An automated selection algorithm for nonlinear solvers in MDO

There are two major types of approaches that are used for the multidisciplinary analysis (MDA) of coupled systems: fixed-point-iteration-based approaches and coupled Newton-based approaches. Fixed-point-iteration approaches are easier to implement, but can require a large number of iterations or div...

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Vydáno v:Structural and multidisciplinary optimization Ročník 58; číslo 2; s. 349 - 377
Hlavní autoři: Chauhan, Shamsheer S., Hwang, John T., Martins, Joaquim R. R. A.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2018
Springer Nature B.V
Témata:
Algorithms
Computational Mathematics and Numerical Analysis
Engineering
Engineering Design
Optimization
Research Paper
Solvers
Source code
Switches
Theoretical and Applied Mechanics
Coupling strength
Hybrid
Nonlinear block Gauss–Seidel
Newton
MDA
Complex systems
ISSN:1615-147X, 1615-1488
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Shrnutí:There are two major types of approaches that are used for the multidisciplinary analysis (MDA) of coupled systems: fixed-point-iteration-based approaches and coupled Newton-based approaches. Fixed-point-iteration approaches are easier to implement, but can require a large number of iterations or diverge for strongly coupled problems. On the other hand, coupled-Newton approaches have superior convergence orders, but generally require more effort to implement and have more expensive iterations. Additionally, these two major approaches have many variations, including hybrid approaches where the MDA begins with a fixed-point iteration and then switches to a coupled-Newton approach after a certain number of iterations. However, there is a lack of criteria to govern how to select between these approaches, and when to switch between them in a hybrid approach. This paper compares these approaches and provides an algorithm that can be used to automatically select and switch between them. The proposed algorithm is implemented using OpenMDAO, NASA’s open-source framework for multidisciplinary analysis and optimization, and is tested using OpenAeroStruct, an open-source low-fidelity tool for aerostructural optimization. The results show that the proposed algorithm provides a balance of improved robustness and speed.
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ISSN:1615-147X
1615-1488
DOI:10.1007/s00158-018-2004-5