Premium
Use of Halley's Method in the Nonlinear Finite Element Analysis
Author(s) -
Plate Carolin,
Papadopoulos Panayiotis,
Müller Ralf
Publication year - 2010
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201010277
Subject(s) - mathematics , nonlinear system , rate of convergence , newton's method , convergence (economics) , von mises yield criterion , mathematical analysis , finite element method , computer science , physics , computer network , channel (broadcasting) , quantum mechanics , economics , economic growth , thermodynamics
Halley's method is a higher order iteration method for the solution of nonlinear systems of equations. Unlike Newton's method, which converges quadratically in the vicinity of the solution, Halley's method can exhibit a cubic order of convergence. The equations of Halley's method for multiple dimensions are derived using Padé approximants and inverse one‐point interpolation, as proposed by Cuyt. The investigation of the performance of Halley's method concentrates on eight‐node volume elements for nonlinear deformations using Staint Venant‐Kirchhoff's constitutive law, as well as a geometric linear theory of von Mises plasticity. The comparison with Newton's method reveals the sensibility of Halley's method, in view of the radius of attraction but also demonstrates the advantages of Halley's method considering simulation costs and the order of convergence. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)