Postdoc: Portable Parallel Preconditioning

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This project will study parallel preconditioners used by iterative methods to solve general sparse linear systems of equations. The new preconditioning algorithms will be based on Incomplete Factorization of Complete Matrices (IFCM; for example, ILU) and Complete Factorization of Incomplete Matrices (CFIM). The latter approach is rather new. The PI plans to extend the combinatorial algorithms developed in the parallel direct methods to the construction of parallel preconditioners. By exploiting both structural and algebraic features of the original matrix, they will design parallel linear solvers with a blend of techniques along the continuous spectrum from pure iterative to pure direct methods. The new preconditioners are independent of problem domain, and hence are suitable to be used in general-purpose library software. Besides fundamental algorithms research, the PI will produce widely usable parallel libraries and tools for computational scientists and engineers. The preconditioning software will be based on and augment the best available parallel direct-method software and tools, some of which is being developed in the PIs thesis work. The new algorithms and libraries will be bench marked in several applications, such as unsymmetric sparse eigenvalue computation, groundwater remediation modeling, and Stokesian dynamics models of colloidal suspensions.