TSTT Personnel: David Brown (LLNL), Kyle Chand (LLNL), Bill Henshaw (LLNL), Patrick Knupp (SNL)
Accelerator Personnel: Nate Folwell (SLAC), Kwok Ko (SLAC)
TSTT interactions with the SciDAC Advanced Computing for 21st Century Accelerator Science and Technology Center have been primarily focused on the computational electromagnetics group headed by Kwok Ko at the Stanford Linear Accelerator (SLAC).
The primary codes used for electromagnetic simulations are a frequency domain code (Omega3P) and a time domain code (Tau3P). At the August 2001 SciDAC Accelerator Kickoff meeting, Ko presented a number of outstanding problems related to meshing and discretization for which he hoped the TSTT Center would be able to provide assistance. The first problem is the widely recognized issue of reducing the time needed to create a mesh starting with a CAD (computer-aided design) model giving the physical geometry for the simulation. There are two main bottlenecks involved in this process. One is the clean-up of the initial geometry such that it can be used for mesh generation. The second bottleneck (for SLAC) concerns the generation of high quality meshes as it relates to accuracy and convergence of the simulation code. Currently, many meshes may be generated before a successful simulation is obtained.
The geometry clean up process consists of removing unwanted detail, healing gaps between surfaces and volumes, and removing non-physical overlaps. This process can be quite tedious and time-consuming, often delaying simulations for months. Both CUBIT (SNLA) and Overture (LLNL) have tools available for CAD cleanup and repair. SLAC has been using the CUBIT tools for some time, and TSTT will provide the Overture “Rapsodi” cleanup tools to SLAC in the near future. In addition, TSTT members have been assisting SLAC in the use of these tools. For example, toward the end of FY02, SLAC presented a very complex tapered waveguide geometry that needed to be cleaned up and meshed as quickly as possible (see Figure 1). The challenge in this geometry is that the position of the beam axis relative to the centroid of the geometric cross-section varies along the waveguide which makes it difficult to achieve sufficient mesh quality. Tim Tautges at SNL/TSTT has been working with the SLAC analysts to clean up this geometry and mesh it using CUBIT. Although this work is not completed, it appears that there will be a major reduction in the time it would have taken the SLAC analysts to mesh this problem themselves.
Figure 1 An all-hexahedral mesh generated for the SLAC waveguide geometry
The second problem posed by Ko concerned Tau3P. The code uses the DSI (Discrete Surface Integral) method which is known to be weakly unstable on non-orthogonal meshes. Because of the complexity of the geometries required for accelerator design, it is not possible, in general, to generate meshes that are completely orthogonal. Although Tau3P partially stabilizes the DSI method by invoking a time-domain filtering technique, the overall simulation process is not very robust because simulations must often be terminated prematurely at some ‘cutoff’ time due to instability. A much more desirable situation would be to have a stable method where the only quality issue would be the accuracy of each simulation.
SLAC analysts have long observed that the cutoff time is highly sensitive to mesh properties such as orthogonality and smoothness. Based on the hypothesis that the Tau3P cutoff time might be correlated to some measure of quality of the mesh used in the calculation, a collaboration was started between N. Folwell (SLAC) and P. Knupp (SNLA), to systematically identify the major correlations between cutoff time and mesh properties. An empirical study showed that there were strong correlations between cutoff time and mesh properties such as smoothness, element shape, and the minimum edge length. The strength of the correlations varied depending on whether a calculation used the Tau3P filtering technique or not; it also depended on whether the simulation involved a beam or a pulse. This work is nearing completion. Results will be used in FY03 to aid the creation of better (more stable) meshes for SLAC.
More recently, we have also begun a study of the DSI (and similar) methods with the goal of stabilizing the underlying discretization. At LLNL, Bill Henshaw has been studying DSI-like methods as applied to wave equations in general to see if this might be possible. Preliminary results have included the derivation of sufficient conditions for stability of the method on triangular meshes in 2D. We understand how to construct a first-order accurate method that is stable on triangular meshes, and also how to stabilize DSI by adding high-order artificial dissipation. Further work will be required to develop techniques that will perform well on general meshes for 3D electromagnetic simulations.