SIAM IMR25: Program

Artificial Intelligence in Mesh Generation: Transforming Computational Science and Engineering

Abdullah Dabdoub, Ecole Normale Supérieure Paris-Saclay
Sami Abdelmalek, University of Chlef and the Algerian Foundation for Science and Technology (AFST)
Abdelkader Krimi, Ecole Polytechnique de Montreal - University of Montreal
Mohamed Labadi, University of Chlef and Frontiers Labs

Keywords: Meshing, High-Fidelity Meshes, Artificial Intelligence, Machine Learning, Multi-Physics Simulation, Computational Efficiency

Abstract

Artificial intelligence and machine learning are revolutionizing mesh generation by enabling the creation of high-quality meshes that enhance computational efficiency and accuracy in simulations. This paper examines the integration of AI techniques into mesh generation workflows, focusing on optimization-driven methodologies. AI-based approaches allow for the automatic adjustment of mesh parameters, producing meshes that represent complex geometries with high fidelity. These advancements are particularly impactful in multi-physics modeling and simulation, where mesh quality is critical for accurate, robust, and efficient computational workflows. The work highlights the implications of these innovations for computational science and engineering, discussing challenges and opportunities in adopting AI-based mesh generation techniques.

Supervised Learning for Computer-Aided Design (CAD): Towards Clean-up and Defeaturing

Nick Winovich, Sandia National Laboratories
Michael Penwarden, Sandia National Laboratories
Clint Stimpson, Sandia National Laboratories
Steven Owen, Sandia National Laboratories
Sam Parry, Sandia National Laboratories

Keywords: CAD, defeaturing, supervised learning, machine learning, mesh quality prediction

Abstract

Computer-Aided Design (CAD) models are a core component of the industrial design process; however, they often require significant modifications to facilitate computational simulations that accurately reflect the target physics. This defeaturing process involves carefully modifying the geometry to meet meshing, physics, and computational requirements to enable efficient and accurate simulations. Defeaturing is essential for preparing CAD models for simulation, but it demands substantial user expertise and is often time-consuming, creating a bottleneck in the design-to-simulation workflow. To address this, we propose a machine learning approach aimed at automating the defeaturing process while keeping expert input in the loop. Our approach uses mesh quality metrics as proxies for simulation suitability, leveraging machine learning to predict the necessary CAD operations based on anticipated mesh out- comes. We develop new machine learning features for predicting meshing outcomes, extending the feature sets developed in previous work [2, 4, 3]. Using models from the open-source ABC repository [1], we compile an extensive training dataset to address issues with variability in meshing outcomes and improve the generalization capabilities of the models. We train and evaluate a collection of random forest and neural network models to predict mesh quality based on the geometric features extracted from the CAD models. Initial results show the potential for high-accuracy mesh quality predictions to be made prior to meshing, enabling analysts to automatically identify problematic regions. In future research, we plan to extend this procedure to per- form engineering-specific and physics-based defeaturing; we also plan to explore applications of reinforcement

To Mesh or Not to Mesh: Opportunities and Challenges of AI/ML for Mesh-based and Meshfree Computational Methods

Abdullah Dabdoub, Ecole Normale Supérieure Paris-Saclay
Abdelkader Krimi, Ecole Polytechnique de Montreal - University of Montreal
Samir Abdelmalek, University of Chlef and the Algerian Foundation for Science and Technology (AFST)
Sofiane Bousabaa, Sorbonne Université (Institut Jean Le Rond d'Alembert) and ONERA
Mohamed Labadi, University of Chlef and Frontiers Labs

Keywords: Mesh-based methods, Meshless methods, Artificial Intelligence, Machine Learning, Multi-Physics Simulation, Computational Efficiency

Abstract

Artificial intelligence (AI) and machine learning (ML) are revolutionizing computational methods, offering innovative solutions for challenges in both mesh-based and meshfree (or meshless) approaches. This paper explores the transformative potential of AI/ML in these paradigms, analyzing their respective opportunities and limitations. For mesh-based methods, AI enables advancements in automatic mesh generation, adaptive refinement, and error estimation, leading to more efficient solvers and higher fidelity in simulations. In contrast, meshfree methods, characterized by their flexibility and adaptability, benefit significantly from AI-driven optimization of point distributions, kernel parameterization, and novel boundary condition handling.

By comparing the impact of AI/ML on these two computational frameworks, we identify areas where these technologies provide incremental enhancements versus those enabling paradigm-shifting breakthroughs. The paper also examines the challenges of integrating AI, including computational overhead, algorithmic scalability, and data requirements, offering insights into future research directions. This comparative study underscores the potential of AI/ML to redefine computational science and engineering, particularly in tackling complex multi-physics problems and advancing next-generation simulation capabilities.

Mesh Adaptation with Cell Size Control for hypersonic flow simulations

Brieuc Praud, CEA
Laurent Muscat, CEA
Jérôme Breil, CEA

Keywords: mesh generation, mesh adaptation, Voronoi mesh, Lloyd’s algorithm, hypersonic flows

Abstract

Unstructured meshes are essential in the field of physics computation, both for discretizing complex geometries and for adapting to the underlying physical phenomena. Polygonal meshes constructed from Voronoi diagrams, despite being tougher to construct, sometimes provide several assets over triangular meshes based on Delaunay triangulations. These specific assets depend on the numerical method that is used. High quality meshes are obtained from specific Voronoi diagrams called Centroidal Voronoi Tessellations (CVTs). The process for building such diagrams can also be harnessed to perform mesh adaptation. The purpose of this work is to introduce a formulation of cell size control on Voronoi meshes as a root finding problem relying on a new initialization method for weighted Lloyd’s algorithm to speed up the construction of a proper mesh. The method is finally applied to the simulation of a hypersonic flow.

Monte Carlo Tree Search Based Block Decomposition of CAD Models

Cristina Garcia-Cardona, Garcia-Cardona
Rao Garimella, Los Alamos National Laboratory
Navamita Ray, Los Alamos National Laboratory
Jean-Christophe Janodet, IBISC Lab
Franck Ledoux, CEA
Paul Bourmaud, CEA

Keywords: MCTS, CAD decomposition, Automatic method

Abstract

Decomposition of CAD models into shapes amenable for automatic meshing such as blocks is a crucial step in hexahedral mesh generation. In this paper, we propose a Monte Carlo Tree Search (MCTS) based approach to obtain possible decomposition solutions for a given CAD model which can be subsequently used for mesh generation. This prototype study shows promise in automating the decomposition of complex shapes into blocks and could be combined in the future with a machine learning methods to enhance the method.

Fast and Robust Hexahedral Mesh Optimization via Augmented Lagrangian, L-BFGS, and Line Search

Yongjie Zhang, Carnegie Mellon University
Hua Tong, Carnegie Mellon University

Keywords: hexahedral mesh optimization, jacobian, L-BFGS, line search, augmented Lagrangian

Abstract

We present a new software package, ``HexOpt,’’ for improving the quality of all-hexahedral (all-hex) meshes by maximizing the minimum mixed scaled Jacobian-Jacobian energy functional, and projecting the surface points of the all-hex meshes onto the input triangular mesh. The proposed HexOpt method takes as input a surface triangular mesh and a volumetric all-hex mesh. A constrained optimization problem is formulated to improve mesh quality using a novel function that combines Jacobian and scaled Jacobian metrics which are rectified and scaled to quadratic measures, while preserving the surface geometry. This optimization problem is solved using the augmented Lagrangian (AL) method, where the Lagrangian terms enforce the constraint that surface points must remain on the triangular mesh. Specifically, corner points stay exactly at the corner, edge points are confined to the edges, and face points are free to move across the surface. To take the advantage of the Quasi-Newton method while tackling the high-dimensional variable problem, the Limited-Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm is employed. The step size for each iteration is determined by the Armijo line search. Coupled with smart Laplacian smoothing, HexOpt has demonstrated robustness and efficiency, successfully applying to 3D models and hex meshes generated by different methods without requiring any manual intervention or parameter adjustment.

Exploring polyhedral mesh generation from Delaunay tetrahedral meshes

Magdalena Álvarez, University of Chile
Nancy Hitschfeld-Kahler, University of Chile
Sergio Salinas-Fernández, University of Chile

Keywords: Volume mesh generation, arbitray shape, Polylla

Abstract

In this paper, we present the conceptual framework and a new algorithm for building polyhedral cells by the union of tetrahedrons. Two tetrahedrons are joined if the shared face fulfills some criteria. As preliminary results, statistics of the polyhedral cells generated by using the face area and the face in-circle radius metrics as joining criteria, are shown and discussed.

Efficient nearest neighbor searching on the sphere for computing Voronoi diagrams

Philip Caplan, Middlebury College

Abstract

Power diagrams (a generalization of Voronoi diagrams) can be used to perform particle-based fluid simulations of the atmosphere by solving a semi-discrete optimal transport problem at each time step of the simulation. Such an approach requires calculating several spherical Voronoi diagrams at each time step, so this calculation must be as efficient as possible. Voronoi diagrams can be efficiently computed by iteratively intersecting each cell with the halfspaces defined between a site and each of its nearest neighbors until the radius of security is reached. Computing these nearest neighbors for points on the sphere with a kd-tree is slower compared to using a kd-tree for points distributed in a cube. Alternatively, once an initial Voronoi diagram is obtained, the dual Delaunay edges incident to each site can be traversed in a breadth-first manner to compute nearest neighbors for subsequent Voronoi diagram calculations. Another idea employs a Spherical Quadtree to find the triangles containing each site at successive subdivisions of an octahedron, which are then used to find nearest neighbors. The performance of all three nearest neighbor approaches is first analyzed, and then the resulting Voronoi diagrams are used to perform particle-based fluid simulations on the sphere.

Data Structures for Fast Polyhedral Intersections in 3D

Daniel Shevitz, Los Alamos National Laboratory
Rao Garimella, Los Alamos National Laboratory
Joseph Donato, Los Alamos National Laboratory

Keywords: Computational Geometry, Polyhedral Intersection

Abstract

The operation of intersecting two polyhedra is fundamental to intersection based remap and interpolation. This is done under the assumption that one of the two polyhedra is convex and we clip the other polyhedra with the planes representing the faces of the convex polyhedra. R3D is a widely used library for such operation which implements the algorithm of Sugihara. In this paper, we describe the implementation of R3D, its shortcomings, and propose a novel implementation named J3D which provides substantial performance improvements.

Quadrilateral Parameterization and Layout Simplification for Open Surfaces Using Homotopy Theory

Rene Hiemstra, TU Darmstadt
Xianfeng David Gu, Stony Brook University
Thomas J. R. Hughes, University of Texas at Austin
Kendrick Shepherd, Brigham Young University

Keywords: Quadrilateral mesh, mesh simplification, isogeometric analysis

Abstract

Quadrilateral mesh generation plays a critical role in generating shell models for structural analysis, for reconstructing computer-aided design spline models, and for mapping and sweeping operations for volumetric meshes. Recent techniques for quadrilateral mesh generation focus on defining a layout-inducing parameterization and then prescribing appropriate constraints, often through integer-based optimization, to both ensure validity of the parameterization and to yield meshes with high quality connectivity between singular points. In this work, we present an alternative approach to prescribe connectivity constraints for parameterization- based quadrilateral mesh generation based on homotopy theory of branched covering spaces defining quadrilateral layouts. Important theoretical motivation is first discussed, after which the theory is leveraged for automated layout improvement for a variety of industrial shell structures.

Topological Evolution of Semiconductor Meshes

Sandeep Koranne, Siemens EDA

Keywords: PDE, parasitic extraction, capacitance fieldsolver, hardware implementation

Abstract

Parasitic extraction using 3D fieldsolvers and 2.5D rule engines for advanced process nodes (such as 3nm and below) require mesh creation and evolution for solving the electrostatic Maxwell’s equation. In this paper, a topological evolution method is described which optimizes the mesh and its underlying matrix memory when the mesh is modified. Unlike temporal evolution, which can use frontiers, and is continuous, topological evolution can undergo local as well as non-local modifications, making this a challenging problem. Moreover, design sizes in VLSI now routinely require this evolution for mesh sizes of 100 million elements; therefore computation and memory efficiency are central to the design of this method. We consider the following problems:

• Should the mesh be a regular bitmap or irregular Hanan grid?
• As the topology of the wire under consideration changes, should the mesh be reconstructed from scratch or can we evolve the mesh by incrementally changing some mesh elements?
• Can an unrolled linked list implementing the mesh prove helpful for evolution and even refinement?
• Are signed distance fields better at representing trapezoids?
• The proposed meshing and analysis scheme should be amenable to hardware synthesis and GPU implementation

Fast Approach for intersecting Numerous Polyhedra with scalability on Gpus: FANG

Daniel Shevitz, Los Alamos National Laboratory
Rao Garimella, Los Alamos National Laboratory
Jacob Jones, Los Alamos National Laboratory

Keywords: Polyhedra Intersection, GPUs, Remap, Moment Calculation

Abstract

Polyhedron intersection is a fundamental problem in computational geometry with applications in fields such as interface reconstruction, high-order remap, and nu- merical methods requiring polyhedra moments. Tra- ditional methods for polyhedra intersection based on the ”Clip-and-Cap” method are hard to port to GPUs for harnessing their parallel processing capabili- ties. This is because the computational complexity of a kernel that clips an arbitrary polyhedron with a plane can be highly variable whereas GPUs and other accel- erators, prefer simple kernels with fixed complexity. In this paper, we propose a novel approach to efficiently compute polyhedra-polyhedra intersections on GPUs by decomposing all polyhedra into tetrahedra and per- forming exclusivley tetrahedra-tetrahedra intersections in parallel. This method, while increasing the number of intersection tests, reduces and bounds the complex- ity of each intersection operation making it amenable to porting to the GPU. We optimize the efficiency of the tetrahedra-tetrahedra intersection algorithm by pre- computing bounding boxes to eliminate non-intersecting pairs and using static arrays to avoid dynamic mem- ory allocation. Additionally, we address the efficient implementation of tetrahedra-plane intersections, iden- tifying five geometric cases and precomputing resulting topologies for rapid lookup. Our approach simplifies the problem of polyhedra intersection and reduces it to many smaller computations, making it well-suited for applications requiring high-performance geometric pro- cessing. Experimental results validate the effectiveness and scalability of our method on CPUs with with the porting and testing on GPUs planned as the next steps

Direct Alpha-Shape on the GPU

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

Keywords: computational geometry, GPU computing, alpha-shapes, triangulations, delaunay triangulations

Abstract

In this note, we describe an innovative method for computing the triangulation of the alpha-shape of a point set displaying two benefits. First, it avoids the computation of the Delaunay triangulation – hence directly computing the alpha-shape. Second, it is entirely local and efficient on the GPU. Our method is two orders of magnitude faster than CGAL’s implementation.

High-Order Mesh Adaptivity Using Goal-Oriented Error Estimation

Tzanio Kolev, Lawrence Livermore National Laboratory
Ketan Mittal, Lawrence Livermore National Laboratory
Boyan Lazarov, Lawrence Livermore National Laboratory
Mathias Schmidt, Lawrence Livermore National Laboratory
Vladimir Tomov, Lawrence Livermore National Laboratory

Keywords: mesh adaptivity, goal-oriented, TMOP, adjoint sensitivity

Abstract

We explore a new approach to goal-oriented mesh optimization in PDE-driven computational simulations. Targeting high-order mesh adaptivity, the approach combines geometric quality optimization with control of the PDE solution error. By leveraging the Target-Matrix Optimization Paradigm (TMOP) in conjunction with adjoint sensitivity analysis, the method employs a goal-oriented error estimation framework to optimize the mesh adaptively. We demonstrate that the optimized mesh simultaneously achieves good geometric quality and reduces the PDE solution error in regions critical to a predefined computational objective.

High-Order Mesh Validity Detection

Tarik Dzanic, Lawrence Livermore National Laboratory
Tzanio Kolev, Lawrence Livermore National Laboratory
Ketan Mittal, Lawrence Livermore National Laboratory

Abstract

High-order meshes are essential for achieving optimal convergence rates on domains with curved surfaces, mesh alignment with physical flow/fields, moving mesh simulations, and symmetry preservation. A well known challenge with high-order curvilinear meshes is ensuring the positivity of the Jacobian determinant everywhere in the mesh. We present a novel technique to bound polynomial extrema in high-order finite element approximations. This technique is used to compute bounds on the Jacobian determinant in each element to determine mesh validity. We also incorporate these bounds in $r$-adaptivity to guarantee the positivity of Jacobians in the optimized mesh if the initial mesh is valid.

Simplified Dense and Coarse higher-order Mesh Generation Using Moving Least Squares

Cornelis Vuik, Delft University of Technology
Matthias Möller, Delft University of Technology
Vijai Kumar Suriyababu, Delft University of Technology

Keywords: surface reconstruction, moving least squares, higher order mesh, distance fields

Abstract

Higher-order surface and volume meshes are essential for better approximating PDEs. While a large body of literature focuses on PDE solvers for higher-order methods, there is still a need for robust grid generators that can produce higher-order surface/volume meshes. We propose practical workflows that provide fully automatic processes for higher-order mesh generation. We utilize the MLS algorithm, demonstrating its robustness in higher-order surface reconstruction. We also show its effectiveness in generating higher-order meshes in geometries with non-uniform triangulation, aided by intermediate support structures. Building on the recent advancements in surface multigrid methods, we propose the simplest coarse higher-order mesh generation approach to date. We illustrate the proposed workflows with a handful of examples to showcase their utility and effectiveness.

Hexahedral Mesh Generation for Swept Splines Using Foliations

Kendrick M. Shepherd, Brigham Young University
Caleb B. Goates, Brigham Young University

Keywords: splines, sweeps, meshing, computational geometry

Abstract

We introduce a method to create trivariate parameterizations of swept geometries from which we can create hexahedral cell complexes for trivariate splines and hex meshes. Starting with a linear tetrahedral mesh, we solve a discrete Laplace equation and use the level sets of the resulting discrete harmonic function as a two-dimensional foliation of the swept geometry. We can then extend an unstructured bivariate mesh over the sweep source surface to the entire swept geometry using bijective maps between foliation leaves. Our approach overcomes several difficulties found in harmonic function gradient tracing approaches. We also discuss under what conditions this method creates sweep-appropriate foliations, and the applications of these limitations to other harmonic-function-based approaches.

Large-Scale Mesh Curving for the 5th High-Lift Prediction Workshop

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

Keywords: Mesh curving; Large scale; Complex geometry

Abstract

To take advantage of unstructured high-order methods, practitioners require a high-order curved mesh that discretizes the computational domain. To address this need, we have developed a curving technique to generate geometrically accurate distributed meshes composed of optimal-quality elements. Remarkably, our curving method has allowed us to provide meshes for the challenging geometries of the High-Lift Prediction Workshop. Our meshes have been tested and shown to be suitable for simulation purposes, yielding accurate solutions consistent with wind tunnel data.

In this work, we will describe the development of our curving method and its unique features, such as using floating meshes to approximate a virtual model and fully converge the optimization process to obtain optimal-quality curved meshes. We will also detail the challenges of generating meshes for the 5th High-Lift Prediction Workshop and our conclusions on large-scale mesh curving for complex geometries.

A flexible and path-preserving algorithm for curvilinear $P^2$ mesh generation based on Riemann geometry

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, Constrained delaunay triangulation, High-order error

Abstract

We propose a new framework for curvilinear mesh generation and adaptation that consists of several key components: A new algorithm for generating boundary mesh points ensures a uniform distribution along each boundary line. A flexible algorithm for generating mesh points in the computational domain allows meshing in optional numbers of directions or combinations thereof. A constrained Delaunay triangulation method that preserves the vertex generation paths. An enhanced algorithm for curving straight-sided edges improves the accuracy and efficiency of curvilinear edge triangles. Improvements in both the straight-sided edge swapping and curvilinear edge swapping algorithms increase the overall efficiency.

Grid generation and image registration

Baihan Zhao, University of Texas at Arlington
Zicong Zhou, University of North Texas
Guojun Liao, University of Texas at Arlington

Abstract

This paper has two parts. In Part 1, We describe a new grid generation method which generates grids with prescribed Jacobian determinant and curl vector field. The method is based on an optimal control approach which minimizes a functional consisting of the Jacobian determinant and curl under the constraint of a Poisson equation. In Part 2, we apply the grid generation method to image registration problem, which is the process of aligning similar pixels of two or more images and expressing the pixel correspondence by a deformed grid. The grid generation method provides a new methodology for the image registration problem. We show how to find the registration grid in the space of smooth and unfolded grids controlled by the Jacobian determinant and curl vector. Numerical examples with brain images will be presented to demonstrate the effectiveness of the new method.

A geometric method for automatic generation of orthogonal grids on meander-like regions

Gustavo Adolfo Restrepo Arboleda, Universidad Nacional de Colombia
Marco Paluszny, Universidad Nacional de Colombia

Keywords: orthogonal mesh, meander-like region, automatic grid generation

Abstract

We present a method to generate approximately orthogonal meshes over meander-like regions. Essentially, it depends on two conformal maps f(z) = 0.5(z + 1/z) and f(z) = (z + 1)(z − 1) that allow to transfer orthogonally gridded regions in an annulus to tiles that populate the meander-like region. The tiles are built using confocal lemniscates, ellipses and hyperbolas which are stitched together to create an approximately orthogonal grid on the whole meander-like region which is adapted to both boundaries. The quality of the grid is assessed using standard criteria involving angles and areas. As opposed to previous work we do not use sequential non linear optimization, instead we compare normalized segments of boundary with elements in a database. The database consists of approximately 50 thousand discretized arcs of lemniscates, ellipses and hyperbolas. The computational efficiency of the comparison process is improved by clusterizing the database, this reduces the comparison to the fitting of normalized segments of the meander-like region with cluster representatives.

Quad Mesh Density Control using Optimal Transport

Yuyang Cao, Stony Brook University
Yue Wang, Stony Brook University
Yiming Zhu, Dalian University of Technology
Hang Si, Cadence Design Systems Inc
Zhongxuan Luo, Dalian University of Technology
Xianfeng Gu, Stony Brook University
Na Lei, Dalian University of Technology

Keywords: quad mesh, density control, optimal transport

Abstract

Surface quadrilateral mesh generation plays a fundamental role in CAD/CAE fields. It is crucial to control the density of the meshing structures in practice.

In this work, a novel method for controlling the density of quad meshes is proposed based on the Optimal Mass Transport theory (OT). This method has a rigorous mathematical foundation and efficient and robust computational algorithms. It provides the designers with the flexibility to control the meshing density by prescribing arbitrary probability density functions on the surface. This work demonstrates the efficiency and efficacy of the method using topological disk models, in principle, the method can be generalized to surfaces with arbitrary topologies.

Quadrilateral Mesh Generation for High Genus Surfaces with Multiple Boundaries Based on Symmetric Abel Differentials

Yiming Zhu, Dalian University of Technology
Xiaopeng Zheng, Dalian University of Technology
Zhongxuan Luo, Dalian University of Technology
Hang Si, Cadence Design Systems Inc
Xianfeng David Gu, Stony Brook University
Na Lei, Dalian University of Technology

Keywords: Quad Mesh, Symmetric Abel Differential, Hodge Decomposition

Abstract

This study introduces a quadrilateral mesh generation method tailored for high-genus surfaces with multiple boundaries, utilizing symmetric Abel differentials. Grounded in robust theoretical principles, this method generates high-quality quad meshes characterized by exceptional orthogonality and minimal singularity presence. Additionally, the grid lines are strategically aligned with the boundaries, enhancing the mesh’s structural integrity and applicability in complex modeling scenarios.

Polycubes via Dual Loops

Kevin Verbeek, TU Eindhoven
Bettina Speckmann, TU Eindhoven
Maxim Snoep, TU Eindhoven

Keywords: polycube, polycube map, polycube segmentation

Abstract

We present a complete characterization of polycubes of any genus based on their dual structure: a collection of oriented loops which run in each of the axis directions and capture polycubes via their intersection patterns. A polycube loop structure uniquely corresponds to a polycube. We also describe all combinatorially different ways to add a loop to a loop structure while maintaining its validity; similarly, we show how to identify loops that can be removed from a polycube loop structure without invalidating it. Our characterization gives rise to an iterative algorithm to construct provably valid polycube-maps for a given input surface; polycube-maps are frequently used to solve texture mapping, spline fitting, and hexahedral meshing. We showcase some results of a proof-of-concept implementation of this iterative algorithm.

Validity-first automatic polycube labeling for CAD models

Christophe Bourcier, CEA
Franck Ledoux, CEA
Sébastien Mestrallet, CEA

Keywords: hexahedra, hex-mesh, block-structured, polycube, labeling, CAD models

Abstract

For many simulation codes, block-structured hex meshes remain preferred while their automatic generation is unsolved. We investigate the usage of a polycube-based approach. More specifically, we focus on the labeling stage which consists in assigning each boundary facet to one of the 6 signed principal axis. Similar works are confronted with 2 challenges: over-constraining validity criteria, and the mixed-up processing of validity criteria with quality metrics. We tackled these obstacles with automatic routines based on semi-global labeling operators. Our approach is successfully tested on CAD models, which are of interest for many numerical simulation problems.

C1-Smooth Parametrization of Polynomial Shapes over Polygonal Domains

Marcel Campen, Osnabrück University
Payam Khanteimouri, Osnabrück University

Keywords: high-order, triangle meshing, smoothness, continuity

Abstract

The generation of meshes and mesh-based parametrizations for given geometric domains is a cornerstone of modeling and analysis. Of particular interest in this context are spaces of increased smoothness, in terms of the continuity order across elements. We describe a method to, by means of higher-order mesh generation, construct a parametrization of 2D shapes with curved boundaries, with a focus on C1-continuity. Different from previous work, this method guarantees the absence of inversions or degeneracies as well as exact conformance to the given polynomial boundary. It leverages recent results on higher-order triangle mesh generation with guaranteed quality bounds. These bounds enable us to formulate an optimization problem aiming for continuity while maintaining validity.

Fast practical untangling of curvilinear meshes

Guillaume Coiffier, Université catholique de Louvain
Amaury Johnen, Université catholique de Louvain
Jean-François Remacle, Université catholique de Louvain

Keywords: High order meshing

Abstract

What is proposed here is to systematically reduce the untangling of any high-order elements to the problem of untangling simplices (triangles in 2D and tetrahedra in 3D). First, we present a general way of expressing the validity of a high-order element by calculating linear combinations of areas of well-chosen simplices. We then show how to adapt [3] to these linear combinations of simplices. Examples of 2D boundary layer untangling are presented with P2 and P3 elements. The algorithm is then adapted to P2 tetrahedra.

Texas oilfield in Bluebonnets

Alexander Rand, Siemens
Ken Blake, Siemens
Kevin Jones, Siemens
Ian Young, Siemens
Ryan Lin, Siemens
Scott Canann, Siemens
Sumit Paranjabe, Siemens
Tuo Liu, Siemens

Mesh Generation for the Simulation of Metal Casting Processes

Robert Schneiders, Magma Giessereitechnologie GmbH
Andreas Schulz, Magma Giessereitechnologie GmbH
Jan Thomsen, Magma Giessereitechnologie GmbH

Single Surface Spline Reconstruction by Distortion-Minimizing Flattening

Rebecca Rasmussen, Brigham Young University
Kendrick Shepherd, Brigham Young University

Keywords: Spline reconstruction, isogeometric analysis

Abstract

Structural integrity of a variety of engineering structures is frequently best assessed using a two-dimensional shell midsurface embedded in three-dimensional space, rather than the full volumetric representation of the model. However, computer-aided geometric design models are seldom suitable for downstream operations, including structural analysis, because the models are comprised of multiple trimmed surfaces that prove problematic when coupled using known solver methods. In this research, we present automated, theory-based techniques to convert open B-rep and mesh surfaces into analysis-ready spline models represented as a single trimmed spline surface—a representation used in many state-of-the-art isogeometric analysis representations. Here, a parametric domain of an open geometric model is defined by flattening a surface into the Euclidean plane and then optimizing its geometry to approximate an isomorphism. An approximating spline is then defined based on the correspondence between the original surface and its parametric domain. Interpolation and extrapolation operations are defined to naturally extend the spatial domain of the original geometry to be valid for the entire reconstructed spline surface. We demonstrate the success of the method in reconstructing and analyzing CAD models of both aerospace and automotive interest.

Automatic Multi-Material Mesh Generation for the Simulation of Metal Casting Processes

Jan Thomsen, MAGMA Giessereitechnologie GmbH
Andreas Schulz, MAGMA Giessereitechnologie GmbH
Robert Schneiders, MAGMA Giessereitechnologie GmbH

Keywords: Mixed element mesh; multi material; automatic; robust

Abstract

We describe a robust algorithm for the automatic generation of mixed-element meshes for multimaterial domains. Geometries are given as a set of overlapping triangulations, with minimal requirements to geometric quality. The algorithm overlays a geometry with a simple base mesh which is then adapted to the internal and external boundaries. Invalid elements are dealt with by smoothing, splitting, topology changes and optimization so that only valid elements remain. No user intervention is required.

Tusqh: Topological Control of Volume-Fraction Meshes Near Small Features and Dirty Geometry

Kendrick Shepherd, Brigham Young University Department of Civil and Construction Engineering
Scott Mitchell, Sandia National Laboratories, Center for Computing Research
Brian Shawcroft, Brigham Young University Department of Civil and Construction Engineering and Sandia National Laboratories, Center for Computing Research

Abstract

This work develops a framework through which meshes with user-specified homology can be created from potentially dirty geometry by coupling background grids, persistent homology, and a generalization of volume fractions. For a mesh with fixed grid size, the topology of the output mesh changes predictably and monotonically as its volume-fraction threshold decreases. Topological anti-aliasing methods are introduced to resolve pinch points and disconnected regions that are artifacts of user choice of grid size and orientation, making the output meshes suitable for downstream processes including analysis. The methodology is demonstrated on geographical, mechanical, and graphics models in 2D and 3D using a custom-made software called Tusqh. The work demonstrates that the proposed framework is viable both for generating meshes on topologically invalid geometries and for automatic defeaturing of small geometric artifacts. Finally, the work shows that although subdividing the background grid frequently improves the topological and geometrical fidelity of the output mesh, there are simple 2D examples for which the topology does not converge under refinement for volume-fraction codes.

Parallelization of the Finite Element-based Mesh Warping Algorithm Using Hybrid Parallel Programming

Suzanne Shontz, University of Kansas
Abir Haque, University of Kansas

Keywords: Mesh Warping, Finite Element, Hybrid Parallel Programming, Message Passing Interface

Abstract

Warping large volume meshes has applications in biomechanics, aerodynamics, image processing, and cardiology. However, warping large, real-world meshes is computationally expensive. Existing parallel implementations of mesh warping algorithms do not take advantage of shared-memory and one-sided communication features available in the MPI-3 standard. We describe our parallelization of the finite element-based mesh warping algorithm for tetrahedral meshes. Our implementation is portable across shared and distributed memory architectures, as it takes advantage of shared memory and one-sided communication to precompute neighbor lists in parallel. We then deform a mesh by solving a Poisson boundary value problem and the solution of the resulting linear system with multiple right-hand sides in parallel. Our results demonstrate excellent efficiency and strong scalability on up to 32 cores on a single node. Furthermore, we show a 90% increase in speedup with 256 cores distributed uniformly across 64 nodes versus our largest single node speedup while observing sublinear speedups overall.

Linear-algebraic representation and transformation of unstructured meshes

Daniel Shapero, University of Washington

Keywords: mesh generation, computational geometry, algebraic topology

Abstract

This paper will show some new approaches for implementing common transformations to the connectivity or topology of an unstructured mesh. The key enabling technology for our approach is to borrow ideas from algebraic topology: we use the boundary operators of a chain complex to represent the mesh. Boundary operators are really just integer matrices. By representing the objects of study using the language of linear algebra, we can use linear algebraic reasoning and intuition to define transformations. We show how to implement a few common transformations on the boundary operator representation: merging cells, splitting cells on a new vertex, and splitting a cell on facets. The source code for these transformations becomes short and easy to test.