A Fully Algebraic Multigrid Software Package for Automated Solution of Unstructured Sparse Linear Systems on High Performance Computers

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This project is to design robust and efficient computational kernel software for solving large sparse unstructured linear systems on high performance computers. Such large scale problems can only be solved by iteritive techniques. The iterative techniques under our consideration include multilevel preconditioning techniques and algebraic multigrid methods. Our goal is to unify these two groups of methods and to take advantage of both and avoid the disadvantages of either.We will investigate, design, and test algebraic preconditioners that offer the scalability of multigrid techniques, the parallelism of domain decomposition methods, and the robustness of incomplete LIU preconditioners.We will also use a factored sparse approximate inverse technique to replace standard iterative schemes in algebraic multigrid methods. Such an approach may increase the robustness of our methods and improve their parallelism. Graph partitioning of submatrices is to be used to balance loads among processors. The proposed research will result in a software package that may be used by researchers and engineers as kernel software in large scale numerical simulations andcomputations.The general purpose high performance iterative solvers from this research project are expected to make significant impact in the field of applied scientific computing. The results of the research will make a clear judgment concerning the relative advantages and disadvantages of algebraic multigrid methods and multilevel incomplete LU preconditioning methods. The research has applications in aerospace, semiconductor, reservoir simulation, combustion, ocean/climate modeling, and pollution tracking