## Multi-Method Linear SolversI conduct research on multimethod linear solvers, i.e., solvers that combine more than one underlying algorithm to improve the performance of large-scale simulations in collaboration with Sanjukta Bhowmick (Columbia University), Lois McInnes (Argonne), and Padma Raghavan (Penn. State). We have developed adaptive
solvers, which use heuristics to select a solution method to better
match the changing attributes of linear systems generated in different
stages of an application. We have also developed composite
solvers, which use a sequence of methods on the same linear system to
improve reliability.The diagram to the right illustrates an example runtime scenario of the components involved in multimethod linear system solution, which is a part of an application, such as the solution of a nonlinear PDE. We have demostrated the effectiveness of composite and adaptive linear solver techniques in a number of applications, such as a driven cavity flow simulation, and simulation of flow around an airfoil. |

- S. Bhowmick, L. McInnes, B. Norris, and P. Raghavan. ``The Role
of Multi-Method Linear Solvers in PDE-Based Simulations,'' in
*Proceedings of the 2003 International Conference on Computational Science and its Applications, ICCSA 2003*, Montreal, Canada May 18 - May 21, 2003. Lecture notes in Computer Science 2677, Editors V. Kumar, M. L. Gavrilova C. J. K. Tan, and P. L'Ecuyer, pp. 828-839, 2003. Also available as MCS preprint ANL/MCS-P1027-0203. - L. McInnes, B. Norris, S. Bhowmick, and P. Raghavan, "Adaptive
Sparse Linear Solvers for Implicit CFD Using Newton-Krylov Algorithms,"
in
*Proceedings of the Second MIT Conference on Computational Fluid and Solid Mechanics*, Massachusetts Institute of Technology, Boston, USA, June 17-20, 2003. Also available as MCS preprint ANL/MCS-P998-0902.

Project website: http://www.mcs.anl.gov/~curfman/multimethod.html.