An improved finite element meshing strategy for dynamic optimization problems
type: Item
instance of: scholarly article
title: An improved finite element meshing strategy for dynamic optimization problems
zbMATH Open document ID: 1426.90248
DOI: 10.1155/2017/4829195
author: Minliang Gong
author: Aipeng Jiang
author: Quannan Zhang
author: Haokun Wang
author: Junjie Hu
author: Yinghui Lin
published in: Mathematical Problems in Engineering
publication date: 2018-11-05T00:00:00Z
review text: Summary: The finite element orthogonal collocation method is widely used in the discretization of differential algebraic equations (DAEs), while the discrete strategy significantly affects the accuracy and efficiency of the results. In this work, a finite element meshing method with error estimation on noncollocation point is proposed and several cases were studied. Firstly, the simultaneous strategy based on the finite element is used to transform the differential and algebraic optimization problems (DAOPs) into large scale nonlinear programming problems. Then, the state variables of the reaction process are obtained by simulating with fixed control variables. The noncollocation points are introduced to compute the error estimates of the state variables at noncollocation points. Finally, in order to improve the computational accuracy with less finite element, moving finite element strategy was used for dynamically adjusting the length of finite element appropriately to satisfy the set margin of error. The proposed strategy is applied to two classical control problems and a large scale reverse osmosis seawater desalination process. Computing result shows that the proposed strategy can effectively reduce the computing effort with satisfied accuracy for dynamic optimization problems.
Mathematics Subject Classification ID: 90C39
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 49M25
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 65N30
zbMATH DE Number: 6972142
Wikidata QID: Q59147574
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/4829195
OpenAlex ID: W2739240916
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description: scientific article; zbMATH DE number 6972142