The goal of this research is the development, implementation and evaluation of efficient numerical methods for certain partial differential equations on high performance parallel architectures. Problems studied will include the time-dependent Schrodinger equation, the Poisson-Boltzmann equation and a (simplified) global spectral model from meteorology. The Schrodinger equation ap?ears in various application areas such as computational chemistry, atomic physics molecular dynamics, and also in certain approaches to modeling acoustic propagation in the ocean and in optics. The families of numerical methods to be considered include operator splitting methods (e.g. ADI), multigrid, spectral methods, cyclic reduction and Pade-based like preconditioned Krylov subspace methods will be included. In this project, the PI will build upon past experience with the Intel hypercubes, the Connection Machine, multiprocessor Crays and the Alliant, to develop and implement parallel methods for the new generation of parallel supercomputers, such as the CM5 and the Intel Touchstone machines. This research will shed light on what numerical methods are appropriate for high performance parallel architectures.
