IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v488y2025ics0096300324005800.html
   My bibliography  Save this article

Efficient simulation of mixed boundary value problems and conformal mappings

Author

Listed:
  • Han, Qiansheng
  • Rasila, Antti
  • Sottinen, Tommi

Abstract

We present a stochastic method for the simulation of Laplace's equation with a mixed boundary condition in planar domains that are polygonal or bounded by circular arcs. We call this method the Reflected Walk-on-Spheres algorithm. The method combines a traditional Walk-on-Spheres algorithm with use of reflections at the Neumann boundaries. We apply our algorithm to simulate numerical conformal mappings from certain quadrilaterals to the corresponding canonical domains, and to compute their conformal moduli. Finally, we give examples of the method on three dimensional polyhedral domains, and use it to simulate the heat flow on an L-shaped insulated polyhedron.

Suggested Citation

  • Han, Qiansheng & Rasila, Antti & Sottinen, Tommi, 2025. "Efficient simulation of mixed boundary value problems and conformal mappings," Applied Mathematics and Computation, Elsevier, vol. 488(C).
    • Handle: RePEc:eee:apmaco:v:488:y:2025:i:c:s0096300324005800
    DOI: 10.1016/j.amc.2024.129119
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300324005800
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2024.129119?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. Yang, Xuxin & Rasila, Antti & Sottinen, Tommi, 2019. "Efficient simulation of the Schrödinger equation with a piecewise constant positive potential," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 315-323.
    2. Xuxin Yang & Antti Rasila & Tommi Sottinen, 2017. "Walk On Spheres Algorithm for Helmholtz and Yukawa Equations via Duffin Correspondence," Methodology and Computing in Applied Probability, Springer, vol. 19(2), pages 589-602, June.
    3. Wesley Pacheco Calixto & Bernardo Alvarenga & Jesus Carlos da Mota & Leonardo da Cunha Brito & Marcel Wu & Aylton José Alves & Luciano Martins Neto & Carlos F. R. Lemos Antunes, 2010. "Electromagnetic Problems Solving by Conformal Mapping: A Mathematical Operator for Optimization," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-19, February.
    Full references (including those not matched with items on IDEAS)

    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. Yang, Xuxin & Rasila, Antti & Sottinen, Tommi, 2019. "Efficient simulation of the Schrödinger equation with a piecewise constant positive potential," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 315-323.

    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:488:y:2025:i:c:s0096300324005800. 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.