Numerical Geometry, Grid Generation and Scientific Computing

1. Front Matter

   Pages i-xx

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2. Delaunay-Voronoi Theory and Applications

   1. Front Matter

      Pages 1-1

      PDF

   2. Local Groups in Delone Sets

      • Nikolay Dolbilin

      Pages 3-11

   3. Manifolds of Triangulations, Braid Groups of Manifolds, and the Groups \(\Gamma _{n}^{k}\)

      • Denis A. Fedoseev, Vassily O. Manturov, Igor M. Nikonov

      Pages 13-36

   4. A Proof of the Invariant-Based Formula for the Linking Number and Its Asymptotic Behaviour

      • Matt Bright, Olga Anosova, Vitaliy Kurlin

      Pages 37-60

   5. The Singularity Set of Optimal Transportation Maps

      • Zhongxuan Luo, Wei Chen, Na Lei, Yang Guo, Tong Zhao, Xianfeng Gu

      Pages 61-80

   6. Polygonal and Polyhedral Delaunay Meshing

      • Vladimir Garanzha, Liudmila Kudryavtseva

      Pages 81-93

   7. On Decomposition of Embedded Prismatoids in \(\mathbb {R}^3\) Without Additional Points

      • Hang Si

      Pages 95-111

   8. Out-of-core Constrained Delaunay Tetrahedralizations for Large Scenes

      • Ziya Erkoç, Aytek Aman, Uğur Güdükbay, Hang Si

      Pages 113-124

3. Adaptive Meshing

   1. Front Matter

      Pages 125-125

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   2. Size Gradation Control for Anisotropic Hybrid Meshes

      • Lucille-Marie Tenkes, Frédéric Alauzet

      Pages 127-139

   3. Adjoint Computation on Anisotropic Meshes in High-fidelity RANS Simulations

      • Francesco Clerici, Frédéric Alauzet

      Pages 141-155

   4. Moving Deforming Mesh Generation Based on the Quasi-Isometric Functional

      • Vladimir A. Garanzha, Liudmila Kudryavtseva

      Pages 157-178

   5. Adaptive Grids for Non-monotone Waves and Instabilities in a Non-equilibrium PDE Model

      • Paul A. Zegeling

      Pages 179-198

   6. RBF-VerBSS Hybrid Method for Mesh Deformation

      • Jihai Chang, Fei Yu, Jie Cao, Zhenqun Guan

      Pages 199-212

   7. A Uniform Convergence Analysis for a Bakhvalov-Type Mesh with an Explicitly Defined Transition Point

      • Thái Anh Nhan

      Pages 213-226

   8. On a Comprehensive Grid for Solving Problems Having Exponential or Power-of-First-Type Layers

      • V. D. Liseikin, S. Karasuljic, A. V. Mukhortov, V. I. Paasonen

      Pages 227-240

   9. Preserved Structure Constants for Red Refinements of Product Elements

      • Sergey Korotov, Jon Eivind Vatne

      Pages 241-248

4. Meshing and CAD

   1. Front Matter

      Pages 249-249

      PDF

   2. Global Parametrization Based on Ginzburg-Landau Functional

      • Victor Blanchi, Étienne Corman, Nicolas Ray, Dmitry Sokolov

      Pages 251-262

The focus of these conference proceedings is on research, development, and applications in the fields of numerical geometry, scientific computing and numerical simulation, particularly in mesh generation and related problems. In addition, this year’s special focus is on Delaunay triangulations and their applications, celebrating the 130th birthday of Boris Delaunay.

In terms of content, the book strikes a balance between engineering algorithms and mathematical foundations. It presents an overview of recent advances in numerical geometry, grid generation and adaptation in terms of mathematical foundations, algorithm and software development and applications.

The specific topics covered include: quasi-conformal and quasi-isometric mappings, hyperelastic deformations, multidimensional generalisations of the equidistribution principle, discrete differential geometry, spatial and metric encodings, Voronoi-Delaunay theory for tilings and partitions, duality in mathematical programming and numerical geometry, mesh-based optimisation and optimal control methods. Further aspects examined include iterative solvers for variational problems and algorithm and software development. The applications of the methods discussed are multidisciplinary and include problems from mathematics, physics, biology, chemistry, material science, and engineering.

• Delaunay Triangulation
• Finite Volume Method
• Iterative Solvers
• Mesh Adaptation
• Mesh Generation
• Numerical Geometry
• Quasi‐isometric Mapping
• Variational Principle
• Voronoi Diagram

• Dorodnicyn Computing Centre, Federal Research Center of Informatics and Control, Russian Academy of Sciences Moscow, Moscow, Russia

  Vladimir A. Garanzha

• Berlin, Germany

  Lennard Kamenski

• Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin, Germany

  Hang Si