Iterative Methods for Large Sparse Linear Systems Arising from Partial Differential Equations

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The purpose of this investigation is to develop, test, and analyze iterative methods for computing the solutions of large, sparse linear systems arising from the discretization of elliptic partial differential equations. The focus of the research is on partial elimination techniques for two-cycle problems, iteration schemes for nonsymmetric systems derived from non-self-adjoint problems, preconditioners, and parallel computations. An analytic study on benchmark problems, including systems from three-dimensional models, will be combined with numerical experimentation using both serial and parallel computers.