IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v320y2018icp271-281.html
   My bibliography  Save this article

A nonlinear multigrid method for inverse problem in the multiphase porous media flow

Author

Listed:
  • Liu, Tao

Abstract

In this paper, we consider a parameter identification problem for the nonlinear convection–diffusion equation in the multiphase porous media flow. A nonlinear multigrid method is proposed for the recovery of permeability. This method works by dynamically adjusting the objective functionals at different grids so that they are consistent with each other, and ultimately reduce, the finest grid objective functional. In this manner, the nonlinear multigrid method can efficiently compute the solution to a desired fine grid inverse problem. Numerical results illustrate that the proposed multigrid approach both dramatically reduces the required computation and improves the reconstructed image quality.

Suggested Citation

  • Liu, Tao, 2018. "A nonlinear multigrid method for inverse problem in the multiphase porous media flow," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 271-281.
    • Handle: RePEc:eee:apmaco:v:320:y:2018:i:c:p:271-281
    DOI: 10.1016/j.amc.2017.09.039
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300317306677
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2017.09.039?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. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1157-1160, December.
    2. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(5), pages 1025-1031, October.
    3. Choi, Yongho & Jeong, Darae & Kim, Junseok, 2017. "A multigrid solution for the Cahn–Hilliard equation on nonuniform grids," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 320-333.
    4. Liu, Tao, 2016. "Reconstruction of a permeability field with the wavelet multiscale–homotopy method for a nonlinear convection–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 432-437.
    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. Tao Liu & Di Ouyang & Lianjun Guo & Ruofeng Qiu & Yunfei Qi & Wu Xie & Qiang Ma & Chao Liu, 2023. "Combination of Multigrid with Constraint Data for Inverse Problem of Nonlinear Diffusion Equation," Mathematics, MDPI, vol. 11(13), pages 1-15, June.

    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. Dolf Talman & Zaifu Yang, 2012. "On a Parameterized System of Nonlinear Equations with Economic Applications," Journal of Optimization Theory and Applications, Springer, vol. 154(2), pages 644-671, August.
    2. Subramanian, S.V. & Subramanyam, Malavika A. & Selvaraj, Sakthivel & Kawachi, Ichiro, 2009. "Are self-reports of health and morbidities in developing countries misleading? Evidence from India," Social Science & Medicine, Elsevier, vol. 68(2), pages 260-265, January.
    3. World Bank, 2002. "Costa Rica : Social Spending and the Poor, Volume 1. Summary of Issues and Recommendations with Executive Summary," World Bank Publications - Reports 15330, The World Bank Group.
    4. Emin Karagözoğlu, 2014. "A noncooperative approach to bankruptcy problems with an endogenous estate," Annals of Operations Research, Springer, vol. 217(1), pages 299-318, June.
    5. Hernández-Hernández, M.E. & Kolokoltsov, V.N. & Toniazzi, L., 2017. "Generalised fractional evolution equations of Caputo type," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 184-196.
    6. Simon Levin & Anastasios Xepapadeas, 2021. "On the Coevolution of Economic and Ecological Systems," Annual Review of Resource Economics, Annual Reviews, vol. 13(1), pages 355-377, October.
    7. Juan Moreno-Ternero & Antonio Villar, 2006. "The TAL-Family of Rules for Bankruptcy Problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(2), pages 231-249, October.
    8. Lee, Hiro & van der Mensbrugghe, Dominique, 2005. "The impact of the US safeguard measures on Northeast Asian producers: General equilibrium assessments," MPRA Paper 82288, University Library of Munich, Germany.
    9. Hoang Ngoc Tuan, 2015. "Boundedness of a Type of Iterative Sequences in Two-Dimensional Quadratic Programming," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 234-245, January.
    10. Wang, Daojuan & Hain, Daniel S. & Larimo, Jorma & Dao, Li T., 2020. "Cultural differences and synergy realization in cross-border acquisitions," International Business Review, Elsevier, vol. 29(3).
    11. Wulf Gaertner & Richard Bradley & Yongsheng Xu & Lars Schwettmann, 2019. "Against the proportionality principle: Experimental findings on bargaining over losses," PLOS ONE, Public Library of Science, vol. 14(7), pages 1-18, July.
    12. Zhou, H. & Uhlaner, L.M., 2009. "Knowledge Management in the SME and its Relationship to Strategy, Family Orientation and Organization Learning," ERIM Report Series Research in Management ERS-2009-026-ORG, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    13. Turpie, J.K. & Marais, C. & Blignaut, J.N., 2008. "The working for water programme: Evolution of a payments for ecosystem services mechanism that addresses both poverty and ecosystem service delivery in South Africa," Ecological Economics, Elsevier, vol. 65(4), pages 788-798, May.
    14. Tilman Br�ck & Patricia Justino & Philip Verwimp & Andrew Tedesco & Alexandra Avdeenko, 2013. "Measuring Conflict Exposure in Micro-Level Surveys," HiCN Working Papers 153, Households in Conflict Network.
    15. Erik Ansink & Hans-Peter Weikard, 2012. "Sequential sharing rules for river sharing problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(2), pages 187-210, February.
    16. Koichi Hamada & Asahi Noguchi, 2005. "The Role of Preconceived Ideas in Macroeconomic Policy: Japan's Experiences in the Two Deflationary Periods," Working Papers 908, Economic Growth Center, Yale University.
    17. Jingyi Xue, 2018. "Fair division with uncertain needs," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(1), pages 105-136, June.
    18. Dipak R. Pant, 2013. "Managing the global waste in the 21st century: As an anthropologist views it," LIUC Papers in Economics 263, Cattaneo University (LIUC).
    19. Mikhail A. Sokolovskiy & Xavier J. Carton & Boris N. Filyushkin, 2020. "Mathematical Modeling of Vortex Interaction Using a Three-Layer Quasigeostrophic Model. Part 1: Point-Vortex Approach," Mathematics, MDPI, vol. 8(8), pages 1-13, July.
    20. van der Laan, Gerard & Talman, Dolf & Yang, Zaifu, 2011. "Solving discrete systems of nonlinear equations," European Journal of Operational Research, Elsevier, vol. 214(3), pages 493-500, November.

    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:apmaco:v:320:y:2018:i:c:p:271-281. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.