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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| Published in: | Finite elements in analysis and design Vol. 209; p. 103801 |
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| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
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15.10.2022
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| ISSN: | 0168-874X, 1872-6925, 1872-6925 |
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| Abstract | 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. |
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| AbstractList | 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. 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. |
| ArticleNumber | 103801 |
| Author | Harzallah, Ridha Morch, Hélène Yuan, Sibo Duchêne, Laurent Habraken, Anne Marie |
| Author_xml | – sequence: 1 givenname: Hélène orcidid: 0000-0002-9656-3558 surname: Morch fullname: Morch, Hélène email: helene.morch@uliege.be organization: ArGEnCo Department, MSM Team, University of Liège, Quartier Polytech 1, Allée de la Découverte 9, Liège, 4000, Belgium – sequence: 2 givenname: Sibo surname: Yuan fullname: Yuan, Sibo organization: ArGEnCo Department, MSM Team, University of Liège, Quartier Polytech 1, Allée de la Découverte 9, Liège, 4000, Belgium – sequence: 3 givenname: Laurent surname: Duchêne fullname: Duchêne, Laurent organization: ArGEnCo Department, MSM Team, University of Liège, Quartier Polytech 1, Allée de la Découverte 9, Liège, 4000, Belgium – sequence: 4 givenname: Ridha surname: Harzallah fullname: Harzallah, Ridha organization: John Cockerill Energy, Avenue Greiner 1, 4100, Seraing, Belgium – sequence: 5 givenname: Anne Marie surname: Habraken fullname: Habraken, Anne Marie organization: ArGEnCo Department, MSM Team, University of Liège, Quartier Polytech 1, Allée de la Découverte 9, Liège, 4000, Belgium |
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| Cites_doi | 10.1090/S0025-5718-66-99924-8 10.1016/j.mcm.2010.12.032 10.3184/096034007X207589 10.1016/j.mechmat.2020.103393 10.1016/j.solener.2017.12.003 10.1016/S0749-6419(01)00029-8 10.1016/j.cam.2009.09.035 10.1115/1.3264257 10.1017/S0004972700030586 10.1007/s11075-008-9227-2 10.1016/S0893-9659(04)90104-8 10.1109/ICNN.1995.488968 10.1016/j.ijsolstr.2017.07.031 10.1016/j.ijplas.2008.03.009 10.1007/s11075-012-9585-7 |
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| Snippet | 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... |
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| SubjectTerms | 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 |
| Title | A review of higher order Newton type methods and the effect of numerical damping for the solution of an advanced coupled Lemaitre damage model |
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