The Terascale Optimal PDE Simulations (TOPS) ISIC
PI: David Keyes (ODU), TSTT Point of Contact: M. Shephard (RPI)

The solution of large-scale PDE problems typically leads to a large, sparse linear or nonlinear algebraic system. Dimensions easily range into the hundreds of millions. With the emergence of hierarchical computing systems and inexpensive clusters this number will dramatically rise in the next few years. Suboptimal algebraic solution strategies can easily dominate the computational time and often mean the difference between being able or not being able to solve a problem. Efficiency in a terascale environment is a must. Fortunately, the TOPS ISIC is addressing these issues and developing the optimal multiscale solution software and strategies needed for the applications cited in this proposal and others intending to use our mesh and discretization libraries. This is an excellent opportunity for cooperation and collaboration. Reversing the perspective, the meshing software, adaptive procedures, and discretization library to be developed by this effort provide the TOPS ISIC with a source of algebraic systems that will be obtained by the most advanced technologies.

Initial interactions with TOPS have focused on a careful examination of the latest version of PETSc (a key TOPS solver technology) and its integration into Trellis. The integration into the new version of Trellis has been carried out for fixed mesh analysis using the Trellis DOF manager to coordinate the linkage with the overall global systems and to provide the assembler with the mesh entity level contributors. The contributors have been assembled into appropriate PETSc structures for solution. Initial parallel analyses are underway and efforts to ensure efficiency are beginning.

An examination of the issues surrounding the support of adaptive calculations has been started by determining which PETSc structures will best support such simulations. One natural selection is the matrix free GMRES method. We plan to investigate the application of the matrix free GMRES for an adaptive calculations. Efforts will then begin on the long-term effort with TOPS developers to determine the most effective methods to combine ITAPS adaptive mesh structures with TOPS solvers.

In addition, we are carefully following the definition of the TOPS vector, matrix, and solver interfaces to ensure that the compatibility of our discretization library. These interfaces are still under development (primarily at ANL) and we have attended several meetings with TOPS scientists to discuss their development as it relates to TSTT functionality.