5IMR Panel Discussion Notes

Paul Chew, Cornell University

Norimasa Chiba, Hitachi, Ltd., Mechanical Engineering Research Lab

Samuel Key, Sandia National Laboratories

David Marcum, Mississippi State University

Renato Perucchio, University of Rochester

Contact Information

Prepared Q1: What are the key technical issues facing mesh generation today in your research/application area?

Paul Chew:

A: Renato Perucchio: You have to define the solid you want to apply hex meshing to. If you're looking for something that is capable of handling all possible solids, then - at present - the problem has no solution and may very well be mathematically intractable.

But for vertical applications within a specific problem domain, the all-hex meshing problem has solutions. In a complete sense, I don't see a future for fully automatic procedures in hexahedral meshing. We won't be able to operate without interactive tools.

Sam Key: Preference is all-hex mesh. The computation mechanics community is trying to make Hexehedral in solid mechanics, which can relieve the pressure.

Q. Incompressible Elements - use full hex and Lagrangian to get internal freedom. Need to pay attention to high steps, too.

Q. I think in one year there will be automatic hex meshers. We'll have number of tools (for specific domains) that put together will solve the general problem. As tools progress, people are more satisfied with what they get. All-hex meshing is less of an issue this year.

Q.Ted Blacker: At what cost can we come up with a semi-automatic mesher, and cease to want a completely automated mesher.

Q. Scott Canann: Is hex meshing the number one topic, or is dealing with geometry problems? Hexes will always be problem, but is it the number one problem?

Q. Joe Walsh - The real issue is producing a mesh that produces quality (analysis) results. In the past one had to go with a hex mesh to get quality analysis results. Limiting factor - geometry mesh (need to clean up). Get efficient error estimation adaptivity going along with it.

Reza Taghavi: Mesh generation is an intermediate step to design, where the computer proposes a solution.

Sam Key: Do you mean high quality mesh generation will take place in background?

Reza Taghavi:. Yes, either in the CAD tool or the analysis tool. Use partial method.

Harley Wattrick: Consider the design process and where meshing fits into it. Hardware suppliers can make a rapid prototype and test it faster then we can mesh it. The CAD problem is a quality issue, if the paradigm is to create the geometry and document it, then the quality issue belongs to the person creating the geometry. Fitting the meshing problem into the whole design thing is a major problem today. How do we get it (information) to go from the meshing environment to product design environment.

Ted Blacker: Re: Sam's large models. Mesh generation will have smaller memory requirements then (on each subdomain v.s. entire domain at once).

Randy Lober: The typical (non-labs) user is not generating meshes of size on the order that Sam suggested.

Comments: What's the feasibility of and need for large meshes like Sam proposes?

In Sam's introductory paradigm, parallel mesh generation is reduced to creating subdomains.

Editorial comment: Seems to be a consensus this year that Hex meshing is very problem domain dependent.

Paul Chew:

Chiba:

Sam Key:

Dave Marcum? Mark Shephard?:

Renato Perucchio:

For generic solid:
· Solid is defined in a solid modeling system.
· Solid is non-manifold.
· Solid is bound by free-form surfaces.
In biomechanical application researchers have began to use voxel models directly as meshes. Essentially the model is the mesh. This is new and challenging but could yield fully automatic tools at least for specific areas of application.

Pedro Marcal: Tools should provide a measure of error at the end of the analysis. We don't have that today, but we could and should.

Narrative: A small debate rages about whether current error analysis technology provides a reliable error estimate for hex meshes. Some say the theory is in place and useful for tet meshes. Some say error estimates are not reliable. Maybe it depends on the subdiscipline.

Gary Miller: We (Gary and a student) did a study of technologies/algorithms mainly in the area of applied mathematics and matrix algorithm. In all cases, its been about 20 years from conception to realization. E.g. QR factorization, interior point methods.

(Perhaps its too early to expect hex meshing to be accepted. Perhaps tet meshing will be accepted fully and there will be no need of hex meshing.)

Various speculations about why 20 years: one theory purely technical. One theory purely social - old users won't switch to new tools, so it takes 20 years for old users to retire and new users to come in who are willing to try something new.

Ted Blacker: The social explanation is based on the assumption that the user is stupid. People may be time pressured for results, but they are not stupid. The explanation for 20 years is that it takes experience for a user to have confidence in the tools. Yes, I'm right. This confidence takes time and experience. Its a matter of practicality - what can I (as a user) trust and what can I get done. Another comment is, re: Pedro Marcal's comment, error analysis is no answer.

Q: We need more theory results. We don't know the conditions under which a hex mesh exists.