| Summary: | In this dissertation, we focus on (1) improving the efficiency of some iterative domain decomposition methods, (2) proposing and developing a novel domain decomposition algorithm, (3) applying these algorithms to the efficient numerical solution of the finite element discretization of the shallow water equations on a 2-D limited area domain and (4) investigating parallel implementation issues. === We have closely examined the iterative Schur domain decomposition method. A modified version of the rowsum preserving interface probing preconditioner is proposed to accelerate the convergence on the interfaces. The algorithm has been successfully applied to the finite element shallow water flow modeling. === The modified interface matrix domain decomposition algorithm is proposed and developed to reduce computational complexity. The numerical results obtained by applying this algorithm to our problem improve upon those obtained by employing the traditional Schur domain decomposition algorithm. === We then investigate parallel block preconditioning techniques in the framework of three frequently used and competitive non-symmetric linear iterative solvers. Two types of existing domain decomposed (DD) preconditioners are employed and a novel one is proposed. The newly proposed third type of DD preconditioners turns out to be computationally the most efficient. === Parallel implementation issues of domain decomposition algorithms are then discussed. Typical parallelization results on the CRAY Y-MP are presented and discussed. === This dissertation also contains a relatively thorough review of two fast growing areas in computational sciences, namely, parallel scientific computing in general and iterative domain decomposition methods in particular as well as a discussion concerning possible future research directions. === Source: Dissertation Abstracts International, Volume: 55-07, Section: B, page: 2766. === Major Professor: I. Michael Navon. === Thesis (Ph.D.)--The Florida State University, 1994.
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