CS&E Postdoctoral Associate: Parallel Iterative Methods and Preconditioners for the Large, Sparse, Symmetric Eigenvalue Problem

点击翻译按钮获取中文摘要

The numerical solution of the large, sparse, symmetric problem is required by many scientific and engineering applications, such as electronic structure calculations. Iterative methods, the only means of meeting these demands, are faced with two challenges. The first involves degenerate or pathologically close eigenvalues, and the second involves matrices of very large size that may not stored. Parallel computing and preconditioning are powerful ways for improving the performance of iterative methods. This proposal has three major goals. First, to extend the parallel preconditioned eigenvalue methods that are used in atomic structure calculations to the complex molecular structure calculations in solid state physics. Second, to extend the existing eigenvalue codes to solve for large number of eigenvalues of very large matrices. Third, to explore further the eigenvalue preconditioning, with application to molecular structure matrices resulting from finite difference/element discretization techniques. Preconditioning for large matrices that cannot be stored are also being examined. Finally, work on domain decomposition preconditioners is continued on both the application and on arbitrary matrices. Domain partitioning ideas is being tested in combination with a coarse solve correction on a properly chosen small system. The aggregation/disaggregation technique is being investigated for creating the small system.