Skip to main content
SpringerLink
Log in

Minimization of p-Laplacian via the Finite Element Method in MATLAB

  • Conference paper
  • First Online:
Large-Scale Scientific Computing (LSSC 2021)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13127))

Included in the following conference series:

Abstract

Minimization of energy functionals is based on a discretization by the finite element method and optimization by the trust-region method. A key tool to an efficient implementation is a local evaluation of the approximated gradients together with sparsity of the resulting Hessian matrix. Vectorization concepts are explained for the p-Laplace problem in one and two space-dimensions.

C. Matonoha was supported by the long-term strategic development financing of the Institute of Computer Science (RVO:67985807). A. Moskovka announces the support of the Czech Science Foundation (GACR) through the grant 18-03834S and J. Valdman the support by the Czech-Austrian Mobility MSMT Grant: 8J21AT001.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Anjam, I., Valdman, J.: Fast MATLAB assembly of FEM matrices in 2D and 3D: edge elements. Appl. Math. Comput. 267, 252–263 (2015)

    MathSciNet  MATH  Google Scholar 

  2. Barrett, J.W., Liu, J.G.: Finite element approximation of the p-Laplacian. Math. Comput. 61(204), 523–537 (1993)

    MathSciNet  MATH  Google Scholar 

  3. Ciarlet, P.G.: The Finite Element Method for Elliptic Problems. SIAM, Philadelphia (2002)

    Book  Google Scholar 

  4. Conn, A.R., Gould, N.I.M., Toint, P.L.: Trust-Region Methods. SIAM, Philadelphia (2000)

    Book  Google Scholar 

  5. Drábek P., Milota J.: Methods of Nonlinear Analysis: Applications to Differential Equations, 2nd edn. Birkhauser (2013)

    Google Scholar 

  6. Lukšan, L., et al.: UFO 2017. Interactive System for Universal Functional Optimization. Technical Report V-1252. Prague, ICS AS CR (2017). http://www.cs.cas.cz/luksan/ufo.html

  7. Rahman, T., Valdman, J.: Fast MATLAB assembly of FEM matrices in 2D and 3D: nodal elements. Appl. Math. Comput. 219, 7151–7158 (2013)

    MathSciNet  MATH  Google Scholar 

  8. Lindqvist, P.: Notes of the p-Laplace Equation (second edition), report 161: of the Department of Mathematics and Statistics. University of Jyvaäskylä, Finland (2017)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The Czech Academy of Sciences, Institute of Computer Science, Pod Vodárenskou věží 2, 18207, Prague 8, Czechia

    Ctirad Matonoha

  2. Faculty of Applied Sciences, Department of Mathematics, University of West Bohemia, Technická 8, 30614, Pilsen, Czechia

    Alexej Moskovka

  3. The Czech Academy of Sciences, Institute of Information Theory and Automation, Pod Vodárenskou věží 4, 18208, Prague 8, Czechia

    Jan Valdman

  4. Department of Computer Science, Faculty of Science, University of South Bohemia, Branišovská 1760, 37005, České Budějovice, Czechia

    Jan Valdman

Authors
  1. Ctirad Matonoha
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alexej Moskovka
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jan Valdman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alexej Moskovka .

Editor information

Editors and Affiliations

  1. IICT-BAS, Sofia, Bulgaria

    Ivan Lirkov

  2. IICT-BAS, Sofia, Bulgaria

    Svetozar Margenov

Rights and permissions

Reprints and permissions

Copyright information

© 2022 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Matonoha, C., Moskovka, A., Valdman, J. (2022). Minimization of p-Laplacian via the Finite Element Method in MATLAB. In: Lirkov, I., Margenov, S. (eds) Large-Scale Scientific Computing. LSSC 2021. Lecture Notes in Computer Science, vol 13127. Springer, Cham. https://doi.org/10.1007/978-3-030-97549-4_61

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-97549-4_61

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-97548-7

  • Online ISBN: 978-3-030-97549-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation