Overview
The purpose of this project is to develop completely parallel versions of
incomplete Cholesky and ILU preconditioners for solving sparse systems of
linear equations. It is widely recognized that the most computationally
expensive part of many modeling and simulation processes is the solution of
the sparse linear equations which arise from the finite difference or
finite element discretizations. Unfortunately, the widely-used and
powerful incomplete Cholesky preconditioning and related techniques are
sequential in nature, and thus they have not been effective on parallel
computer platforms. However, we have developed a new formulation of the
incomplete LU algorithm which solves this problem for an important class of
linear systems of interest for large-scale modeling and simulation
applications. The technique gives almost perfect speedup even on large
numbers of processors without sacrificing the strong convergence properties
of the global ILU and MILU preconditioners. In this project we propose to
apply these parallelization techniques to a broad range of structured
problems, perform basic research on the convergence properties and
parallelization possibilities of ILU preconditioners, and explore the
possibility of using these techniques for the preconditioning of
unstructured problems.
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