Mesh Generation for High Performance Computing: Current Trends and Applications

Unstructured Mesh Quality

Audience: Contains mostly intermediate/advanced material. Some background in mesh generation will be assumed.

1. Mesh Quality Requirements

Basic mesh quality requirements will be described for finite element meshes including positive volume, minimum angle criterion, time-step control, avoidance of hourglass modes, locking, etc.

2. Mesh Quality Metrics

Shape and size metrics for both simplicial and non-simplicial element types will be described.

3. Mesh Smoothing and Improvement

Mesh quality can be improved by various node-movement strategies such as Laplace smoothing. Two- and three- dimensional smoothing techniques will be explored, along with invertibility guarantees, speed, and other issues. Their use in mesh sweeping and morphing algorithms will be described.

4. Mesh Optimization Techniques

Mesh quality metrics can be used to devise discrete objective functions which, when optimized, will produce improved mesh quality with invertibility guarantees.

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