Tensor-Krylov methods for solving large-scale systems of nonlinear equations.

Bader, Brett William

Sandia National Laboratories

关键词: 99 General And Miscellaneous//Mathematics, Computing, And Information Science;    Fluid Flow;    Nonlinear Algebraic Equations.;    Differential Equations, Nonlinear.;    Tensor Algebra.;   

DOI  :  10.2172/919158
RP-ID  :  SAND2004-1837
RP-ID  :  AC04-94AL85000
RP-ID  :  919158

美国|英语

来源: UNT Digital Library

【 摘 要 】

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.