SIAM IMR26: Program

A PDE-Based Method for Feature-Aligned Quadrangulation of 3D Surfaces

Eugen Salzmann, MAGMA Gießereitechnologie GmbH
Jannick Wolters, MAGMA Gießereitechnologie GmbH
Yacine Tayeb, MAGMA Gießereitechnologie GmbH

Keywords: quad meshing, optimization, cross-field

Abstract

We revisit the wave-based quadrangulation method presented by Zhang et al. in 2010 that generates feature-aligned quadrilateral surface meshes suitable as a foundation for hexahedral volumetric meshing. The method’s pipeline begins with the computation of a smooth cross-field that encodes geometric features and curvature information by optimizing for field smoothness while enforcing alignment with the principal curvature directions. Given this cross-field, a scalar wave equation is then solved on the input triangulation. The problem is formulated as a global minimization that fits the gradient of the unknown scalar field to the optimized cross-field, while softly enforcing alignment with precomputed feature lines. We solve this optimization problem using Adaptive Momentum Estimation (ADAM) rather than a Newton-based method, and introduce a novel initialization strategy that improves computational efficiency. From the resulting solution of the wave equation, a coherent patch layout is extracted using a Quasi-Dual Morse–Smale Complex. Each extracted patch is then globally parameterized, taking into account the relative orientation between neighboring patches by solving a global linear system that enforces consistency across patch boundaries. Finally, the parametrization is utilized to produce a feature-aligned quadrilateral surface mesh. The entire pipeline is fully automatic, thanks to a scaling strategy that eliminates the need for the model-specific size field input. Extensive evaluation across diverse geometries of varying complexity demonstrates the robustness of the approach. Quantitative analysis reports runtime performance and mesh quality metrics, confirming the method’s effectiveness in generating consistent quadrangulations suitable for downstream applications including hexahedral meshing.

Towards Higher-Order Block-Structured Meshes on Planar Domains

Pablo BARRERA SÁNCHEZ, Universidad Nacional Autónoma de México
Faisal AMLANI, École Normale Supérieure Paris-Saclay
Ivan MENDEZ CRUZ, École Normale Supérieure Paris-Saclay

Keywords: Higher-order grid generation, block-structured meshing

Abstract

We extend some methods for structured grid generation to higher-order meshing and block-structured meshing with prescribed nodes on polygonal regions.

Intrinsic Surface Meshing Using Geodesic Distances

Jean-François Remacle, Catholic University of Louvain
Christophe Geuzaine, University of Liège
Tim Gabriel, University of Liège

Keywords: intrinsic meshing, geodesic distance, high-order method, mesh coarsening

Abstract

We present an intrinsic meshing process for accurately approximating complex surfaces. Starting from a high-resolution triangulation, intrinsic mesh operations based on geodesic distances adapt the mesh without geometric approximation. Intrinsic elements can then be approximated by high-order polynomial elements suitable for numerical simulations.

Towards Dynamic Adaptation of an Isoparametric Split Boundary Layer

Kaloyan Kirilov, King's College London
David Moxey, King's College London
Ted Stokes, King's College London

Keywords: AMR, dynamic, boundary layer, isoparametric, Nektar++, NekMesh

Abstract

The isoparametric splitting of a thick macro O-type boundary layer mesh to a stack of layers with geometrical progression has been widely used for high-order wall resolved simulations. In this work we propose a mitigation of some of the drawbacks of splitting the O-type macro layer from uniform settings over the whole body to a variable splitting settings for every macro stack. This improves the consistency of the first layer during the mesh generation in regions like proximities and trailing edges. The second focus is to apply the process to a-posteriori AMR, integrated within the spectral/hp framework Nektar++. As a first step, a solution driven a-posteriori isoparametric splitting is introduced by integrating the NekMesh meshing module within the solver data-structure. We demonstrate the proof-of-concept of the AMR process with two and three dimensional academic testcases, showing that the split quad and prism child layers are adapted to a solution driven criteria, the curvature and validity of the high-order mesh are preserved and the solution accuracy is improved. Finally, we discuss the current efforts in proposing a local solution transfer between the initial split and adapted layer suitable for dynamic AMR, using the unique knowledge about the location of the child elements within the O-type layer before and after the adaptation.

The Beauty of Anisotropic Mesh Refinement: Omnitrees for Efficient Dyadic Discretizations

Masado Ishii, RIKEN Center for Computational Science
Jens Domke, RIKEN Center for Computational Science
Theresa Pollinger, RIKEN Center for Computational Science

Keywords: omnitree, octree, structured data, anisotropy

Abstract

Structured adaptive mesh refinement (AMR), commonly implemented via quadtrees and octrees, underpins a wide range of applications including databases, computer graphics, physics simulations, and machine learning. However, octrees enforce isotropic refinement in regions of interest, which can be especially inefficient for problems that are intrinsically anisotropic–much resolution is spent where little information is gained. We present omnitrees as an anisotropic generalization of octrees and related data structures. Omnitrees allow to refine only the locally most important dimensions, providing tree structures that are less deep than bintrees and less wide than octrees. As a result, the convergence of the AMR schemes can be increased by up to a factor of the dimensionality d for very anisotropic problems, quickly offsetting their modest increase in storage overhead. We validate this finding on the problem of binary shape representation across 4,166 three-dimensional objects: Omnitrees increase the mean convergence rate by 1.5x, require less storage to achieve equivalent error bounds, and maximize the information density of the stored function faster than octrees. These advantages are projected to be even stronger for higher-dimensional problems. We provide a first validation by introducing a time-dependent rotation to create four-dimensional representations, and discuss the properties of their 4-d octree and omnitree approximations. Overall, omnitree discretizations can make existing AMR approaches more efficient, and open up new possibilities for high-dimensional applications.

Surrogate point generation and edge curving algorithm for curvilinear mesh adaptation

Shengqi Zhang, Ningbo Institute of Digital Twin, Eastern Institute of Technology.
Ruili Zhang, Ningbo Institute of Digital Twin, Eastern Institute of Technology.

Keywords: Curvilinear mesh generation, Mesh adaptation, Riemannian metric field, Geodesic, AI-driven.

Abstract

Building directly on our prior framework, this paper introduces novel AI(Artificial Intelligence)‑driven algorithms for the efficient computation of geodesics on Riemannian manifolds, with applications to surrogate point generation and straight‑sided edge curving in curvilinear mesh generation and adaptation. We present three core contributions. First, Algorithm 1 establishes the theoretical foundation by detailing the Taylor expansion of the Riemannian metric in both the original and principal axis coordinate systems. Leveraging this local approximation, Algorithm 2 enables rapid generation of geodesic paths from a given initial point and direction.It employs a neural network trained to map local curvature information and the initial directional angle directly to the endpoint of a unit geodesic segment in a principal coordinate frame, thereby circumventing the costly numerical integration of the geodesic equations. Algorithm 3 addresses the computation of the geodesic between two fixed points. By constructing a local principal frame at the midpoint of a straight‑sided edge and utilizing a second neural network, it approximates the midpoint of the geodesic parabola connecting the two given points, which significantly accelerates the path‑finding process. Collectively, these methods leverage fast coordinate transformations and neural network approximations to replace traditional iterative or differential‑equation‑based solvers, offering a promising framework for high‑speed geodesic computation.

LG-HoleNet: A Lightweight Graph Neural Network for Through-Hole Recognition via Differential Geometric Attributes

Jiali Gao, Zhejiang University
Xiaowen Liu, Zhejiang University
Hengyu Zhou, Zhejiang University
Hongfei Ye, Zhejiang University
Jianjun Chen, Zhejiang University
Taoran Liu, Zhejiang University

Keywords: Graph Neural Network, Through-Hole Recognition, Differential Geometry, CAD/CAE Integration, Mesh Generation

Abstract

Automatic recognition of through-hole features is critical for CAD/CAE integration, particularly for mesh generation pre-processing tasks like defeaturing and anisotropic meshing. Traditional rule-based methods struggle with complex topological structures, while existing deep learning approaches often suffer from large model sizes and poor generalization on irregular geometries. We present LG-HoleNet, a lightweight Graph Neural Network (0.03M parameters) that leverages differential geometric attributes (Gaussian and Mean curvature) to achieve robust, rotation-invariant feature recognition. Validated on a novel diverse dataset of 9,273 CAD models, our method achieves 99.88% accuracy and significantly outperforms commercial software and state-of-the-art models in efficiency and recall, facilitating seamless engineering analysis workflows.

Retrieval-Augmented Generation (RAG) for Agentic Geometry Creation

Mike Stees, Lawrence Livermore National Laboratory
Charles Jekel, Lawrence Livermore National Laboratory
Nathan K. Brown, Sandia National Laboratories
Walter Nissen, Lawrence Livermore National Laboratory

Keywords: problem setup, meshing apis, CAD, machine_learning, rag, generative models, large language models

Abstract

Geometry preparation and meshing are frequent bottlenecks in simulation and design cycles. Generative Large Language Models (LLMs) offer tantalizing possibilities, but are diffi- cult to apply when training data are scarce or restricted, such as with proprietary meshing tools. To make use of LLMs in creating geometry with Lawrence Livermore Lab- oratory’s closed-source PMesh meshing application, we use Retrieval-Augmented Generation (RAG) to provide relevant context for user queries. We have a modest test suite cov- ering simple curve and surface creation, as well as moderate geometric ”reasoning”. We tested our RAG using a variety of OpenAI models. The result is a chatbot-style geome- try agent that provides initial meshing functionality despite not having any proprietary PMesh training in its foundation model.

Block Decomposition of General Planar Polygonal Shapes Using a Soft Actor Critic Reinforcement Learning Method

Navamita Ray, Los Alamos National Laboratory
Cristina Garcia Cardona, Los Alamos National Laboratory
Shubendu Singh, Los Alamos National Laboratory
Rao Garimella, Los Alamos National Laboratory

Keywords: Block Decomposition; Reinforcement Learning; Soft Actor Critic

Abstract

We present the results of our research into decomposing planar polygonal shapes into quadrliateral blocks for the purposes of generating a block-structured quad mesh. This work is a development of our original work using Reinforcement Learning to decompose axis-aligned orthogonal polygons into quadrilateral blocks. Our paper describes the extension of the state representation and action set to handle general polygons, presents a new reward function and the effect of its weights on convergence, and demonstrates the performance of the algorithm on a variety of shapes. We show that our method is able to generate nearly all quadrilaterals for all of the shapes but is often unable to avoid one or two triangles which could be split into sub-optimal quads.

Accelerating LES-Based Geometry Optimization with Deep Reinforcement Learning, Mesh Morphing, and Solution Mapping

Gastón Sal-Anglada, Barcelona Supercomputing Center
Bedri Yagiz, Barcelona Supercomputing Center
Abel Gargallo-Peiró, Barcelona Supercomputing Center
Oriol Lehmkuhl, Barcelona Supercomputing Center
Samuel Gómez, Barcelona Supercomputing Center

Keywords: Geometry Optimization, Mesh Morphing, Solution Mapping, High-Order Hexahedral Mesh, Large Eddy Simulation, Deep Reinforcement Learning

Abstract

This work presents an accelerated framework for LES-based geometry optimization that couples Large Eddy Simulation (LES) with Deep Reinforcement Learning (DRL) under high-order meshing constraints. The approach is integrated with the Computational Fluid Dynamics (CFD) solver SOD2D, based on a Continuous Galerkin Spectral Element Method (CG-SEM), which exploits hexahedral spectral elements for computational efficiency but restricts mesh regeneration. Geometric updates are applied to solver-validated high-order meshes via mesh morphing, preserving element connectivity and mesh validity, while solution mapping reuses previously converged flow fields to reduce transient initialization costs. A quasi-offline, batched optimization strategy based on the Soft Actor-Critic (SAC) algorithm efficiently explores the design space, accelerating the optimization process.

A Comparison of Three Refinement Methods with Sharp Edge Preservation on Quadrangular Surface Meshes

Jude Anderson, Los Alamos National Laboratory
Hoby Rakotoarivelo, Los Alamos National Laboratory
Rao Garimella, Los Alamos National Laboratory

Keywords: Higher Order Reconstruction; Uniform Mesh Refinement

Abstract

In this work, we present a comparison of three methods that refine a quadrangular surface mesh while preserving sharp edges to improve its approximation of the implicit smooth geometry that it represents. These surface refinement methods are further used in a procedure to uniformly refine a volume mesh. Lastly, we present convergence results for these methods on simple examples and graphically demonstrate the refinement on more complex models.

Adaptive Mesh Refinement Rules for Tensor-Product Spline-Based Fluid and Electromagnetic Simulations

Kendrick Shepherd, Brigham Young University

Keywords: Adaptivity, high order meshing

Abstract

High order spline-based finite element and isogeometric methods are known to exhibit significantly higher accuracy per degree of freedom than their traditional counterparts, and have made significant inroads for solid mechanics. However, specialized methods including Raviart-Thomas and Nedelec finite elements are necessary to ensure accuracy and stability in fluid mechanics and electromagnetics, where preservation of conservation laws described by the so-called de Rham complex is critical. Unfortunately, straightforward application of adaptive mesh refinement rules used in traditional low- and high-order finite element methods may fail to preserve necessary stability properties for spline-based hierarchical extensions of Raviart-Thomas and Nedelec finite elements. In this presentation, novel mesh refinement rules are defined for hierarchical spline-based de Rham conforming splines that ensure an isomorphism between the finite element space and its infinite-dimensional counterpart. These conditions are an important step towards enabling use of high-order, high-accuracy adaptive spline-based methods in computational fluid mechanics and electromagnetics.

Boundary layer mesh adaptation through a high-order r-adaptation

Kaloyan S. Kirilov, King's College London
Joaquim Peiró, Imperial College London
Jingtian Zhou, Imperial College London

Keywords: High-order mesh adaptation. r adaptation. Boundary layer mesh.

Abstract

High-order scaled resolved simulations often require iterative manual remeshing to resolve boundary layers flow physics. We propose a high-order mesh movement technique within a variational framework for adapting boundary layer meshes a-posteriori. Given a valid curved mesh and a computed flow field, the proposed method first estimates a target over- all boundary-layer height and a desired first layer wall nor- mal thickness. Then using the variational framework it relo- cates the prism or quad layers, preserving the connectivity, geometrical accuracy and validity of the high-order mesh. The method is demonstrated on a flat-plate configuration. The adapted meshes accurately conform to the boundary- layer thickness and the first-layer height, δ99 = 0.99U∞ and y+ = 1 respectively, both calculated a-posteriori from the flow solution.

A metric-aware size-shape measure for anisotropic optimization of curved high-order meshes

Guillermo Aparicio-Estrems, Barcelona Supercomputing Center (BSC-CNS)
Abel Gargallo-Peiró, Barcelona Supercomputing Center (BSC-CNS)
Xevi Roca, Barcelona Supercomputing Center (BSC-CNS)

Keywords: Anisotropic meshes, mesh optimization, high-order meshes, quality metrics, r-adaptation

Abstract

We define a regularized size-shape distortion (quality) measure for curved high-order elements on a Riemannian space. To this end, we measure the deviation of a given element, straight-sided or curved, from the stretching, alignment, and sizing determined by a target metric. The defined distortion (quality) is suitable to check the validity and the quality of straightsided and curved elements on Riemannian spaces determined by constant and point-wise varying metrics. The examples illustrate that the distortion can be minimized to curve (deform) the elements of a given high-order (linear) mesh and try to match with curved (linear) elements the point-wise stretching, alignment, and sizing of a discrete target metric tensor. In addition, the resulting meshes simultaneously match the curved features of the target metric and boundary. Finally, to verify if the minimization of the metric-aware size-shape distortion leads to meshes approximating the target metric, we compute the Riemannian measures for the element edges, faces, and cells. The results show that, when compared to anisotropic straight-sided meshes, the Riemannian measures of the curved high-order mesh entities are closer to unit. Furthermore, the optimized meshes illustrate the potential of curved r-adaptation to improve the accuracy of a function representation. Guillermo Aparicio Estrems acknowledges his AI4S fellowship within the “Generación D” initiative by Red.es, Ministerio para la Transformación Digital y de la Función Pública, for talent attraction (C005/24-ED CV1), funded by NextGenerationEU through PRTR.

AI for Mesh Generation and Model Preparation: A Review

Nathan Brown, Sandia National Laboratories
Nikos Chrisochoides, Old Dominion University
Rao Garimella, Los Alamos National Lab
Xianfen Gu, New York University, Stoneybrook
Franck Ledoux, CEA
Na Lei, Dalian University of Technology
Roshan Quadros, Sandia National Laboratories
Navamita Ray, Los Alamos National Lab
Steven Owen, Sandia National Laboratories

Keywords: CAD decomposition, quadrilateral decomposition, all-hex meshing, block-structured meshing, mesh quality, volumetric parameterization, reinforcement learning, Monte Carlo Tree Search, large language models

Abstract

Artificial intelligence is beginning to ease long-standing bottlenecks in the CAD-to-mesh pipeline. This survey reviews recent advances where machine learning aids part classification, mesh quality prediction, and defeaturing. We explore methods that improve unstructured and block-structured meshing, support volumetric parameterizations, and accelerate parallel mesh generation. We also examine emerging tools for scripting automation, including reinforcement learning and large language models. Across these efforts, AI acts as an assistive technology, extending the capabilities of traditional geometry and meshing tools. The survey highlights representative methods, practical deployments, and key research challenges that will shape the next generation of data-driven meshing workflows.

QuadOpt-RL: Reinforcement Learning Agent for Quad Mesh Optimization

Franck Ledoux, CEA
Jean-Christophe Janodet, IBISC Lab, Univ. Evry, Université Paris-Saclay
Arzhela Roperch, CEA

Keywords: Mesh optimization, reinforcement learning, quadrangular meshes, topology

Abstract

Mesh generation is a crucial stage in numerical simulations that can be very time-consuming for engineers. Although 2D quad meshing is considered a solved problem, we explore using Reinforcement Learning (RL) as an alternative approach. In this context, we teach an agent to interact with a mesh through a set of editing actions to improve the mesh quality. In this work we explore different modeling aspects to extend. More specifically, we focus on optimizing TQuad meshes — that is, quad meshes obtained by splitting each triangle of a triangular mesh into three quads. We conduct several analyses focusing particularly on the mesh observation process and the RL algorithm employed. The result is an RL agent that can autonomously perform a series of operations that significantly improve quadrilateral meshes.

CubeFlipNet: Reinforcement Learning for HexMesh Generation via Cube-Flip Operations with a Polycube Alignment Prior

Lu He, School of Software, Dalian University of Technology
Qitao Deng, College of Science, Jiangxi University of Science and Technology
Haoyang Xu, School of Software, Dalian University of Technology
Yanjun Liang, School of Software, Dalian University of Technology
Na Le, School of Software, Dalian University of Technology

Keywords: Hexahedral meshing,Polycube,PPO,reinforcement learning

Abstract

Automatic generation of high-quality hexahedral meshes is a long-standing challenge in CAD/CAE. To address this challenge, we propose CubeFlipNet, a new method that leverages deep reinforcement learning to drive cube-flip operations for 3D hexahedral mesh generation. CubeFlipNet is the first to combine discrete action selection with continuous key-point placement learning: within an RL framework, the agent simultaneously decides which cube-flip operation to perform and where to place new vertices. To improve training stability and convergence, we incorporate a polycube alignment prior into the reward design as a soft constraint to guide policy learning. We evaluate the performance of CubeFlipNet in the experimental section, and finally discuss the current limitations of the framework and outline potential extensions to more complex mesh generation tasks.

Non-Euclidean elasticity for r-adaptation

Julia Docampo-Sanchez, Barcelona Supercomputing Center (BSC-CNS)
Guillaume Houzeaux, Barcelona Supercomputing Center (BSC-CNS)
Oriol Lehmkuhl, Barcelona Supercomputing Center (BSC-CNS)
Abel Gargallo-Peiro, Barcelona Supercomputing Center (BSC-CNS)
Sergi Perez-Escudero, Barcelona Supercomputing Center (BSC-CNS)

Keywords: r-adaptation, elasticity, non-Euclidean metric, AMR, optimization

Abstract

This work proposes a new r-adaptation strategy based on a linear, isotropic formulation of non-Euclidean elasticity. The method interprets mesh adaptation as the deformation of an elastic body driven by a prescribed metric that encodes the desired size field. Two complementary formulations are introduced: one posed in the reference configuration and one in the deformed configuration. In contrast to existing nonlinear, optimization-based r-adaptation schemes, which often suffer from high computational cost, the proposed approach relies on solving a simple linear elasticity problem. This enables efficient and robust node relocation without altering mesh connectivity. Numerical results demonstrate that the proposed method generates high-quality adapted meshes that accurately capture isotropic size fields, maintaining the computational efficiency required for integration into large-scale AMR frameworks.

High-Order Mesh r-Adaptivity with Tangential Relaxation and Guaranteed Mesh Validity

Veselin Dobrev, Lawrence Livermore National Laboratory
Tzanio Kolev, Lawrence Livermore National Laboratory
Vladimir Tomov, Lawrence Livermore National Laboratory
Ketan Mittal, Lawrence Livermore National Laboratory

Keywords: high-order mesh, r-adaptivity, tangential relaxation, mesh validity

Abstract

High-order meshes are crucial for achieving optimal convergence rates in curvilinear domains, preserving symmetry, and aligning with key flow features in moving mesh simulations, but their quality is challenging to control. In prior work, techniques based on Target-Matrix Optimization Paradigm (TMOP) were developed to adapt a given high-order mesh to the geometry and solution of the partial differential equation (PDE). Here, we extend this framework to address two key gaps in the literature for high-order mesh $r$-adaptivity. First, we introduce tangential relaxation on curved surfaces using solely the discrete mesh representation, eliminating the need for access to underlying geometry (e.g., CAD model). Second, we ensure positivity of the Jacobian determinant throughout the domain and not just at a discrete set of quadrature points. This determinant positivity is essential for using the the high-order mesh resulting from the proposed method with arbitrary quadrature schemes.The proposed approach is demonstrated to be robust using a variety of numerical experiments.

Iterative metric rescaling for mesh adaptation with a prescribed node count

Guillaume Houzeaux, Barcelona Supercomputing Center (BSC-CNS)
Abel Gargallo-Peiro, Barcelona Supercomputing Center (BSC-CNS)
Julia Docampo-Sanchez, Barcelona Supercomputing Center (BSC-CNS)

Keywords: node control, metric adaptivity, AMR, anisotropy

Abstract

Metric-based Adaptive Mesh Refinement (AMR) provides control over element sizes and anisotropy, improving the simulation quality while efficiently allocating computational resources. A common challenge arises, however, when a user specifies a target number of nodes: the adapted mesh often deviates from this target. This deviation comes from the approximated relation between the metric and the expected node count, as well as the approximations introduced during mesh generation. In this work, we propose an iterative metric rescaling approach that compensates for such deviations by dynamically adjusting the metric to guide the adaptation process toward the desired node count. Our method applies to both 2D and 3D meshes and is independent of the specific AMR strategy. We present a series of validation cases and practical simulations, where the proposed rescaling scheme reliably achieves the prescribed node count (within a user-defined tolerance) without requiring manual tuning of adaptation parameters. This ensures precise control of computational budgets while maintaining high-quality meshes.

Robust and Efficient 3D alpha-shapes on GPU

Jonathan Lambrechts, UCLouvain
Jean-François Remacle, UCLouvain
Nathan Tihon, UCLouvain

Keywords: Alpha-Shapes, GPU, Delaunay

Abstract

Tihon et al. (2025) have shown that it is possible to construct the $\alpha$-shape of a set of point completely in parallel without first computing the Delaunay Triangulation. However their algorithm is only two dimensional and is not robust. In this paper, we extend their method to 3 dimensions and make it robust by using exact predicates and the simulation of simplicity on the GPU. Furthermore, we extend the overall method to space-varying $\alpha$. These properties makes our algorithm a very good candidate for the Particle Finite Element Methods.

Flexible Data Structures for Efficient and Reliable Shared-Memory Parallel Meshing

Franck Ledoux, CEA DAM
Cédric Chevalier, CEA DAMe
Elyas Elaziz, ENS Paris Saclay
Isaïe Muron, CEA DAM

Keywords: data structure, transactional memory, remeshing, parallelism, correctness

Abstract

Parallelizing remeshing algorithms presents significant challenges due to the variety of operations involved in meshing kernels. These operations all have different characteristics; they may be read-heavy, write-heavy, affect topology or geometry, and may require allocation of new elements. These differences make it difficult to identify memory access patterns for both optimization and correct synchronization. We aim to address these problems without relying on conflict avoidance, and propose an alternative approach to ensure data integrity in the context of parallel meshing. To that end, we leverage a specific mesh representation based on combinatorial maps, as well as Software Transactional Memory for synchronization. We illustrate the flexibility of our structure using three usual algorithms and their parallelization. We show STM manages conflicts with minimal algorithmic changes from original implementations. Our work offers a robust framework for parallel remeshing, with promising multi-thread performance

GPU-accelerated processing of polygonal meshes in compact space

Sergio Salinas-Fernández, DCC, Universidad de Chile
Jose Fuentes-Sepúlveda, Universidad de Concepción
Nancy Hitschfeld-Kahler, DCC, Universidad de Chile
Diego García-Espinoza, DCC, Universidad de Chile

Keywords: compact data structure, polygonal meshes, gpu programming

Abstract

We present a new compact half-edge data structure for storing polygonal meshes designed to work in the GPU, that allows one to read information of a mesh and traverse inside the mesh in parallel. For this, we adapted a planar graph compact data structure called PEMB to be used inside a GPU. To test the data structure we built a new version of the polygonal mesh generator Polylla in GPU compact space, and compared it against its GPU non-compact version, the sequential non-compact and compact versions. This last version takes a compact mesh and generates a non-compact mesh, while the proposed here works by taking a compact input mesh and giving a compact output mesh. We also measured and compared the performance of the queries on the GPU compact data structure against the queries on the sequential non-compact and compact data structures. The results show that comparing the generation of an output mesh in GPU compact vs sequential compact is $2x$ faster, and the compact queries made in GPU are $43x$ faster than the sequential compact queries.

Runge-Stable High-Order Bases on Uniform Nodes: Interpolation and Geometry Mapping

Jean-François Remacle, UCLouvain
Amaury Johnen, UCLouvain

Keywords: High-order mesh generation, Curved finite elements, Finite element geometry mapping, Polynomial interpolation on uniform grids, Runge’s phenomenon

Abstract

This paper introduces three bases for high–order approxima- tion on uniform nodes in one dimension, aimed at mitigating Runge’s phenomenon. The Runge–Stable Rational (RSR) basis is a numerically constructed, fully interpolatory basis; the Quasi–Lagrange Polynomial (QLP) basis is a polyno- mial surrogate obtained by minimizing a derivative misfit to RSR and is quasi–interpolatory. Both RSR and QLP deliver stable approximations on uniform grids and, in practice, achieve errors comparable to interpolation on Chebyshev nodes—sometimes outperforming it—although they do not attain the optimal asymptotic convergence of classical Lagrange interpolation as the mesh size h → 0. The Hierarchical Selective–Runge (HSR) basis is a polynomial hierarchy that isolates endpoint–dominated modes; it underpins a scale–invariant, data–adaptive score that predicts when uniform–grid Lagrange is safe and when a stabi- lized alternative should be preferred. Numerical experiments exhibit a clear crossover: for coarse grids (large h), RSR and QLP reduce L∞ and L2 errors for f and f′ relative to Lagrange; for fine grids (small h), Lagrange regains its superior convergence rate. A simple decision rule, driven by the HSR–based score, automatically switches between Lagrange and a stabilized basis with negligible overhead, retaining Lagrange when advantageous and selecting RSR/QLP precisely when Runge effects would otherwise dominate.

Surface Remeshing Based on Quasi-Conformal Mapping

Ranran Ji, DUT-RU ISE, Dalian Unviersity of Technology
Hang Si, DUT-RU ISE, Dalian Unviersity of Technology
Yuxue Ren, Academy for Multidisciplinary Studies, Capital Normal University

Keywords: Surface Remeshing;Quasi Conformal Mapping;Yamabe Flow

Abstract

This paper presents a novel quasi-conformal mapping-based approach for high-quality adaptive mesh generation on complex surfaces, addressing the geometric distortion limitations inherent in conventional methods. The framework achieves breakthroughs through three key stages: first, constructing an initial parameterization and optimizing it into a quasiconformal map with a controllable dilatation; second, performing high-quality adaptive remeshing on the resulting isotropic parameter domain; and finally, mapping the optimized mesh back to 3D space via an inverse mapping. The core advantage of this method lies in its ability to actively guide geometric distortion—strategically redistributing unavoidable distortion to non-critical regions, thereby achieving isotropic parameterization in feature-rich areas. Experimental results demonstrate clear advantages over existing techniques, offering a more reliable mesh generation solution for computational physics and geometric modeling applications.

A Framework for Robust 2D Interface Reconstruction from Higher-Order Moments

Christoph Garth, RPTU Kaiserslautern-Landau
Pavel Bochev, Sandia National Laboratories
Denis Ridzal, Sandia National Laboratories
Roxana Bujack, Los Alamos National Laboratory
Michael Will, RPTU Kaiserslautern-Landau

Keywords: finite elements, interface reconstruction, moments

Abstract

Multimaterial flows with moving boundaries between non-mixing fluids frequently occur in real-world experiments and physical simulations. These dynamic interfaces emerge during the solution process rather than being predetermined. Developing accurate, robust, and computationally efficient interface reconstruction algorithms is essential for simulating these flows. The moment-of-fluid method shows promise, particularly because it relies solely on local cell data, enabling highly parallelizable computations. In particular, the use of higher-order moments has resulted in unprecedented reconstruction accuracy. Methods using these moments compute a polynomial that approximates the characteristic function of the fluid domain and produce an initial guess of the interface by computing an isocontour, which is then decimated and enhanced using nonlinear optimization. However, this approach also presents specific algorithmic and software challenges. First, higher-order polynomials are prone to Gibbs-like oscillations. Second, while direct methods offer excellent performance in this context, they suffer from relatively high condition numbers of the moment matrices. Finally, the fixed isovalue and the nonlinear optimization step can also undermine the stability of the higher-order-moments approach. In this paper, we present a mathematical and algorithmic framework that overcomes these challenges and enables robust and computationally efficient reconstruction of high-fidelity dynamic interfaces. Our approach combines finite-element representations, to mitigate polynomial oscillations, with an iterative least-squares solver, adaptive isovalues, and several improved optimization schemes.

Space-time hole-like control volumes connecting in time 2D & 3D Voronoi meshes with topology changes

Matej Klima, University of Verona
Elena Gaburro, University of Verona

Keywords: Voronoi mesh, Arbitrary-Lagrangian-Eulerian schemes, topology changes, high order methods, hyperbolic equations

Abstract

The framework of this work is that of direct Arbitrary-Lagrangian-Eulerian (ALE) methods of high order of accuracy for solving hyperbolic equations with a greatly reduced dissipation on convection terms and a better track of contact discontinuities and material interfaces.

These explicit methods are characterized by i) a computational domain, in our case a Voronoi-like tessellation, which moves together with the fluid flow and thus is changing at any time-step, ii) a mesh velocity chosen as close as possible to the local fluid velocity but which can be eventually slightly modified in order to improve the quality of the resulting moved mesh, and iii) a one-step direct high order procedure that evolves the solution in time, so from one mesh to another, via integration over space-time control volumes connecting the two meshes, without the need of any projection-reconstruction step.

What has become clear over the past years is that in order to guarantee a good quality of the moving mesh, we cannot just relocate, stretch and deform the elements, but also so-called topology changes (change of the elements shape and connectivity) should be allowed. The crucial step here consists in being able to build, even around a topology change, the space-time control volumes connecting elements with different shapes and neighborhood at successive time-steps. Unfortunately, just linking the existing elements, by collapsing or expanding their edges, leaves a hole in the space-time. Thus, we have decided to fill it by considering an additional space-time degenerate hole-like element.

In this talk, I will first describe the shape and the numerical treatment of a hole-like element in the 2D+time framework within a direct ALE ADER Discontinuous Galerkin (DG) method. Then, after having justified the stability of this ALE ADER-DG approach, I will present a full characterization of the 3D+time=4D degenerate hole-like elements that arise as consequence of 2-3, 3-2 and 4-4 flips on the underlying Delaunay tetrahedralization.

Scalable Mesh Coupling for Atmospheric Wave Simulation

Tim Griesbach, University of Bonn
Matthew Zettergren, Embry-Riddle Aeronautical University
Scott Aiton, Boise State University
Jonathan Snively, Embry-Riddle Aeronautical University
Donna Calhoun, Boise State University
Carsten Burstedde, University of Bonn
Hannes Brandt, University of Bonn

Keywords: Mesh Coupling, Adaptive Mesh Refinement, Atmospheric Wave Simulation

Abstract

We describe the application of a scalable algorithm for interpolating solution data in the overlapping mesh region of two solvers. This feature is essential to obtain a globally consistent solution for in-situ coupled atmospheric wave simulation. We provide timings and discuss a real-world application run.

Enhancing mesh curving robustness for explicit wall modeled large-eddy simulation

Xevi Roca, Barcelona Supercomputing Center - BSC
Eloi Ruiz-Gironés, Barcelona Supercomputing Center - BSC

Keywords: Mesh curving; Complex geometry; Explicit time integrator

Abstract

For wall modeled large-eddy simulation (WMLES), we enhance our mesh curving method to generate high-order meshes suitable for solving the inviscid part with explicit time-marching. To fulfill the mesh requirements for practical explicit time-marching, it is helpful to slightly violate the geometric accuracy in some regions. Note that the simulation waiting time is determined by the time-step, and this one is limited by the most restrictive distance between mesh points. Unfortunately, in aeronautics, it is challenging to meet the mesh point spacing needs especially next to aircraft surfaces exposed to high velocity flow. For instance, exposed regions leading to highly pronounced tangencies (e.g., slat recovery surfaces) and small element size (e.g., narrow surfaces at the trailing edges). If we accept a geometric discrepancy of the local element size between the target geometry and the initial straight-edged mesh, then it is easier to fulfill the point spacing requirements for explicit methods.

However, the problem is that this geometric discrepancy in the challenging regions makes the mesh curving process brittler. Solving this robustness problem is of major importance. Without a valid curved mesh fulfilling the point spacing requirements, the time-steps might be so small that the simulation waiting time might be inadmissible for the engineers. Our solution is to enhance our distortion-based continuation curving method by fixing the high-order points of the problematic surface triangles. Specifically, the selected triangles are fixed to their position in the initial straight-edged mesh. To fix them, the user can provide an initial list of triangles to fix and the rest of fixed triangles are automatically detected. To detect them, at each continuation iteration of the curving method, we fix for the rest of the curving stage those triangles that lead to an infinite distortion. Accordingly, the procedure automatically accepts geometric discrepancy between the curved mesh and the target geometry only on the problematic regions. The main benefit of our enhancement is that the resulting curved high-order meshes are valid and feature larger mesh point spacing. Hence, the resulting meshes are suitable for faster inviscid explicit time-marching in WMLES.

Level-Set–Based Actuator Disc Modeling for Adaptive Wind Farm Simulations

Julia Docampo-Sánchez, Barcelona Supercomputing Center (BSC-CNS)
Guillaume Houzeaux, Barcelona Supercomputing Center (BSC-CNS)
Abel Gargallo-Peiró, Barcelona Supercomputing Center (BSC-CNS)
Alice Novell-Mazzara, Barcelona Supercomputing Center (BSC-CNS)

Keywords: Actuator disc modeling, Level-set methods, Adaptive mesh refinement, Anisotropic metric, Wind farm simulation, Atmospheric boundary layer, Tetrahedral mesh

Abstract

We present a three-dimensional workflow for wind-farm simulation on tetrahedral meshes based on a level-set representation of the Actuator Disc (AD) model. The framework assumes a terrain-following Atmospheric Boundary Layer (ABL) mesh as input and embeds each turbine without requiring a geometry-conforming discretization. A signed-distance function, constructed from the turbine geometric parameters, is used both to identify disc-intersecting elements for AD forcing and to define a smooth interface function that marks a narrow band around each disc where additional resolution is needed. From this interface and selected flow quantities we construct an anisotropic mesh metric that prescribes the local element sizes. Metric-based adaptation concentrates resolution where required, within the disc, near wake, and boundary layer, while preserving coarse resolution elsewhere. This enables fully adaptive wind-farm simulations with resolution targeted precisely where required.

Monte-Carlo Tree Search for Hexahedral Block-structured Mesh Generation

Paul Bourmaud, CEA
Franck Ledoux, CEA
Jean-Christophe Janodet, Université Évry Paris-Saclay
Nicolas Le Goff, CEA

Keywords: mcts, block-structured, hexahedra

Abstract

In an industrial context the creation of block-structured hexahedral meshes is costly in terms of engineering time, as they are generated using interactive CAD-meshing software. While some of those provide the tools necessary for decomposing a geometric model into smaller meshable sub-volumes, others are block-based, meaning that an engineer will instead edit an hexahedral block structure, or blocking, by using the operations at their disposal such as block creation, extrusion, split, deletion, pillowing, … while classifying the blocking entities onto the geometric ones to represent the model adequately. For a given model the engineer relies on their expertise to choose a sequence of operations that will produce a desirable blocking. We applied a single-player Monte Carlo Tree Search (SP-MCTS) to this decision-making problem, modelling it so that a state is the blocking and its entities’ association on the geometry and the set of possible actions is restricted to axis-aligned blocks split and block deletion. The classification of blocking entities onto the geometry is not part of the action set and is instead a heuristic, called at every step after an action on the blocking is taken. A reward function based on the number of geometric entities captured is used to evaluate the score of a state, the selection policy of the tree is a Single Player Upper Confidence Bound for Trees (SP-UCT) and the simulation policy is random. Our method was applied on a dataset of single-volume geometric models and we exhibit some preliminary results. In particular, on cases with axis-aligned features our SP-MCTS consistently returns valid blockings. We obtained mixed results where curved or non axis-aligned feature are concerned, and future works include introducing handling of those features by focusing on the classification heuristic and analysing the SP-MCTS behavior.

Multi-Block Grids via Polycubes

Stevie-Ray Janssen, Royal Netherlands Aerospace Centre
Bettina Speckmann, TU Eindhoven
Kevin Verbeek, TU Eindhoven
Maxim Snoep, TU Eindhoven

Keywords: multi-block grid, polycube

Abstract

Multi-block grids are widely used for high-fidelity computational fluid dynamics (CFD) simulations in aerospace. However, constructing high-quality multi-block grids for complex geometries is still a largely manual, time-intensive process which relies on human expertise. This abstract reports on the collaborative efforts of the Royal Netherlands Aerospace Centre (NLR) and researchers from TU Eindhoven to automate a crucial step in the multi-block grid pipeline, namely the constructions of a so-called polycube segmentation of the input geometry.

Spectral boundary conditions for volumetric frame fields design

Yuri Nesterenko, Siemens Digital Industries Software

Keywords: frame fields, spherical harmonics, immersed boundary

Abstract

Using the 4th and the 3rd degree spherical harmonics as the representations of volumetric frames, we describe a simple algebraic technique for combining multiple orientation constraints into a single quadratic penalty term. In particular, the given technique allows to solve volumetric frame fields design problems using a coarse-to-fine strategy on hierarchical grids with immersed boundaries.

Multi-source to multi-target swept mesh generation

Sumit Paranjape, Siemens DISW

Keywords: Sweeping, M-N,

Abstract

Sweeping is a powerful tool for generating good quality hexahedral or hex dominant meshes in extrusion volumes also known as 2.5D volumes. One-to-one (1-1) and many-to-one (M-1) sweeping procedures are well established but sweeping multiple sources to multiple targets (M-N) is a challenging problem because the existing algorithms suffer from robustness issues while dealing with complex models. This research note highlights recent developments in M-N swept mesh generation within Simcenter STAR-CCM+. Our method involves bi-directional transport of boundary edge patches along guide surfaces, imprinting of internal edges patches using cage-based morphing or affine transformation defined on closed loop of vertices on the boundary edge patches and combining incoming edge patches with new edge patches at each sweep level. Subsequent partitioning of the sources and target surfaces with the imprinted edge patches yields a 1-1 correspondence between each source and target face patch. We maintain a map between all matched 0,1 & 2 dimensional topological entities across all source and target sweep levels. The sweeping algorithm ensures that any m-dimensional mesh entity associated to a n-dimensional topological entity (n≥m) at any source sweep level is swept to the matched n-dimensional topological entity at the target sweep level. We have extended this procedure to work with a collection of contacting volumes. Furthermore, we have added tools to facilitate fast identification of all source and target surfaces in a collection of volumes. These developments have made M-N swept meshing a viable option for targeting complex industrial models.

Efficient point-in-body queries on triangulated surfaces

Jacob Jones, Los Alamos National Laboratory
Konstantin Lipnikov, Los Alamos National Laboratory
Hoby Rakotoarivelo, Los Alamos National Laboratory

Keywords: point-in-body queries, winding number

Abstract

An efficient point-in-body query method on closed triangu- lated surfaces is presented. It is targeted for material volume fractions initialization within multi-material simulations. It relies on the notion of winding number to determine whether a point is inside the volume enclosed by the discrete surface or not. Its key point is the hierarchical evaluation of the winding number using an accelerating tree constructed from a recursive planar subdivision of the domain. It achieves comparable accuracy to that of a CAD method on complex shapes, while being faster.

Sharp Features Graph Extraction from Segmented 3D Images for Mesh Generation

Emmanuel Faure, LIRMM, Univ Montpellier, CNRS
Noura Faraj, LIRMM, Univ Montpellier
Jane Tournois, GeometryFactory
Ange Clément, LIRMM, Univ Montpellier, CNRS, GeometryFactory

Keywords: sharp feature extraction segmented 3D image

Abstract

We present a method to extract a sharp feature graph from a segmented 3D image on a subvoxel level of precision, that can be used for mesh generation. In previous methods, measures of sharpness on images yield rough estimates of sharp line positions. Hence, additional steps are needed to extract a precise feature graph of sharp lines along the highest values of such measures. First, a sharpness evaluation is conducted on the surface elements of an image. Then, from this measure, smooth elements are discarded, and a graph thinning process generates lines that are guaranteed to be positioned along the highest values of the measure. We propose a thinning process with priority that preserves the underlying graph topology. The result is refined with a correction step and an optimization phase to ensure the correct placement of lines and corners along estimated normals. We present some results on various images to show the robustness of our method.

3D Mesh Orthogonalization and Regularization Based on a Weighted Line Sweeping Method

Baptiste HUBERT, CEA
Jérôme Breil, CEA
Florent Nauleau, CEA

Keywords: Hypersonic, Orthogonalization, Regularization, Adaptation

Abstract

This work focuses on studying and adapting existing methods for regularizing structured 3D meshes, particularly for application in complex geometries encountered in hypersonic flow simulations. The mesh regularization techniques are modified to orthogonalize the mesh at solid walls and to control the first cell size, enabling accurate capture of boundary layer phenomena. The regularization method is based on a 3D-adapted Weighted Line-Sweeping. Multiple test meshes were generated to determine an optimal combination of weights that ensures mesh orthogonality near walls and maintains suitable aspect ratios upstream. The approach should handle multi-block configurations, including the management of triple points at block intersections in particular with \textit{O-grid} meshing. Additionally, mesh distribution is optimized to effectively resolve critical physical effects such as pressure, temperature, and density gradients associated with detached shock waves. Validation is performed through numerical simulations of hypersonic flows, with results compared with reference data to assess accuracy. These methods are implemented within an existing computational fluid dynamic code.

Hybrid Block-Structured Grids for Complex Ocean Domains

Jonathan Schmalfuß, University of Bayreuth
Vadym Aizinger, University of Bayreuth
Roberto Grosso, Friedrich-Alexander-Universität Erlangen-Nürnberg
Julian Stahl, Friedrich-Alexander-Universität Erlangen-Nürnberg

Keywords: block-structured grid, ocean mesh, shallow-water equations, finite element method, domain decomposition, feature size

Abstract

We propose a new method to automatically generate hybrid block-structured grids (hBSG) for complex ocean domains suited for numerical simulations. hBSGs may contain structured or unstructured blocks. They combine the performance benefits of block-structured grids with the ability of unstructured grids to control the local resolution and accurately represent the domain geometry. We discuss three different approaches to determine the placement of structured and unstructured grid blocks. The mesh generation schemes are optimized to guarantee element quality, thereby ensuring numerical stability, while also providing local resolution in accordance with the physical properties of the flow system, thereby minimizing the CFL restrictions on the time step. We evaluate and compare the quality of the meshes with previous methods and show that the performance benefits offered by hBSGs are comparable to those of standard block-structured grids.

Hexahedral Mesh Generation Based on Meromorphic Quadratic Differentials on Surfaces

Yiming Zhu, Dalian University of Technology
Zhihui Qi, Dalian University of Technology
Yuhao Feng, Dalian University of Technology
Xiaopeng Zheng, Dalian University of Technology
Zhongxuan Luo, Dalian University of Technology
Hang Si, Dalian University of Technology
Xianfeng Gu, Stony Brook University
Na Lei, Dalian University of Technology

Keywords: Hexahedral Mesh, Meromorphic differential, Ricci Flow, Foliation

Abstract

We introduce a novel method for structured hexahedral mesh generation based on meromorphic quadratic differentials with closed trajectories. The horizontal trajectories define a foliation that naturally induces a cylindrical decomposition of the surface and disk decompositions around poles. Extending this foliation into the interior yields volumetric decompositions into cylindrical and hemispherical components. Hexahedral blocks are then constructed within each component by fixing quadrilateral meshes on shared interfaces, followed by consistent assembly. Our pipeline consists of four stages: skeleton extraction, computation of the foliation aligned with the skeleton topology, surface and volumetric decomposition, and final hexahedral meshing. Compared with conventional skeleton-based approaches, our method naturally overcomes the challenge of constructing homomorphic mappings in concave regions. Moreover, the conformal nature of quadratic differentials enhances the orthogonality quality of the hex-mesh boundary. Given a skeleton, the computation of meromorphic quadratic differentials is theoretically guaranteed, making our algorithm both robust and efficient.

Surface Quadrilateral Mesh Generation Based on Weierstrass P Function

Yiming Zhu, Dalian University of Technology
Qiankun Nie, Stony Brook University
Siquan Sun, Dalian University of Technology
Siyu Fang, Stony Brook University
Zhongxuan Luo, Dalian University of Technology
Hang Si, Dalian University of Technology
Xianfeng Gu, Stony Brook University
Na Lei, Dalian University of Technology

Keywords: Quadrilateral Mesh, Meromorphic Function, Ricci Flow, Abel-Jacobi

Abstract

The generation of structured surface quadrilateral meshes is pivotal in solid and physical modeling, as well as in numerous other engineering disciplines. In this work, we present a novel approach for quadrilateral mesh generation on genus one surfaces based on the Weierstrass $\wp$ functions. Recent advancements have established the connection between meromorphic quartic differentials and quadrilateral meshes and have unveiled the governing equations—the Abel-Jacobi condition—for their singularities. The Weierstrass $\wp$ function provides a doubly periodic meromorphic function on the complex plane, which, when composed with a conformal mapping from the surface to the plane, directly induces a meromorphic function on the genus one Riemann surface. This function can be further transformed into a meromorphic quartic differential in accordance with the Abel-Jacobi condition, which naturally induces a quadrilateral mesh. Also, we can go step further from Weierstrass $\wp$ function to get $\sigma$-function, which can also be used to construct meromorphic functions on genus one Riemann surfaces. Our method is grounded in a rigorous theoretical framework and leverages the Weierstrass $\wp$ function and $\sigma$-function to achieve conformal surface parameterization, leading to quadrilateral meshes with high orthogonality and uniform local size transition. Furthermore, the algorithm allows users to prescribe the positions and indices of singularities of the quad-mesh. To demonstrate the simplicity, efficiency and versatility of our approach, we provide numerical experiments that confirm its theoretical validity and illustrate its practical advantages.

Agent-Guided Geometry Decomposition for Hex Meshing via Heterogeneous Graph Neural Network

Nick Winovich, Sandia National Laboratories
Corey Ernst, Sandia National Laboratories
Nya Hardy, Sandia National Laboratories
William Quadros, Sandia National Laboratories

Keywords: Geometry Decomposition, Dimension Reduction, Hex Meshing, Hybrid Meshing, Graph Neural Network

Abstract

All-hexahedral (all-hex) meshes remain a staple for high-consequence simulations because they deliver higher accuracy per degree of freedom, improved stability, and faster convergence relative to tetrahedral meshes. Yet, generating all-hex meshes for complex 3D CAD models still hinges on a labor-intensive, tedious geometry decomposition step, where expert users identify sweeping directions and mappable subregions and manually formulate a sequence of decomposition commands (a.k.a. WebCuts). In this work, we first reduce a 3D CAD boundary representation (B-Rep) model to a discrete chordal-axis skeleton (CAT); this skeleton is then mapped to a 1D bipartite graph with surface and curve nodes carrying geometric, topological, and meshing attributes. A heterogeneous graph neural network (GNN) agent is trained using a synthetic training data set specifying valid WebCut actions (labels). During inference, the agent performs multi-label node classification on the heterogeneous graph to predict WebCut actions (five surface actions and three curve actions). During training and inference, we enforce ID invariance, normalize directional features, and maintain local-to-global maps so that every prediction can be translated into actionable Cubit® WebCut command string. On a held-out lattice test set, our approach attains up to 98.7% per-action accuracy. We integrate the predictions into the Cubit® Meshing PowerTool to provide ranked previews and one-click execution, substantially reducing manual effort and time-to-mesh. Finally, we demonstrate that the proposed framework effectively generalizes to out-of-distribution geometries, achieving ~85% accuracy for WebCut predictions on complex, industrial 3D CAD models.

Learning-Based Prediction of Tetrahedral Mesh Quality under Nondeterministic Meshing

Nick Winovich, Sandia National Laboratories
Steven J. Owen, Sandia National Laboratories
Sam Parry, Sandia National Laboratories

Keywords: quality prediction, machine learning, tetrahedral meshing, defeaturing, non-deterministic meshing

Abstract

This study focuses on pre-meshing quality prediction for tetrahedralization of CAD geometries while accounting for the non-deterministic behavior of mesh generators. Our approach aims to enhance the defeaturing process and reduce the time required to achieve simulation readiness. We train supervised models using CAD-native, size-invariant features derived from vertices, curves, and surfaces, capturing essential geometric properties such as topology, curvature, angular relations, proximity, and valence. Labels are generated from repeated meshing to estimate the distribution of scaled-Jacobian (SJ) values. A dual-regressor model jointly predicts the minimum SJ and its dispersion, facilitating pass/fail screening and prioritized edits. Experimental results demonstrate accurate, size-robust quality forecasts across various models, along with a practical prioritization policy that builds upon previous advancements in learning-guided defeaturing.

Curvature Driven Surface Deformation based on Alexandrov Rigidity Theory

Yuanpeng Liu , Stony Brook University
Linhan Shen, Hunter College High School
Hang Si, Dalian University of Technology
Xianfeng Gu, Stony Brook University
Na Lei, Dalian University of Technology

Keywords: Surface Deformation, Ricci Flow, Alexandrov Rigidity Theorey

Abstract

Building on the Alexandrov rigidity theorem, we introduce a novel method for curvature-driven convex surface deformation with applications in mechanical engineering, CAD, computer graphics, and medical imaging. Our algorithm begins with a user-specified target Gaussian curvature, from which the corresponding Riemannian metric is calculated using discrete surface Ricci flow. The surface embedding is then efficiently determined by optimizing a convex energy with Newton’s method. The theoretical guarantees for solution existence and uniqueness are grounded in Ricci flow theory and the Alexandrov rigidity theorem. This approach provides a robust and mathematically sound foundation for developing a new class of surface deformation models.

Hyperbolic Birkhoff Curve Shortening Algorithm on Surfaces

Wei Chen, Capital Normal University
Yiming Zhu, Dalian University of Technology
Zhihui Qi, Dalian University of Technology
Si hang, Dalian University of Technology
Zhongxuan Luo, Dalian University of Technology
Xianfeng Gu, Stony Brook university
Na Lei, Dalian University of Technology

Keywords: Ricci Flow, Hyperbolic, Homotopic, Shortest loop, Pants decomposition

Abstract

This work proposes a novel Birkhoff loop shortening algorithm on surfaces based on hyperbolic surface Ricci flow. First, the hyperbolic uniformization metric of the surface is computed using the hyperbolic discrete surface Ricci flow. Second, the Birkhoff method is applied to shorten the input loop locally. At each step, a neighborhood of the loop is isometrically embedded onto the Poincar'{e} disk, and the loop segment inside the neighborhood is replaced by a geodesic segment. Therefore the total length of the loop decreases monotonously during process, and eventually the loop converges to the unique geodesic in its homotopy class. As a direct application, the algorithm is used for surface pants decomposition with the optimal cutting loops, which greatly improves the robustness of the decomposition.

The numerical experimental results demonstrate the method is highly effective and robust in practice and useful for downstream geometric processing tasks.

Block-structured quadrilateral meshing using colored medial axis

Etienne Corman, CNRS
Franck Ledoux, CEA
Nicolas Ray, Inria
Dmitry Sokolov, Université de Lorraine
Tristan Cheny, Loria

Keywords: Quadrilateral meshing, block-structured mesh, medial axis, combinatorial approach

Abstract

Block-structured meshes are widely used in high-performance computing due to their efficiency in numerical simulations, memory access, and domain partitioning for parallel processing. Medial-axis-based algorithms have been considered as a promising approach for automatically decomposing a domain into quadrilateral blocks while ensuring a minimal number of singular vertices. TopMaker, developed by D.Rigby, is a notable example, providing a robust decomposition strategy. However, it suffers from limitations such as the capture of curved block boundaries, poor geometric quality, and the presence of non-quadrilateral blocks.
In this paper, we propose an improved block decomposition method that enhances TopMaker by integrating integer optimization for subdivision selection and incorporating additional singular nodes to better approximate the domain geometry. Our approach assigns a mesh template to each point of the medial axis, greatly improving the block quality while ensuring a valid conforming quadrilateral decomposition. We evaluate our approach on a large range of 2D domains and demonstrate its ability to generate high-quality block-structured meshes. The results highlight the robustness, efficiency, and practicality of our method for automated quadrilateral block decomposition. Our method also extends to multi-material models with intricate internal constraints but at a the cost of lost of some existence guaranty of the output mesh.