IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v247y2026icp483-499.html

Numerical analysis of scattering on combinatorial graphs

Author

Listed:
  • Brio, M.
  • Caputo, J.-G.

Abstract

We investigate numerically the scattering of waves on discrete graphs. After reviewing in detail the scattering theory: unitarity of the scattering matrix and conditions for total reflection and transmission, we propose an efficient algorithm to compute the reflection and transmission spectral coefficients. We analyze the well-posedness of the scattering problem and give conditions on a graph Laplacian eigenvector (bound state) and the leads for the corresponding eigenvalue to cause a complete reflection or transmission. Various configurations of input and output leads are studied illustrating how specific vertex-lead connections can result in total reflection for bound states and total transmission. The impedance of the leads is shown to influence the spectral coefficients in a predictable manner. Furthermore, for a given input lead we show that the total transmission of a wavepacket can be maximized by appropriately selecting the exit lead. Finally, we analyze the spectral signatures of defects within the graph and find that they vary depending on both the defect’s location and its spectral characteristics.

Suggested Citation

  • Brio, M. & Caputo, J.-G., 2026. "Numerical analysis of scattering on combinatorial graphs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 247(C), pages 483-499.
    • Handle: RePEc:eee:matcom:v:247:y:2026:i:c:p:483-499
    DOI: 10.1016/j.matcom.2026.03.027
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475426001199
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2026.03.027?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

    for a different version of it.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:247:y:2026:i:c:p:483-499. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.