonstrating a robust and automated alternative to traditional methods.

Sizing fields stored on triangular background grids control the quality and cost of unstructured mesh generation. Piecewise-linear interpolation on raw Stereolithography (STL) background grids can introduce high-density banding artifacts near discrete geometric transitions, leading to unnecessary local over-refinement. We propose GCN-HOSF, a two-stage framework in which a Graph Convolutional Network (GCN) approximates an expensive rule-based numerical detector, and a High-Order Sizing Field (HOSF) corrects the predicted banding conditions without changing the original STL connectivity. This design avoids global refinement and topological subdivision while preserving a lightweight background-grid representation. Across 179 paired validation cases, GCN-HOSF reduced the mean number of generated surface-mesh elements by 62.01% relative to the initial STL-derived sizing field while leaving the background-grid cell count unchanged. In the four computational-performance cases, it reduced the stage-summed workflow time by 3.57%–97.06% compared with LIU and by 3.11%–72.50% compared with GCN-SF, although extreme mesh-quality degradation may still occur for pathological geometries.

Triangle meshes frequently exhibit defects such as self-intersections and low-quality elements. Existing intersection resolution methods either lack robustness due to floating-point inaccuracies or incur high computational costs by processing meshes globally. We propose a robust and efficient method for repairing meshes with intersecting triangles that combines localized processing with rational number computations. The core challenge we address is converting exact intersection repair results to stable floating-point representation without reintroducing intersections. Our solution embeds intersecting regions into tetrahedral meshes for constrained optimization, naturally preventing surface intersections during the conversion process. Our approach begins with a preprocessing step that refines the mesh and localizes intersection issues by separating intersecting and intersection-free regions. For each intersecting region, we ensure the robustness of intersection calculations by using rational numbers. Subsequently, the intersection repair results are stably converted from rational to floating-point representation using a constrained boundary tetrahedral mesh optimization method. The repaired local meshes are then stitched back into the intersection-free mesh, followed by a remeshing step to enhance overall mesh quality. Experimental results on complex models demonstrate that our method significantly reduces computational overhead while producing high-quality, intersection-free meshes suitable for downstream applications.

Hybrid meshes are widely adopted in industry due to their generation efficiency and superior capability to balance computational accuracy and cost. However, initially generated hybrid meshes often compromise element regularity to guarantee topological validity and boundary fitting, making mesh smoothing an indispensable post-processing procedure to rectify local distortions. Since heterogeneous elements in hybrid meshes involve divergent optimization objectives, most existing smoothing methods remain restricted to isomorphic meshes such as all-triangular or all-quadrilateral meshes. Furthermore, the majority of current approaches struggle to effectively eliminate negative-area elements, which severely limits their practical applicability in complex scenarios.To address these challenges, we proposes EAGLE, an Element-Aware Graph Learning Engine, for unsupervised hybrid mesh smoothing. The framework integrates three key components: (1) a lightweight graph neural network to extract features of heterogeneous mesh elements, (2) a geometric constraint module to maintain structural consistency during the smoothing process, and (3) a plug-and-play loss function to support end-to-end unsupervised optimization. Extensive experiments conducted on surface meshes with several geometries verify that the proposed method achieves superior performance over existing baselines across various evaluation metrics. Notably, the EAGLE shows impressive robustness through its zero-shot generalization when applied to isomorphic meshes.

Adaptive mesh refinement (AMR) is widely used in computational electromagnetics, but its efficiency is strongly affected by the initial discretization. We propose Simulation-Informed Mesh Seeding (SIMS), a simulation-informed initialization strategy for adaptive discretization in electromagnetic simulations. Using pre-simulation features including geometry, materials, and boundary conditions, SIMS predicts physics-aware, sheet-wise mesh resolution targets and converts them into executable mesh seeding through an engineering-driven post-processing step. Implemented as a lightweight module at the initialization stage of standard FEM workflows, SIMS improves the starting discretization for the subsequent adaptive simulation process. For an eight-pole coaxial cavity filter, SIMS reduces AMR passes from 16 to 5 and yields a 4.34 & times; speedup with unchanged S-parameter characteristics. These results demonstrate the value of simulation-informed initial discretization for accelerating adaptive EM simulation.

Vortices play a central role in transport, mixing, aerodynamic loading, and energy transfer in unsteady flows. Accurate vortex identification is crucial for understanding these phenomena. However, existing vortex identification methods remain limited in their ability to objectively identify and accurately localize compact vortex cores. Their performance can also deteriorate in the presence of noise and perturbations encountered in practical flow fields. We present FGPA-VT, a transformer-based vortex identification framework that combines feature-guided adaptive pathline seeding with physics-augmented pathline representations in 2D unsteady flows. Feature-guided pathline seeding concentrates trajectories in dynamically active regions to capture compact vortical structures, while physics-augmented representations incorporate complementary descriptors to enhance the discrimination of vortical motion. Extensive experiments show that the proposed framework improves precision by 11.89 percentage points over the baseline, while maintaining high detection accuracy across diverse out-of-distribution and noisy conditions and offering efficient training and inference. More broadly, this work demonstrates the potential of integrating adaptive seeding with physics-augmented learning as a general framework for robust and objective flow-structure identification.

This paper proposes a hybrid unstructured mesh generation method for turbomachinery simulations, aiming to overcome the limitations of conventional approaches in geometric adaptability, size control, viscous boundary-layer resolution, and automation. A hybrid surface representation framework is first constructed, in which the discrete surface representation serves as the background mesh for size control, while the continuous surface representation defines the geometric boundary for mesh generation. A unified topological data structure is then established to manage the discrete representation, continuous representation, and mesh model in a consistent manner. To handle the complex geometric configurations of turbomachinery, feature recognition and local mesh refinement techniques are developed, and the size function is defined on the optimized background mesh. An efficient size-function smoothing strategy is further proposed to ensure a smooth transition between regions with different mesh densities. The proposed method is validated through numerical simulations of several representative turbomachinery cases, and the predicted results are compared with experimental data as well as with those obtained using the commercial software packages ICEM-CFD and Pointwise. The results demonstrate that the proposed method achieves comparable or superior mesh quality while significantly improving mesh generation efficiency, and the simulation results show good agreement with experimental data.

Automatic recognition of through-hole features is a critical step in achieving seamless CAD/CAE integration and accelerating engineering analysis pre-processing, such as mesh generation and feature suppression. However, traditional rule-based or hint-based methods struggle to handle complex topological structures. Meanwhile, existing deep learning methods are often limited by the lack of diversity in training data, large model sizes, and a lack of specific optimization for the geometric characteristics of through holes, resulting in limited generalization ability. To address these issues, this paper proposes LG-HoleNet, a lightweight Graph Neural Network framework based on differential geometric attributes, designed for through-hole feature recognition in complex B-Rep models. This method converts the B-Rep model into an attributed graph structure. It innovatively introduces differential geometric quantities, such as Gaussian curvature and mean curvature, as core features. By combining these with engineering semantic attributes like area ratio and loop number, the method constructs a node feature representation that is invariant to rigid transformations. Furthermore, to address the lack of diversity in existing datasets, we constructed and released a large-scale and diverse dataset containing 9273 CAD models. This dataset covers complex base shapes such as spheres and swept bodies, as well as non-standard through-hole features like elliptical cylinders. Experimental results show that LG-HoleNet achieves a recognition accuracy of 99.88% and a recall of 99.89% with only 0.03 M parameters. Compared with existing advanced models such as Hierarchical CADNet and AAGNet, our method demonstrates stronger generalization ability in cross-dataset testing. Compared with the commercial software SolidWorks, it offers significant advantages in both speed and accuracy when handling complex and irregular through holes. The source code and dataset will be released upon acceptance.

We introduce a robust algorithm for generating tetrahedral meshes that strictly conform to the geometry and connectivity of valid non-self-intersecting piecewise-linear complexes (PLCs). A key challenge in this task is the control of Steiner point placement. While optimizing Steiner point placement is NP-hard, eliminating boundary Steiner points remains practically important for preserving boundary topology and interface connectivity. To address this challenge, we introduce the concept of flip-hard configurations (FHCs), which characterize local situations where constraint recovery cannot proceed using flip operations alone. Based on this observation, we enhance the classical boundary recovery pipeline with FHC-guided interior Steiner insertion, robust boundary Steiner relocation, and local mesh optimization under floating-point arithmetic. These mechanisms reduce the reliance on boundary Steiner points and mitigate numerical failures caused by finite-precision rounding. We evaluate the proposed algorithm on all 5,468 valid models from the Thingi10K dataset. In these experiments, the implementation successfully produced constrained tetrahedralizations for all models, and all generated meshes contain Steiner-point-free boundaries while preserving the input PLC topology.

We propose a new advancing layer method for surface boundary layer mesh generation, implemented based on an improved Advancing-Front/Local-Reconnection (AFLR) framework. To mitigate issues caused by mapping distortion in the parametric domain, the entire algorithm is carried out directly in physical space. The improvements include a hybrid strategy that combines indirect and direct methods to compute new point locations, and a procedure to insert new points on a conformal initial mesh in physical space. A metric-based energy criterion under an anisotropic metric tensor field is introduced to guide the local reconnection operation. In addition, we present a detailed framework for constructing anisotropic metric fields on surfaces to support high-quality mesh generation. We compare our method against the original AFLR and commercial software such as Pointwise, demonstrating superior mesh quality. Finally, we apply our algorithm to realistic engineering models and perform numerical simulations to verify its effectiveness.

ABSTRACT Turbomachinery features complex geometry and flow‐field characteristics, which impose strict requirements on mesh generation. This study proposes a periodic boundary‐layer mesh generation scheme for turbomachinery. Semi‐structured prismatic mesh is widely used to resolve boundary‐layer flows in viscous flow simulations. However, ensuring the periodicity of the boundary‐layer mesh during the mesh generation process remains a challenging and underexplored problem. To address this issue, a feature recognition method based on periodic affine transformation is first developed. Using the resulting periodic transformation function, a bottom‐up periodic boundary‐layer mesh generation framework is developed, including periodic surface meshing, calculation of periodic marching directions and distances, invalid element removal, transition element correction, and compatible far‐field tetrahedral mesh generation. Validations on typical turbomachinery benchmarks, including NASA Stage 35, NASA C3X, and Rolls‐Royce ACE, show that the simulation results agree well with experimental data and results obtained using commercial software. These results verify the dependability of the developed approach and its practical value in turbomachinery analysis.

This study presents a scalable approach for generating large-scale unstructured meshes efficiently with a multilevel parallelism to overcome bottleneck problems in applications. A multi-threaded domain decomposition method is developed for generating numerous watertight subdomains on distributed systems. A high-performance Delaunay mesh kernel for mesh generation and optimization is integrated with an MPI-based framework designed for dynamic task management and load balancing. The above components are integrated to generate a large-scale mesh with billions of elements. To testify to the effectiveness of the proposed method, experiments with complicated aerospace models were performed on parallel machines with multiple cores. The running time of domain decomposition and mesh generation was reduced significantly, and more than one hundred billion elements were successfully generated in less than two hours with thousands of cores on supercomputers. The hybrid parallelization demonstrates a pleasant efficiency and scalability of the hybrid parallelization. The results also illustrate the ability to generate billions of high-quality elements in a more balanced load, and the numerical simulation of large-scale mesh represents a prominent future for parallel applications in industry.

The sizing field defined on a triangular background grid is pivotal for controlling the quality and efficiency of unstructured mesh generation. However, creating an optimal background grid that is geometrically conforming, computationally lightweight, and free of artifacts such as banding is a significant challenge. This paper introduces a novel, adaptive background grid simplification (ABGS) framework based on a Graph Convolutional Network (GCN). We reformulate the grid simplification task as an edge classification problem and train a GCN model to efficiently predict optimal edge collapse candidates. The model is guided by a custom loss function that holistically considers both geometric fidelity and sizing field accuracy. This data-driven approach replaces a costly procedural evaluation, accelerating the simplification process. Experimental results demonstrate the effectiveness of our framework across diverse and complex engineering models. Compared to the initial dense grids, our simplified background grids achieve an element reduction of 64.47%–97.15%, leading to a 23.83%–77.84% decrease in sizing field query times.

The sizing function is essential for generating high-quality meshes efficiently. To address the issues of abrupt size transitions and the high computational costs present in existing sizing function algorithms, we propose the first LP-based global gradient-limited sizing function with adaptive error control for unstructured mesh generation. Building upon an established convex optimization model, the method employs a piecewise linear approximation of the nonlinear gradient constraints, reducing model complexity. A rigorous error analysis quantifies the approximation accuracy and guides the design of an adaptive refinement strategy that balances constraint accuracy with computational efficiency. Numerical experiments demonstrate that the proposed algorithm consistently achieves smooth and well-controlled size transitions, exhibits superior time efficiency, and generates high-quality meshes, outperforming nonlinear programming, GradH-correction, and H-correction approaches. These results confirm the effectiveness and robustness of the LP-based framework and highlight its suitability for large-scale engineering applications.

Automated recognition and simplification of fillet features in CAD models is critical for CAE analysis, yet it remains an open challenge. Traditional rule-based methods lack robustness, while existing deep learning models suffer from poor generalization and low accuracy on complex fillets due to their generic design and inadequate training data. To address these issues, this paper proposes an end-to-end, data-driven framework specifically for fillet features. We first construct and release a large-scale, diverse benchmark dataset for fillet recognition to address the inadequacy of existing data. Based on it, we propose FilletRec, a lightweight graph neural network. The core innovation of this network is its use of pose-invariant intrinsic geometric features, such as curvature, enabling it to learn more fundamental geometric patterns and thereby achieve high-precision recognition of complex geometric topologies. Experiments show that FilletRec surpasses state-of-the-art methods in both accuracy and generalization, while using only 0.2%-5.4% of the parameters of baseline models, demonstrating high model efficiency. Finally, the framework completes the automated workflow from recognition to simplification by integrating an effective geometric simplification algorithm.

We propose a fast intersection-free remeshing of triangular meshes that robustly and efficiently generates high-quality non-intersecting meshes. Conducting intersection checks on all local operations during remeshing to prevent intersections represents the principal efficiency bottleneck. Our method is based on a key observation: intersections primarily occur in structurally complex regions. Accordingly, we develop an adaptive method to identify these key regions and perform intersection checks only for local operations within these regions during remeshing, significantly improving the algorithmic efficiency. Our method is an order of magnitude faster than traditional approaches that perform intersection checks on all local operations. Furthermore, we introduce a flip-aware extension mechanism that effectively avoids triangle flipping by constraining the optimization space of local operations, thereby avoiding the formation of irregular sharp edges. We also employ an adaptive iterative size field to eliminate banding phenomenon and propose a quasi-geometric size field adjustment method to quickly achieve smooth size transitions, thereby improving mesh quality. Compared to state-of-the-art methods, our method consistently and quickly generates higher quality non-intersecting meshes. In addition, we have validated the robustness and efficiency of our method, using all 5,469 non-intersecting valid models from the Thingi10K dataset.

Prismatic/tetrahedral hybrid meshes are widely used in CFD simulations involving RANS calculations. However, premature termination during Advancing Layer Method (ALM) generation often necessitates using highly distorted pyramidal elements, compromising overall mesh quality and hindering subsequent tetrahedral mesh generation. To address this, we propose a robust full-layer prismatic mesh generation scheme based on recent advances in piecewise linear bijective mapping. Our scheme iteratively deforms an initial mesh towards an orthogonal target, minimizing the bijective mapping energy via a robust, area/volume-preserving As-Rigid-As-Possible mapping method. Extending to complex geometry in 3D, we further introduce an interpolation-based prismatic mesh generation method, enabling the generation of computationally suitable meshes for complex geometries.

This paper presents a new algorithm, Weighted Squared Volume Minimization (WSVM), for generating high-quality tetrahedral meshes from closed triangle meshes. Drawing inspiration from the principle of minimal surfaces that minimize squared surface area, WSVM employs a new energy function integrating weighted squared volumes for tetrahedral elements. When minimized with constant weights, this energy promotes uniform volumes among the tetrahedra. Adjusting the weights to account for local geometry further achieves uniform dihedral angles within the mesh. The algorithm begins with an initial tetrahedral mesh generated via Delaunay tetrahedralization and proceeds by sequentially minimizing volume-oriented and then dihedral angle-oriented energies. At each stage, it alternates between optimizing vertex positions and refining mesh connectivity through the iterative process. The algorithm operates fully automatically and requires no parameter tuning. Evaluations on a variety of 3D models demonstrate that WSVM consistently produces tetrahedral meshes of higher quality, with fewer slivers and enhanced uniformity compared to existing methods.

This paper presents a novel method for generating higher-order meshes for CAD surfaces by leveraging minimal surface theory to improve element shapes. We explore the concept of higher-order mesh distortion through deformation gradients and introduce an energy function designed to minimize the surface area of these meshes, providing a theoretical justification for its effectiveness in untangling. The process of mesh generation starts with segmenting CAD surfaces into linear elements, followed by the insertion of higher-order nodes within these elements. These nodes are then projected onto the CAD surface to form the initial higher-order elements. By optimizing energy functions related to minimal surfaces and the projection distances, we achieve high-quality, geometrically accurate higher-order surface meshes. Our method has been validated on complex geometries, showcasing its potential in creating effective higher-order meshes for industrial CAD models.

This paper introduces the MeshAC package, which generates three-dimensional adaptive meshes tailored for the efficient and robust implementation of multiscale coupling methods. While Delaunay triangulation is commonly used for mesh generation across the entire computational domain, generating meshes for multiscale coupling methods is more challenging due to intrinsic discrete structures such as defects, and the need to match these structures to the continuum domain at the interface. The MeshAC package tackles these challenges by generating meshes that align with fine-level discrete structures. It also incorporates localized modification and reconstruction operations specifically designed for interfaces. These enhancements improve both the implementation efficiency and the quality of the coupled mesh. Furthermore, MeshAC introduces a novel adaptive feature that utilizes gradient-based a posteriori error estimation, which automatically adjusts the atomistic region and continuum mesh, ensuring an optimal balance between accuracy and efficiency. This package can be directly applied to the geometry optimization problems of a/c coupling in static mechanics, with potential extensions to many other scenarios. Its capabilities are demonstrated for complex material defects, including straight edge dislocation in BCC W and double voids in FCC Cu. These results suggest that MeshAC can be a valuable tool for researchers and practitioners in computational mechanics.