Notes on Panel Discussion at 11th International Meshing Roundtable
September 17, 2002
Statler Hotel, Ithaca, New York

Notes recorded and transcribed by Steve Vavasis, panel host & moderator

This panel was supported in part by NSF grant ACI 0085969 on Adaptive Software. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Questions to be addressed by the panelists

What software advances are needed to make adaptivity more useable and popular among the computational community at large? Which major computational problems represent the greatest successes for adaptivity? Which major problems have defied adaptive solution?

Panelist presentations

Presentation by Marsha Berger (New York University)

In my work I use two kinds of adaptivity: adaptivity for the geometry and adaptivity for the solution. Adaptivity should never hurt a computation, and hopefully will help. But even with adaptivity, a good enough initial mesh is still needed. Adaptivity today still requires human intervention. Some issues holding back adaptivity are: How can you adapt to a curved surface in the middle of a flow solve? Error estimation is still a bottleneck. There are also user-interface issues, for example, determining which fields to adapt to. There is nothing like a PetSC for adaptivity. Some of the main successes for adaptivity are shock dynamics, astrophysics and combustion.

Presentation by Hugues Hoppe (Microsoft Research)

A major distinction in computer graphics is structured versus unstructured. Local adaptivity not always needed in graphics. In graphics, one prefers adaptivity that is incremental and amortizable. Hardware implementations of adaptivity are preferable. Adaptivity in graphics is view dependent, which is different from scientific computing. A binary tree is a useful data structure that could go into hardware. Shape deformation problems require adaptivity.

Presentation by George Karniadakis (Brown University)

Turbulence presents a particular challenge for adaptivity because high order methods are needed, and there is no dominant feature. The problem with turbulence is that there are many scales. Turbulence is very geometry-dependent, and the success of adaptivity depends on geometry. For instance, geometry locally changes the Reynolds number. Some bottlenecks to parallelism and adaptivity in MPI and OpenMP are: p-refinement, thread creation, and barrier operations. Some other issues for handling adaptivity are: Hybrid or nonconforming mesh generation for adaptivity; lack of mathematical error estimators means physical criteria must be used; ALE solvers are still slow.

Presentation by Rob Leland (Sandia National Laboratories)

An issue with adaptivity is the integration of error estimators. Also, adaptivity in hex meshes is still very difficult. Shock hydro problems on hex meshes are not solvable adaptively yet. Priorities at the lab are mainly on meshing and geometry, so adaptivity does not get as much attention. Intuition among the users of simulation software concerning errors is lacking. Also lacking is a good coupling between error estimates and mesh generation on subsequent steps.

Presentation by Mark Shephard (RPI)

Adaptivity is not widely used because: Code structure does not support changing the underlying mesh; there are insufficient computational resources; adaptive simulation is not integrated into the design process. Good error estimators for elliptic problems are well known. Estimates for higher order elements and goal oriented estimators such as vorticity-tracking are underdeveloped (although see work by Oden). AOMD software for adaptive meshes makes the coding easier. Anisotropic error estimates also need developing. Use of adaptivity in design and in management of simulation is the main gap.

Discussion between the panel and audience

Question from Tim Tautges

How difficult is it to put adaptivity into existing codes?

Shephard: RPI writes their own adaptive codes from scratch. Industry wants adaptive software integrated with existing nonadaptive code. Industry doesn't need optimized software. Leland: SIERRA provides an adaptive infrastructure for Sandia codes, but it is still tough to retrofit adaptivity. Berger: If adaptivity is not more widely integrated, then it won't be widely used. Karniadakis: Adaptivity is not always the bottleneck. Correct physical modeling may be the main problem. Shephard: Viseon airflow computations were carefully validated, so at least in that instance physics was not the problem.

Question from Scott Mitchell

How important is PetSC-like software?

Berger: There is CCA-AMR plus about six efforts to develop a good infrastructure for adaptivity. The problem is that it is very diffcult to provide useful interfaces to complex analysis codes. Shephard: Keep in mind that PetSC is just a library of parallel solvers.

Question from Reza Taghavi

Adaptivity is like design optimization: previously, design optimization was available only in closed codes, but now is implemented as standalone software. Perhaps there could be standalone adaptivity implemented via checkpoint/restart.

Berger: The real question is how automatable a standalone program could be. Shephard: Industry demands standalone implementations.

Question from Tom Peters

Adaptivity often localizes on geometric details. Why not have a better CAD-solver interface? Also, how can we get estimates of errors due to geometric flaws? Can adaptivity give feedback to the designer?

Shephard: If the geometry is piecewise linear, then the solver will adapt to the wrong model. It's better to ask the CAD system to find a point. Licensing expense for the CAD system may or may not be an issue. We can also have adaptivity ask the designer about length parameters. But for that we need a higher level infrastructure that is missing.

Question from Dimitri Mavriplis

Currently, error estimators are lacking for many problems. There is no point in adaptivity if there is no good error estimator.

Karniadakis: Errors in the physical modeling must also be considered, as well as discretization errors. Shephard: OK to use mathematically sound but nonrigorous estimators for adaptivity. Hoppe: Only geometric errors matter for graphics. Perceptual errors are current hot research topic. Leland: Adaptivity should also lead to greater efficiency.

Question from Todd Munson

How about adaptivity in video games, and in the interaction between geometry and graphics?

Hoppe: Physically realistic modeling is a hot topic in graphics. Adaptivity in graphics is not done so much at run time as at authoring time.

Question from Lori Freitag

In addition to computing the results, there is also a bottleneck in visualization.

Hoppe: There is much progress in model simplification. See IEEE Visualization Proceedings. There is work even on out-of-core model simplification.

Question from Carl Diegert

Are there simplification tools available from Microsoft?

Hoppe: Yes, in Direct3D, and they're supposed to be fast.

Question from Scott Mitchell

Why is adaptivity more successful in graphics?

Hoppe: Simulation is not an issue, and geometry is a simpler problem. Berger & Leland: Graphics should use more simulation. Hoppe: Agreed. There are papers at the SIGGRAPH conference in which the graphics processing unit is used for simulation.

Berger: Going back to the issue of CAD. It's not so easy to integrate a solver with CAD. We'd like to have a lightweight automatic geometric engine for efficiency. Leland: Sandia spends months on geometry and meshing.

Question from Tim Tautges

Which geometric model should be used for adaptivity? What happens when the mesh size is smaller than the geometric feature size? The CAD engine must be part of the adaptivity.

Question from Karl Merkley

What about adaptivity for multiphysics?

Shephard: The simplest solution is for the finest mesh to be selected, although this is not optimal. Karniadakis: It's best to find a norm that combines the user's criteria from each physical application. Leland: If multiple grids are used, then parallel grid transfer is very difficult.

Question from Ted Blacker

Using the CAD engine for adaptivity creates problems of expense and bandwidth.

Shephard: We must convince the CAD companies that this application of CAD is important and useful so they make multiple licenses affordable.