For the most part, scientists will be solving hyperbolic equations, which run efficiently on scalar machines like NCSA's CM-5. Bottlenecks occur when computing the partial differential equations needed for solving elliptical problems. Typical methods deal with all scales on a fine grid which wastes resources. Multigrid methods cheaply eliminate the high- frequency error components on the fine grid and deal with lower frequency errors on coarser grids where they are more easily handled. Refining the method Saied and Saylor are working towards adapting a more effective multigrid approach.
Scientists say the numerical solution can drift from the true solution due to numerical error.
Multigrid is the engine making the car go down a curved road. He describes the curved road as an elliptical problem and notes that it is his and Saied's task to make the computations run smoothly. The difficulties stem from the global data dependencies, and hence global communication requirements, of elliptical problems. Saylor and Saied note that their work is still in the early stages. This project will exploit scalable computing to develop software tools using NCSA's CM-5 and the Pittsburgh Supercomputing Center's T3D system.