Iterative methods for large scale nonlinear and linear systems. Final report, 1994--1996
The major goal of this research has been to develop improved numerical methods for the solution of large-scale systems of linear and nonlinear equations, such as occur almost ubiquitously in the computational modeling of physical phenomena. The numerical methods of central interest have been Krylov subspace methods for linear systems, which have enjoyed great success in many large-scale applications, and newton-Krylov methods for nonlinear problems, which use Krylov subspace methods to solve approximately the linear systems that characterize Newton steps. Krylov subspace methods have undergone a remarkable development over the last decade or so and are now very widely used for the iterative solution of large-scale linear systems, particularly those that arise in the discretization of partial differential equations (PDEs) that occur in computational modeling. Newton-Krylov methods have enjoyed parallel success and are currently used in many nonlinear applications of great scientific and industrial importance. In addition to their effectiveness on important problems, Newton-Krylov methods also offer a nonlinear framework within which to transfer to the nonlinear setting any advances in Krylov subspace methods or preconditioning techniques, or new algorithms that exploit advanced machine architectures. This research has resulted in a number of improved Krylov and Newton-Krylov algorithms together with applications of these to important linear and nonlinear problems.
- Research Organization:
- Utah State Univ., Logan, UT (United States). Dept. of Mathematics and Statistics
- Sponsoring Organization:
- USDOE Office of Energy Research, Washington, DC (United States)
- DOE Contract Number:
- FG03-94ER25221
- OSTI ID:
- 527567
- Report Number(s):
- DOE/ER/25221--1; ON: DE97009203
- Country of Publication:
- United States
- Language:
- English
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