IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v89y2013icp50-68.html
   My bibliography  Save this article

A reduced-order finite volume element formulation based on POD method and numerical simulation for two-dimensional solute transport problems

Author

Listed:
  • Luo, Zhendong
  • Li, Hong
  • Sun, Ping
  • An, Jing
  • Navon, Ionel Michael

Abstract

Proper orthogonal decomposition (POD) method has been successfully used in the reduced-order modeling of complex systems. In this paper, we extend the applications of POD method, i.e., combine the classical finite volume element (FVE) method with the POD method to obtain a reduced-order FVE formulation with lower dimensions and sufficiently high accuracy for two-dimensional solute transport problems, which have real life practical applications. We then provide error estimates between the reduced-order POD FVE solutions and classical FVE solutions and we provide implementation of an extrapolation algorithm for solving the reduced-order FVE formulation. Thus, we provide the theoretical basis for practical applications. A numerical example is then used to ascertain that the results of numerical computation are consistent with the theoretical derivations. Moreover, it is shown that the reduced-order FVE formulation based on POD method is both feasible and efficient for solving two-dimensional solute transport problems.

Suggested Citation

  • Luo, Zhendong & Li, Hong & Sun, Ping & An, Jing & Navon, Ionel Michael, 2013. "A reduced-order finite volume element formulation based on POD method and numerical simulation for two-dimensional solute transport problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 89(C), pages 50-68.
    • Handle: RePEc:eee:matcom:v:89:y:2013:i:c:p:50-68
    DOI: 10.1016/j.matcom.2012.11.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037847541300044X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2012.11.012?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Li, Baibing & Martin, Elaine B. & Morris, A. Julian, 2002. "On principal component analysis in L1," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 471-474, September.
    2. K. Kunisch & S. Volkwein, 1999. "Control of the Burgers Equation by a Reduced-Order Approach Using Proper Orthogonal Decomposition," Journal of Optimization Theory and Applications, Springer, vol. 102(2), pages 345-371, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Luo, Zhendong & Teng, Fei & Chen, Jing, 2018. "A POD-based reduced-order Crank–Nicolson finite volume element extrapolating algorithm for 2D Sobolev equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 146(C), pages 118-133.
    2. Bai, Feng & Wang, Yi, 2022. "A reduced order modeling method based on GNAT-embedded hybrid snapshot simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 199(C), pages 100-132.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Plat, Richard, 2009. "Stochastic portfolio specific mortality and the quantification of mortality basis risk," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 123-132, August.
    2. Kondylis, Athanassios & Whittaker, Joe, 2008. "Spectral preconditioning of Krylov spaces: Combining PLS and PC regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2588-2603, January.
    3. Ouyang, Yaofu & Li, Peng, 2018. "On the nexus of financial development, economic growth, and energy consumption in China: New perspective from a GMM panel VAR approach," Energy Economics, Elsevier, vol. 71(C), pages 238-252.
    4. Paschalis Arvanitidis & Athina Economou & Christos Kollias, 2016. "Terrorism’s effects on social capital in European countries," Public Choice, Springer, vol. 169(3), pages 231-250, December.
    5. Weili Duan & Bin He & Daniel Nover & Guishan Yang & Wen Chen & Huifang Meng & Shan Zou & Chuanming Liu, 2016. "Water Quality Assessment and Pollution Source Identification of the Eastern Poyang Lake Basin Using Multivariate Statistical Methods," Sustainability, MDPI, vol. 8(2), pages 1-15, January.
    6. Cling, Jean-Pierre & Delecourt, Clément, 2022. "Interlinkages between the Sustainable Development Goals," World Development Perspectives, Elsevier, vol. 25(C).
    7. Hino, Hideitsu & Wakayama, Keigo & Murata, Noboru, 2013. "Entropy-based sliced inverse regression," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 105-114.
    8. Angelucci, Federica & Conforti, Piero, 2010. "Risk management and finance along value chains of Small Island Developing States. Evidence from the Caribbean and the Pacific," Food Policy, Elsevier, vol. 35(6), pages 565-575, December.
    9. Poskitt, D.S. & Sengarapillai, Arivalzahan, 2013. "Description length and dimensionality reduction in functional data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 98-113.
    10. Taner Akan & Tim Solle, 2022. "Do macroeconomic and financial governance matter? Evidence from Germany, 1950–2019," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 17(4), pages 993-1045, October.
    11. Paolo Rizzi & Paola Graziano & Antonio Dallara, 2018. "A capacity approach to territorial resilience: the case of European regions," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 60(2), pages 285-328, March.
    12. Pérez, Claudia & Claveria, Oscar, 2020. "Natural resources and human development: Evidence from mineral-dependent African countries using exploratory graphical analysis," Resources Policy, Elsevier, vol. 65(C).
    13. Zeynep Ozkok, 2015. "Financial openness and financial development: an analysis using indices," International Review of Applied Economics, Taylor & Francis Journals, vol. 29(5), pages 620-649, September.
    14. Asongu, Simplice A & Odhiambo, Nicholas M, 2019. "Governance,CO2 emissions and inclusive human development in Sub-Saharan Africa," Working Papers 25253, University of South Africa, Department of Economics.
    15. Anne M. Lausier & Shaleen Jain, 2018. "Diversity in global patterns of observed precipitation variability and change on river basin scales," Climatic Change, Springer, vol. 149(2), pages 261-275, July.
    16. Puppo, L. & Pedroni, N. & Maio, F. Di & Bersano, A. & Bertani, C. & Zio, E., 2021. "A Framework based on Finite Mixture Models and Adaptive Kriging for Characterizing Non-Smooth and Multimodal Failure Regions in a Nuclear Passive Safety System," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    17. Zarzo, Manuel & Martí, Pau, 2011. "Modeling the variability of solar radiation data among weather stations by means of principal components analysis," Applied Energy, Elsevier, vol. 88(8), pages 2775-2784, August.
    18. Simplice A. Asongu & Nicholas M. Odhiambo, 2021. "Income Levels, Governance and Inclusive Human Development in Sub-Saharan Africa," Applied Research in Quality of Life, Springer;International Society for Quality-of-Life Studies, vol. 16(1), pages 71-103, February.
    19. Simplice A. Asongu & Nicholas M. Odhiambo, 2019. "Inclusive development in environmental sustainability in sub‐Saharan Africa: Insights from governance mechanisms," Sustainable Development, John Wiley & Sons, Ltd., vol. 27(4), pages 713-724, July.
    20. Oliveira, Marcos William da Silva & da Silva, Núbia Rosa & Manzanera, Antoine & Bruno, Odemir Martinez, 2015. "Feature extraction on local jet space for texture classification," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 439(C), pages 160-170.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:89:y:2013:i:c:p:50-68. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.