Scalable Iterative Solution of Large Linear Systems with Applications in Fluid Dynamics, Radiation Transport and Markov Chains

Emory University, Atlanta GA

Investigators

Abstract

The solution of large systems of linear equations remains one of the main bottlenecks in many numerical simulations throughout computational science and engineering. Despite much recent progress, there is still a great need for improved iterative solvers in such areas as fluid dynamics, radiation transport, magnetohydrodynamics, image processing, computational mechanics, acoustics, and so forth. The increasingly important area of data mining and information retrieval also makes heavy use of sparse matrix techniques and necessitates reliable and scalable algorithms for linear equations and eigenvalue problems. The PI will investigate efficient iterative solvers with a focus on preconditioning techniques for nonsymmetric and indefinite problems. The PI proposes to use a blend of algebraic and problem-specific techniques to construct robust and scalable solvers for linear systems arising from discretizations of problems from fluid dynamics and radiation transport, as well as for solving large sparse complex symmetric systems and for computing the stationary vector of Markov chains. The ultimate goal of research in computational mathematics is to provide scientists and engineers the algorithmic and software tools needed for the solution of challenging scientific and technical problems of increasing size and complexity. The competitiveness of American science and technology greatly benefits from (and to a large extent depends on) the creation of innovative computational methods and software and by the continuous improvement of existing techniques. Progress in the solution of the problems targeted by the PI will have a positive impact on science and engineering by enabling faster and more detailed computer simulations. In addition, several graduate students (and possibly a few undergraduates) will be impacted by this research either through direct involvement, or through the positive effects this research will have on the PI's teaching of computational and applied mathematics courses at Emory University.