Mesh Generation for High Performance Computing: Current Trends and Applications

SC2000 Tutorial

A full day (6 hours) tutorial will be presented at the SC2000 High Performance Computing Conference to be held in Dallas, Texas, November 4-10 2000. The tutorial will provide an overview of current mesh and grid generation technology with application to todays High Performance Computing needs. Instructors will be researchers from Sandia National Laboratory's, Parallel Computing Sciences Department.

Abstract

Mesh generation plays a vital role in computational field simulation for high performance computing. The mesh can tremendously influence the accuracy and efficiency of a simulation. Automated methods for generating both structured and unstructured meshes have been available for many years. This short course will provide an overview of the principal techniques currently in use for constructing computational grids. Triangle, tetrahedral, quadrilateral, hexahedral and mixed element unstructured methods will be discussed as well as elliptic, algebraic and hyperbolic structured methods. Issues related to mesh quality, adaptivity and optimization will also be discussed. While the focus of the course will be on practical application of current mesh generation techniques to high-performance computing, theoretical discussion of current algorithms and techniques will also be included.

Advances in massively parallel and high performance computing have made possible computational simulation at much higher fidelity and finer resolution. This has only widened the bottleneck posed by mesh generation for finite element analysis. The course will present background on tools and techniques for mesh generation for analysis on massively parallel computers. Some issues specific to larger analysis will also be introduced, including techniques for handling model complexity, team-based approach to generating meshes, tools for generating meshes in pieces and assembling the pieces into a larger mesh, and preparing the mesh for input to massively parallel-based analysis.

An introduction to some of the state-of-the-art mesh generation tools available commercially and non-commercially will also be presented. As an example, the course will culminate in a demonstration of the CUBIT mesh generation toolkit developed at Sandia National Laboratories.

Instructors

• Steven J. Owen, Ph.D.
• Scott A. Mitchell, Ph.D.
• Patrick Knupp, Ph.D.
• Timothy J. Tautges, Ph.D.

Tutorial Outline

The following is a brief outline of topics to be covered in the tutorial. For more information, click on a title in the following list.

A Survey of Unstructured Mesh Generation Techology

Instructor: Steven J. Owen, Ph.D.
1. Tetrahedral and Triangle Methods
a. Octree
b. Advancing Front
c. Delaunay

2. Quadrilateral and Hexahedral Methods
a. Mapped Meshing
b. Unstructured Quad Meshing
c. Unstructured Hex Meshing
d. Hex-Dominant Methods

3. Surface Meshing
a. Parametric Space
b. Direct 3D

4. Mesh Post-Processing
a. Smoothing
b. Clean-up
c. Refinement

5. Mesh Generation Software Suvey

Advanced Algorithms - Hexahedral Meshing

Instructor: Scott A. Mitchell, Ph.D.
1. Sweeping
a. Multiple source, single target
b. Multiple source, multiple target
c. Grafting
d. Sweep Forging

2. Plastering
a. HexTet
b. Geode
3. Whisker Weaving

Unstructured Mesh Quality

Instructor: Patrick Knupp, Ph.D.
1. Mesh Quality Requirement
2. Mesh Quality Metrics
3. Mesh Smoothing and Improvement
4. Mesh Optimization Techniques


Structured Grid Generation

Instructor: Patrick Knupp, Ph.D.
1. Mappings and Invertibility
2. Transfinite Interpolation
3. Grid Quality
4. Application to Numerical PDE's
5. One-dimensional grid generation
6. Connections to Differential Geometry
7. Planar Grid Generation
8. Variational Grid Generation
9. Curve and Surface Grid Generation
10. Adaptive Grid Generation


Mesh Generation for Massively Parallel and High Performance Computing-Based Analysis

Instructor: Timothy J. Tautges, Ph.D.

Other Mesh Generation Resources on the Web