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  4. Using surrogate models to accelerate load step methods for nonlinear finite element problems in hyperelasticity
 
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Using surrogate models to accelerate load step methods for nonlinear finite element problems in hyperelasticity

Citation Link: https://doi.org/10.15480/882.14616
Publikationstyp
Journal Article
Date Issued
2024-10-04
Sprache
English
Author(s)
Fesefeldt, Eva Lina 
Mathematik E-10  
Le Borne, Sabine  orcid-logo
Mathematik E-10  
Düster, Alexander  
Konstruktion und Festigkeit von Schiffen M-10  
Radtke, Lars  
Konstruktion und Festigkeit von Schiffen M-10  
TORE-DOI
10.15480/882.14616
TORE-URI
https://hdl.handle.net/11420/54315
Journal
Proceedings in applied mathematics and mechanics  
Volume
24
Issue
3
Article Number
e202400081
Citation
Proceedings in Applied Mathematics and Mechanics 24 (3): e202400081 (2024)
Contribution to Conference
94th Annual Meeting of the International Association of Applied Mathematics and Mechanics, GAMM 2024  
Publisher DOI
10.1002/pamm.202400081
Publisher
Wiley
Finite element methods for displacement problems in hyperelasticity lead to systems of nonlinear equations. These equations are usually solved with Newton's method or a related method. The convergence of Newton's method depends heavily on the proximity of the initial guess to the numerical solution. Load step methods overcome problems with divergence by applying the load in increments, leading to a sequence of sub‐problems with initial guesses closer to the numerical solution of each sub‐problem, supporting the convergence. The downside of this approach is the high computational effort needed to solve the load steps. Based on a benchmark problem in high‐order FEM, we extend traditional load step methods to a new approach exploiting the hierarchical basis used for the spatial discretization of the problem and saving up to 50% of computation time (vs. benchmark).
DDC Class
518: Numerical Analysis
515: Analysis
530: Physics
620: Engineering
621.3: Electrical Engineering, Electronic Engineering
Funding(s)
Projekt DEAL  
Publication version
publishedVersion
Lizenz
https://creativecommons.org/licenses/by/4.0/
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