Iterative Solvers on Parallel Architectures for Partial Differential Equations

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The proposed work is concerned with the development, evaluation and testing of iterative algorithms and programs for solving large sparse systems of linear algebraic equations that typically arise in the numerical solution of partial differential equations by finite difference methods or by finite element methods. The main emphasis is on the efficient use of vector and parallel computer architectures. The research studies focus on parallel iterative algorithms designed for several types of computer architectures. General research studies on certain aspects of iterative algorithms including convergence rates, determination of iterative algorithms, and the treatment of nonsymmetric systems will also be made. A novel feature of the work is the development of hybrid iterative/direct methods designed to combine the best features of both types of methods. Computational kernels and research-oriented software will be developed for parallel architectures. The algorithms and software will be evaluated using a class of test problems and also using linear systems derived from biomedical problems and other physical applications. An important aspect of the work is the collaboration with researchers at other institutions. This will be especially important for the work on hybrid methods.//