A review of higher order Newton type methods and the effect of numerical damping for the solution of an advanced coupled Lemaitre damage model

In this paper, several Newton-type methods of convergence order 2 or higher were tested on various nonlinear systems of equations and on an advanced material law implemented in a finite-element code. The computational speed, numerical efficiency, and robustness of each method were evaluated for each...

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Bibliographic Details
Published in:Finite elements in analysis and design Vol. 209; p. 103801
Main Authors: Morch, Hélène, Yuan, Sibo, Duchêne, Laurent, Harzallah, Ridha, Habraken, Anne Marie
Format: Journal Article
Language:English
Published: Elsevier B.V 15.10.2022
Elsevier BV
Subjects:
Analysis
Applied Mathematics
Computer Graphics and Computer-Aided Design
Engineering, computing & technology
Finite-element model
General Engineering
Ingénierie, informatique & technologie
Newton method
Nonlinear equations
Numerical methods
Nonlinear equations
Newton method
Numerical methods
Finite-element model
ISSN:0168-874X, 1872-6925, 1872-6925
Online Access:Get full text
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Summary:In this paper, several Newton-type methods of convergence order 2 or higher were tested on various nonlinear systems of equations and on an advanced material law implemented in a finite-element code. The computational speed, numerical efficiency, and robustness of each method were evaluated for each studied case. The effect of numerical damping was also studied. The results were then compared to put in light the strengths and weaknesses of each method. The most efficient and robust method for the material law in the finite-element code was identified as the Newton method with a selective numerical damping. •Several Newton-type methods were evaluated for solving various numerical problems.•The methods were compared based on computational speed, efficiency, and robustness.•Classic numerical damping can improve the robustness of some, but not all, methods.•Newton method with selective numerical damping is the most efficient and robust.
Bibliography:scopus-id:2-s2.0-85132741943
ISSN:0168-874X
1872-6925
1872-6925
DOI:10.1016/j.finel.2022.103801