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An Introduction to Mesh Generation Methods and Softwares for - - PowerPoint PPT Presentation

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An Introduction to Mesh Generation Methods and Softwares for Scientific Computing Part I TU Berlin Nov. 24, 2016 My name is Hang Si. Im a senior researcher in Weierstrass Institute (WIAS) in Berlin. My main research interest is mesh

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An Introduction to Mesh Generation Methods and Softwares for Scientific Computing

Part I TU Berlin

  • Nov. 24, 2016
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  • My name is Hang Si. I’m a senior researcher in

Weierstrass Institute (WIAS) in Berlin.

  • My main research interest is mesh generation for

scientific computing. I’m developing the software, TetGen -- a Delaunay-based tetrahedral mesh

  • generator. It is freely available for academic use at

http://www.tetgen.org.

  • Homepage: http://www.wias-berlin.de/people/si
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The topic of this lecture is about mesh generation. But first, what are meshes?

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Meshes in Nature Objects

a view from the airplane the wing of a dragonfly

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Mdeshes in Architechures

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Meshes in Daily life

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  • Meshes are partitions of geometric
  • bjects.
  • Meshes are discrete representations of

continuous objects.

  • Meshes may be called differently in

different areas and literatures, like grids, triangulations, etc.

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Geo Information Science (GIS)

Google earth

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Scientific Visualization

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Meshes Are Tools to Solve Complicated Problems

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Robot Route Plan

work space configuration space visibility graph

Voronoi diagram with obstacles

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Example: The Art Gallery Problem

How many cameras are needed to guard a museum?

22−gon. 7 Guards

1 2 3 1 2 1 2 1 3 2 1 1 3 2 2 1 2 1 3 1 3 2 3 3

  • Triangulate P. 3-color it.
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Meshes are Backbones of 3D Computations and Applications

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Solid & Geometric Modeling

Blender

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Computer Games

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Computer Animations

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Geometry Processing

Multiresolution of scanned data (P. Alliez) Skinning of 3D Objects (A. Jacobson)

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Hobbit 3

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Numerical Simulation

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Simulation Process

3 2

  • 1. Build CAD Model
  • 2. Mesh
  • 3. Apply Loads and

Boundary Conditions

  • 4. Computational Analysis
  • 5. Visualization

2 kN

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Adaptive Simulation Process

3 2

  • 1. Build CAD Model
  • 2. Mesh
  • 3. Apply Loads and Boundary Conditions
  • 4. Computational Analysis
  • 7. Visualization

2 kN

  • 5. Error Estimation

Error?

  • 6. Remesh/Refine/Improve

Adaptivity Loop

Error < ε Error > ε User supplies meshing parameters Analysis Code supplies meshing parameters

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Houdini

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What is Mesh Generation?

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  • Mesh generation is a practice of generating a

polygon or polyhedral mesh that approximates a geometric domain. — Wikipedia

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Why Studying Mesh Generation?

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Mesh Generation is the bottleneck of applications: No mesh, No Run!

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However, the importance of mesh generation is often ignored!

  • … let’s assume there is a mesh …
  • … let T_h be a triangulation whose size h tends to

0, … Typical text which appear in books and literatures:

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  • Automatically generating meshes from arbitrary 3d

geometries is very challenging.

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  • Mesh generation can take orders of magnitude more

man-hours — J. Thompson (Prof. of Areospace, Pioneer of

mesh generation techniques)

Some CAD models, freely available from http://www.grabcad.com

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  • Numerical simulation requires high quality meshes for

achieving accuracy and efficiency.

  • To generate a ``good quality” mesh for the underlying

physical problem is a very challenging task.

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Example: Adaptive FEM for the Wave Equation

⇢

∂2u ∂t2 − µ∆u

= f in Ω , u = 0 in ∂Ω , here µ = 1., f discrete Dirac function.

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Math Engineering Computer Art Science

  • Mesh generation is a topic in which a meaningful combination
  • f different approaches to problem solving is inevitable — H.

Edelsbrunner (Prof. of Math & Computer Science, Pioneer of computational

geometry and topology)

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Resources for Studying Mesh Generations

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Resources on the web

  • S. Owen, survey of mesh generation techniques,

1998.

  • Mesh research corner, maintained by S. Owen.
  • Mesh generation on the web, maintained by R.

Schneider.

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Literatures, Books

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Conferences

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Commercial Softwares

  • Tetmesh-GHS3D, INRIA, France
  • MeshSim, SCOPEC, RPI, Simmetrix Inc. USA
  • VisTools/Mesh, AreoAstro, MIT, Vki Inc, USA
  • GridPro, USA
  • GridGen, USA
  • …
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Open Source Softwares

  • Netgen, TU Vienna, Austra
  • Gmsh, Uni. Liege & Uni C. d. Louvain, Belgium
  • GRUMMP, Uni. British Columbia, Canada
  • Triangle, UC Berkeley, USA
  • CGALmesh, INRIA, France
  • TetGen, WIAS Berlin, Germany
  • …