SIAM International Meshing Roundtable 2023 (Lecture Notes in Computational Science and Engineering, 147)

SIAM International Meshing Roundtable Workshop 2023 Organization
Reviewers
Preface
Contents
Data Structures and Management
Generation of Polygonal Meshes  in Compact Space
	1 Introduction
	2 Background
		2.1 Compact Representation of a Planar Graph
		2.2 Half-Edge Data Structure
		2.3 pemb Data Sructure
		2.4 The Polylla Algorithm
	3 Half-Edge Data Structure Implementation
		3.1 Non-compact Half-Edge: AoS half-edge
		3.2 Compact Half-Edge
		3.3 Additional Data Structures
	4 Half-Edge Polylla Algorithm
		4.1 Label Phase
		4.2 Traversal Phase
		4.3 Repair Phase
	5 Experiments
		5.1 Implementation
		5.2 Datasets
		5.3 Experimental Setup
		5.4 Results
	6 Conclusions and Future Work
	References
Efficient KD-Tree Based Mesh Redistribution for Data Remapping Algorithms
	1 Introduction
	2 Bounding Box Algorithm
	3 Mesh Redistribution Using a KD-Tree
		3.1 Target Mesh Shape Approximation
		3.2 Overlap Detection
		3.3 Mesh Migration
	4 Numerical Results
		4.1 Sphere Shell Mesh
		4.2 Tesseract Mesh
	5 Conclusion
	References
Coupe: A Mesh Partitioning Platform
	1 Introduction
	2 Mesh Partitioning and Load Balancing
		2.1 Balance Oriented Partitioning
		2.2 Geometric Partitioning
		2.3 ``Communication\'\' Optimized Partitioning
		2.4 ``Memory\'\' Optimized Partitioning
		2.5 Other Specificities
	3 Algorithms
		3.1 Direct Algorithms
		3.2 Refinement Algorithms
		3.3 Algorithms Composition
	4 Coupe: A Platform Dedicated to Mesh Partitioning
		4.1 Rust as Primary Development Language
		4.2 Integration with Other Languages
		4.3 The Coupe Toolkit
	5 Experiments
	6 Conclusion and Perspectives
	References
Formal Definition of Hexahedral Blocking operations Using n-G-Maps
	1 Introduction
		1.1 State of the Art
		1.2 Main Contributions and Outlook
	2 Representing Block Structures with n-G-Maps
		2.1 N-G-Map to Represent Topology
		2.2 Orbits and Geometry Classification
		2.3 Atomic Modification Operations
	3 Hexahedral Blocking Operations
		3.1 Sheet Selection
		3.2 Sheet Collapse
		3.3 Sheet Insertion
	4 Conclusion and Future Works
	References
Machine Learning
Machine Learning Classification  and Reduction of CAD Parts
	1 Introduction
	2 Background
	3 Overview
	4 Features
	5 Ground Truth
	6 Machine Learning Methods
		6.1 Neural Network
		6.2 Ensemble of Decision Trees
	7 In-Situ Classification
	8 Results
	9 Comparison
	10 Implementation
		10.1 Training
		10.2 Prediction
	11 Reduction of CAD Parts
		11.1 Fastener Reduction
		11.2 Spring Reduction
	12 Conclusion
	References
Predicting the Near-Optimal Mesh Spacing for a Simulation Using Machine Learning
	1 Introduction
	2 Mesh Spacing and Control
		2.1 Mesh Spacing Controlled by Sources
		2.2 Mesh Spacing Controlled by a Background Mesh
	3 Target Spacing
	4 Spacing Description Using Sources
		4.1 Generating Point Sources for One Solution
		4.2 Generating Global Sources for a Set of Solutions
	5 Spacing Description Using a Background Mesh
		5.1 Interpolating the Spacing on a Background Mesh
	6 Using a Neural Network to Predict the Spacing
		6.1 Spacing Prediction Using Sources
		6.2 Spacing Prediction Using a Background Mesh
	7 Numerical Examples
		7.1 Near-Optimal Mesh Predictions on the ONERA M6 Wing
		7.2 Near-Optimal Mesh Predictions on the Falcon Aircraft
	8 Concluding Remarks
	References
Mesh Generation for Fluid Applications
Block-Structured Quad Meshing  for Supersonic Flow Simulations
	1 Introduction
		1.1 State of the Art
		1.2 Main Contributions
	2 Terminology and Problem Statement
		2.1 Supersonic Vehicle and Environment
		2.2 Approach Overview
	3 Block-Structured Mesh Generation Algorithm
		3.1 Vehicle Wall Block Discretization
		3.2 Fields Computation
		3.3 Blocking Generation
		3.4 From Blocks to Quadrilaterals
	4 Results and Applications
		4.1 Mesh Quality
		4.2 Navier–Stokes Equations
		4.3 Subsonic NACA 0012 Airfoil
		4.4 Supersonic Diamond Airfoil
	5 Conclusion
	References
Robust Generation of Quadrilateral/Prismatic Boundary Layer Meshes Based on Rigid Mapping
	1 Introduction
		1.1 Prismatic Mesh Generation
		1.2 Rigid Transformation
		1.3 Contribution
	2 Methods Overview
	3 Initial Mesh and Target Mesh Generation
		3.1 Initial Mesh Generation
		3.2 Target Mesh Generation
		3.3 Multiple Normals Configuration
	4 Rigid Mapping
		4.1 Problem Statement
		4.2 Energy Definition
		4.3 Positive Volume Gurantee
	5 Post Process
		5.1 Retention Layer
		5.2 Mesh Refinement
	6 Result
		6.1 IMR
		6.2 30P–30N Airfoil
		6.3 U-Shape
		6.4 DLR F6 (One Layer)
	7 Conclusion and Limitation
	References
Explicit Interpolation-Based CFD Mesh Morphing
	1 Introduction
	2 Mesh Morphing Environment
		2.1 Elements of Morphing Process
		2.2 Preprocessing Environment Interaction
		2.3 Morphing Application Space
	3 Structured Mesh Morphing
		3.1 Morphing Workflow Example
		3.2 Method Performance
	4 Unstructured Mesh Morphing
	5 Concluding Remarks
	References
Mesh Adaption and Refinement
A Method for Adaptive Anisotropic Refinement and Coarsening of Prismatic Polyhedra
	1 Introduction
	2 Methodology
		2.1 Isotropic PUMA Terminology
		2.2 Anisotropic PUMA Terminology
		2.3 Coarsening with PUMA
		2.4 Distributed Parallel PUMA
	3 Examples
		3.1 Refinement of a Tetrahedral Mesh with Boundary Layers
		3.2 Isotropic PUMA for the Dam Break Problem
		3.3 Anisotropic PUMA for Fuselage, Wing Configuration
		3.4 Combined Isotropic and Anisotropic PUMA for Space Capsule Re-Entry
	4 Conclusions
	References
Tetrahedralization of Hexahedral Mesh
	1 Introduction
	2 Background
		2.1 Hexahedral Triangulation
		2.2 Prism Decomposition
	3 General Hex-to-Tet: A General Algorithm for Tetrahedralizing a Hexahedral Complex
		3.1 Generalizing Prism Decomposition to Cubes
		3.2 Decomposition into Five Tetrahedra
		3.3 Solving the Degenerate Cases
		3.4 The Main Algorithm
	4 Conclusion and Future Work
	References
Combinatorial Methods in Grid Based Meshing
	1 Introduction
	2 Background
	3 Related Work
	4 Algorithm
	5 Super Element Generation
	6 Super Element Assignment
	7 Entity Mapping
	8 Results on Examples
	9 Conclusion and Future Work
	References
Estimating the Number of Similarity Classes for Marked Bisection in General Dimensions
	1 Introduction
	2 Preliminaries
		2.1 Simplicial Meshes, Conformity, and Bisection
		2.2 Marked Bisection
		2.3 Unique Mid-Vertex Identifiers
		2.4 Consistent Bisection Edge
		2.5 Similarity Classes
	3 Marked Bisection in General Dimensions
		3.1 Co-Dimensional Marking Process
		3.2 First Bisection Stage: Tree Simplices
		3.3 Second Bisection Stage: Casting to Maubach
		3.4 Third Stage: Maubach\'s Bisection
	4 Estimation of the Number of Similarity Classes
	5 Number of Uniform Refinements to Obtain All the Similarity Classes
	6 Examples
		6.1 Number of Similarity Classes
	7 Concluding Remarks
	8 Algorithms
	References
Cross Field Mesh Generation
Quadrilateral Mesh of Non-simply Connected Domain and Non-planar Surfaces From a Given Cross-Field
	1 Introduction and Related Work
	2 Quadrilateral Mesh From a Cross-Field
		2.1 Cross-Fields Definition
		2.2 Index
		2.3 Compatibility Constrain on the Cross-Field
		2.4 Alignment of Cross-Field
		2.5 Boundary Singularities
	3 Non-simply Connected Domains
	4 Case of Non-planar Surfaces
	5 Conclusion
	References
Ground Truth Crossfield Guided Mesher-Native Box Imprinting for Automotive Crash Analysis
	1 Problem Definition
	2 Previous Work
	3 Mesher-Native Imprinting Strategy
		3.1 Design and Architecture for Mesher-Native Shape Imprinting
		3.2 Mesh Imprinting Box-With-Hole Shape
		3.3 Shape Imprint Driven Multiblocking
	4 Mesh Direction Fields
		4.1 Method I: Minimum Oriented Bounding Box Based (MOBB)
		4.2 Method II: Ground Truth Frame/Cross Field Based (GTFF/GTCF)
	5 Box-With-Hole Orientation
	6 Hole Orientation Inside Box
	7 Meshing Algorithms for the Virtual Faces
		7.1 Washer Mesh Control
		7.2 Templatized Meshers for BWH Face
		7.3 Box Sizing
		7.4 Mesher Selection Algorithm
	8 Mesh Quality for Crash Analysis
	9 Conclusion
	Appendix I
	A UML Sequence Diagram of the Proposed Architecture for Mesher-Native Shape Imprinting
	Appendix II
	Performance Analysis
	References
Integrable Cross-Field Generation Based on Imposed Singularity Configuration—The 2D Manifold Case
	1 Introduction and Related Work
	2 Cross-Field Computation on Prescribed Singularity Configuration
		2.1 Curvature and Levi-Civita Connection on the 2D Manifold
		2.2 Conformal Mapping
	3 Integrability Condition with Isotropic Scaling
		3.1 H PDE on the Boundary
		3.2 H PDE in the Smooth Region on the Interior of M
		3.3 H PDE at Singular Points
		3.4 Boundary Value Problem for H
		3.5 Retrieving Crosses Orientation From H
	4 Preliminary Results
		4.1 Valid Singularity Configurations for Conformal Quad Meshing
		4.2 Dealing with Suboptimal Distribution of Singularities
	5 Integrability Condition with Anisotropic Scaling
		5.1 Local Manifold Basis Generation and θ Initialization
		5.2 Computing (H1,H2) From Imposed barθ
		5.3 Computing θ From (barH1 barH2)
		5.4 Minimizing Integrability Error E Regarding (θ,H1,H2)
	6 Conclusion and Future Work
	References
Element Design
Optimally Convergent Isoparametric upper P squaredP2 Mesh Generation
	1 Introduction
	2 Interpolation Error Model and Metric Tensor
		2.1 Curve Parameterizations
		2.2 Interpolation Error Estimate
		2.3 Optimal Metric
	3 Mesh Generation
		3.1 Principal Directions of the Mesh
		3.2 Vertices Generation and Triangulation
		3.3 Curving the Edges
		3.4 Making the Mesh Valid
		3.5 Edge Swaps
	4 Numerical Results
	5 Conclusion and Future Work
	References
Towards a Volume Mesh Generator Tailored for NEFEM
	1 Introduction
	2 NEFEM Fundamentals
		2.1 NEFEM Rationale
		2.2 Geometric Mapping of NEFEM Elements
	3 NEFEM Surface Mesh Generation
		3.1 Surface Meshing Strategy
		3.2 GS-Points
		3.3 The Sub-Mesh
		3.4 Validity Check
	4 NEFEM Volume Mesh Generation
		4.1 Volume Meshing Strategy
		4.2 Growing Volume Elements
		4.3 Self-intersection Check
	5 Examples
		5.1 A Flat Plate with Two Cylinders
		5.2 A Wing with a Blunt Trailing Edge
		5.3 Falcon Aircraft
	6 Concluding Remarks
	References
Curvilinear Mesh Generation for the High-Order Virtual Element Method (VEM)
	1 Introduction
	2 High-Order VEM Basics
		2.1 Extension to Curved Edges
	3 ``A posteriori\'\' High-Order VEM Mesh Generation
		3.1 Generation of the Straight-Sided Polygonal Mesh
		3.2 API to a CAD Engine for Geometrical Queries
		3.3 CAD Projection of Additional Points
		3.4 Ensuring Mesh Validity
		3.5 Implementation
	4 Verification and Example of Application
		4.1 VEM Verification
		4.2 A Practical 2D Geometry
	5 Conclusions and Further Work
	References
Refining Simplex Points for Scalable Estimation of the Lebesgue Constant
	1 Introduction
	2 Related Work
	3 Neighbor-Aware Coordinates for Point Refinement
		3.1 Outline
		3.2 Neighbor-Aware Coordinates
		3.3 Point Refinement
		3.4 Smooth Gradation
	4 Adaptive Point Refinement
		4.1 Algorithm
		4.2 Stopping Criterion
	5 Results: Estimation of the Lebesgue Constant
		5.1 Verification in 2D and 3D
		5.2 Performance Comparison in 2D
		5.3 Results in 4D, 5D, and 6D
	6 Concluding Remarks
	References