Optimum acceleration factors for iterative solution of linear and nonlinear differential systems Article

Kennon, SR, Dulikravich, GS. (1984). Optimum acceleration factors for iterative solution of linear and nonlinear differential systems . COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 47(3), 357-367. 10.1016/0045-7825(84)90084-7

cited authors

  • Kennon, SR; Dulikravich, GS

authors

abstract

  • A new acceleration concept for iterative schemes is described. The concept is based on elementary variational calculus, and can be readily implemented in the iterative solution of a wide variety of linear and nonlinear differential systems. The method is not limited to finite difference, finite element or finite volume discretization schemes, but only to schemes that are inherently iterative. Most importantly, the method is exact in the sense that optimal relaxation/acceleration factors can be analytically determined for a class of commonly encountered systems possessing simple nonlinearity. For systems exhibiting complex nonlinearity, the method can be applied in a semi-exact but highly accurate fashion using truncated Taylor series. Without any modification, this acceleration method can be directly applied to existing iterative schemes using either orthogonal or completely arbitrary non-orthogonal computational grids, since the formulation of the method is dependent only on the governing differential system. The described method belongs to the general class of minimal residual techniques, but can be applied to nonlinear systems. © 1984.

publication date

  • January 1, 1984

published in

Digital Object Identifier (DOI)

start page

  • 357

end page

  • 367

volume

  • 47

issue

  • 3