CAREER: Robust Preconditioners for Sparse Linear Systems

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This project will develop a new class of robust and parallelizablepreconditioners for the solution of sparse linear systems arising frompartial differential equations. The approach is based on a hierarchicaldecomposition of the matrices associated with the linear system, and isdesigned to improve the effectiveness of the preconditioner withoutcompromising the parallelism inherent in the computation. A formalmethodology will be developed for construction, application, andanalysis of these preconditioners. Effectiveness of these techniqueswill be tested on problems in incompressible fluid simulations. Parallelimplementations of these preconditioners will be developed and theirperformance evaluated for various multiprocessor platforms. Parallellibraries will also be developed and made available to others via theinternet. As part of the educational plan innovative techniques will beemployed for curriculum development in computational science andengineering, and university wide workshops and seminars will beorganized for the research community.