Error driven node placement as applied to one dimensional shallow water equations

Zhenquan Li, Peter Crowhurst, Robert Wood

Research output: Book chapter/Published conference paperConference paper

Abstract

This paper investigates the technique of localised mesh refinement to solve the Shallow Water Equations (SWE), by adding nodes only where needed. The discretization process linearizes the nonlinear equations for solving as a linear system. The nonlinear error values at specific nodes are used to indicate which node will have additional nodes added either side. The process of adding nodes is repeated until the nonlinear error value is below a given threshold, or the predefined maximum number of nodes for that given time step has been reached. This process is restarted again at each time step, allowing the optimization process to efficiently allocate nodes based only on error, avoiding global increases in node numbers across the solution set. © 2015 IEEE.
Original languageEnglish
Title of host publicationUKSim 2015
Subtitle of host publicationProceedings of UKSim-AMSS 17th International Conference on Computer Modelling and Simulation
PublisherIEEE, Institute of Electrical and Electronics Engineers
Pages31-38
Number of pages8
ISBN (Electronic)9781479987139
DOIs
Publication statusPublished - 2016
Event2015 17th UKSim-AMSS International Conference on Modelling and Simulation (UKSim) - Cambridge University, Cambridge, United Kingdom
Duration: 25 Mar 201527 Mar 2015
Conference number: 123957

Publication series

NameIEEE Computer Society Conference Publishing Services (CPS)
PublisherIEEE Computer Society

Conference

Conference2015 17th UKSim-AMSS International Conference on Modelling and Simulation (UKSim)
CountryUnited Kingdom
CityCambridge
Period25/03/1527/03/15

Fingerprint

Water
Nonlinear equations
Linear systems

Cite this

Li, Z., Crowhurst, P., & Wood, R. (2016). Error driven node placement as applied to one dimensional shallow water equations. In UKSim 2015: Proceedings of UKSim-AMSS 17th International Conference on Computer Modelling and Simulation (pp. 31-38). [7576517] (IEEE Computer Society Conference Publishing Services (CPS) ). IEEE, Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/UKSim.2015.31
Li, Zhenquan ; Crowhurst, Peter ; Wood, Robert. / Error driven node placement as applied to one dimensional shallow water equations. UKSim 2015: Proceedings of UKSim-AMSS 17th International Conference on Computer Modelling and Simulation. IEEE, Institute of Electrical and Electronics Engineers, 2016. pp. 31-38 (IEEE Computer Society Conference Publishing Services (CPS) ).
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abstract = "This paper investigates the technique of localised mesh refinement to solve the Shallow Water Equations (SWE), by adding nodes only where needed. The discretization process linearizes the nonlinear equations for solving as a linear system. The nonlinear error values at specific nodes are used to indicate which node will have additional nodes added either side. The process of adding nodes is repeated until the nonlinear error value is below a given threshold, or the predefined maximum number of nodes for that given time step has been reached. This process is restarted again at each time step, allowing the optimization process to efficiently allocate nodes based only on error, avoiding global increases in node numbers across the solution set. {\circledC} 2015 IEEE.",
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Li, Z, Crowhurst, P & Wood, R 2016, Error driven node placement as applied to one dimensional shallow water equations. in UKSim 2015: Proceedings of UKSim-AMSS 17th International Conference on Computer Modelling and Simulation., 7576517, IEEE Computer Society Conference Publishing Services (CPS) , IEEE, Institute of Electrical and Electronics Engineers, pp. 31-38, 2015 17th UKSim-AMSS International Conference on Modelling and Simulation (UKSim), Cambridge, United Kingdom, 25/03/15. https://doi.org/10.1109/UKSim.2015.31

Error driven node placement as applied to one dimensional shallow water equations. / Li, Zhenquan; Crowhurst, Peter; Wood, Robert.

UKSim 2015: Proceedings of UKSim-AMSS 17th International Conference on Computer Modelling and Simulation. IEEE, Institute of Electrical and Electronics Engineers, 2016. p. 31-38 7576517 (IEEE Computer Society Conference Publishing Services (CPS) ).

Research output: Book chapter/Published conference paperConference paper

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N1 - Imported on 03 May 2017 - DigiTool details were: publisher = IEEE Computer Society, 2015. editor/s (773b) = David Al-Dabass; Event dates (773o) = 25-27 March 2015; Parent title (773t) = IEEE International conference on modelling and simulation.

PY - 2016

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N2 - This paper investigates the technique of localised mesh refinement to solve the Shallow Water Equations (SWE), by adding nodes only where needed. The discretization process linearizes the nonlinear equations for solving as a linear system. The nonlinear error values at specific nodes are used to indicate which node will have additional nodes added either side. The process of adding nodes is repeated until the nonlinear error value is below a given threshold, or the predefined maximum number of nodes for that given time step has been reached. This process is restarted again at each time step, allowing the optimization process to efficiently allocate nodes based only on error, avoiding global increases in node numbers across the solution set. © 2015 IEEE.

AB - This paper investigates the technique of localised mesh refinement to solve the Shallow Water Equations (SWE), by adding nodes only where needed. The discretization process linearizes the nonlinear equations for solving as a linear system. The nonlinear error values at specific nodes are used to indicate which node will have additional nodes added either side. The process of adding nodes is repeated until the nonlinear error value is below a given threshold, or the predefined maximum number of nodes for that given time step has been reached. This process is restarted again at each time step, allowing the optimization process to efficiently allocate nodes based only on error, avoiding global increases in node numbers across the solution set. © 2015 IEEE.

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Li Z, Crowhurst P, Wood R. Error driven node placement as applied to one dimensional shallow water equations. In UKSim 2015: Proceedings of UKSim-AMSS 17th International Conference on Computer Modelling and Simulation. IEEE, Institute of Electrical and Electronics Engineers. 2016. p. 31-38. 7576517. (IEEE Computer Society Conference Publishing Services (CPS) ). https://doi.org/10.1109/UKSim.2015.31