New Concept and Parallel Algorithms for Robust Preconditioning in Large Scale Parallel Matrix Computation

Large sparse unstructured matrices arising from various computer simulation and modeling are commonly solved by preconditioned iterative methods. This research project will study and design robust high performance preconditioners for parallel solution of large sparse linear systems, based on a class of multistep successive sparse approximate inverse preconditioning techniques. We will develop new concept and parallel algorithms of multistep successive preconditioning for enhancing the robustness of standard sparse approximate inverse preconditioning techniques, and generalize this concept to the context of other preconditioning techniques. Study will be conducted to show the advantages of such approach to enhance both preconditioning accuracy and factorization stability. We will build portable software packages to implement new preconditioning strategies for solving unstructured general sparse linear systems on high performance parallel computers. The general purpose high performance preconditioned iterative solvers from this research project are expected to make significant impact in the field of applied scientific computing. Our experience and existing strength will ensure that the project be carried out fully as proposed. As U.S. industry is more and more relying on computer aided design and manufacturing, large scale computer simulation and modeling will be a vital component in new products research and development. The outcome of this research will benefit U.S. industry as well as scientific research community by providing more efficient kernel software for large scale computer simulations.