Tensor-Krylov methods for solving large-scale systems of nonlinear equations [electronic resource].
- Published
- Washington, D.C. : United States. Dept. of Energy, 2004.
Oak Ridge, Tenn. : Distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy. - Physical Description
- 40 pages : digital, PDF file
- Additional Creators
- Sandia National Laboratories, United States. Department of Energy, and United States. Department of Energy. Office of Scientific and Technical Information
Access Online
- Restrictions on Access
- Free-to-read Unrestricted online access
- Summary
- This paper develops and investigates iterative tensor methods for solving large-scale systems of nonlinear equations. Direct tensor methods for nonlinear equations have performed especially well on small, dense problems where the Jacobian matrix at the solution is singular or ill-conditioned, which may occur when approaching turning points, for example. This research extends direct tensor methods to large-scale problems by developing three tensor-Krylov methods that base each iteration upon a linear model augmented with a limited second-order term, which provides information lacking in a (nearly) singular Jacobian. The advantage of the new tensor-Krylov methods over existing large-scale tensor methods is their ability to solve the local tensor model to a specified accuracy, which produces a more accurate tensor step. The performance of these methods in comparison to Newton-GMRES and tensor-GMRES is explored on three Navier-Stokes fluid flow problems. The numerical results provide evidence that tensor-Krylov methods are generally more robust and more efficient than Newton-GMRES on some important and difficult problems. In addition, the results show that the new tensor-Krylov methods and tensor- GMRES each perform better in certain situations.
- Report Numbers
- E 1.99:sand2004-1837
sand2004-1837 - Subject(s)
- Other Subject(s)
- Note
- Published through SciTech Connect.
08/01/2004.
"sand2004-1837"
Bader, Brett William. - Funding Information
- AC04-94AL85000
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