Publications

A fast precondition technique has been developed which accelerates the finite difference solutions of the 3D Maxwell's equations for geophysical modeling. The technique splits the electric field into its curl free and divergence free projections, and allows for the construction of an inverse operator. Test examples show an order of magnitude speed up compared with a simple Jacobi preconditioner. Using this preconditioner a low frequency Neumann series expansion is developed and used to compute responses at multiple frequencies very efficiently. Simulations requiring responses at multiple frequencies, show that the Neumann series is faster than the preconditioned solution, which must compute solutions at each discrete frequency. A Neumann series expansion has also been developed in the high frequency limit along with spectral Lanczos methods in both the high and low frequency cases for simulating multiple frequency responses with maximum efficiency. The research described in this report was to have been carried out over a two-year period. Because of communication difficulties, the project was funded for first year only. Thus the contents of this report are incomplete with respect to the original project objectives.

We report on the application of the one-level FETI method to the solution of a class of structural problems associated with the Department of Energy's Accelerated Strategic Computing Initiative (ASCI). We focus on numerical and parallel scalability issues,and discuss the treatment by FETI of severe structural heterogeneities. We also report on preliminary performance results obtained on the ASCI Option Red supercomputer configured with as many as one thousand processors, for problems with as many as 5 million degrees of freedom.

In this work the basic Finite Element Tearing and Interconnecting (FETI) linear system solver and the PARPACK eigensolver are combined to compute the smallest modes of symmetric generalized eigenvalue problems that arise from structures modeled primarily by solid finite elements. Problems with over one million unknowns are solved. A comprehensive and relatively self-contained description of the FETI method is presented.