Tensor-Krylov methods for solving large-scale systems of nonlinear equations.
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.
- Research Organization:
- Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC04-94AL85000
- OSTI ID:
- 919158
- Report Number(s):
- SAND2004-1837; TRN: US200825%%69
- Country of Publication:
- United States
- Language:
- English
Similar Records
An investigation of Newton-Krylov algorithms for solving incompressible and low Mach number compressible fluid flow and heat transfer problems using finite volume discretization
On the performance of tensor methods for solving ill-conditioned problems.