IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v63y2003i6p587-604.html
   My bibliography  Save this article

Green’s function Monte Carlo algorithms for elliptic problems

Author

Listed:
  • Dimov, I.T.
  • Papancheva, R.Y.

Abstract

In many large-scale problems, one is interested to obtain directly an approximate value of a functional of the solution. Here, we consider a special class of grid-free Monte Carlo algorithms for direct computing of linear functionals of the solution of an elliptic boundary-value problem. Such kind of problems appear in environmental sciences, computational physics and financial mathematics. To create the algorithms, we use the Green’s function analysis and define the conditions under which the integral transformation kernel of the integral representation for the boundary-value problem under consideration is non-negative. This analysis is done for a possible set of densities, and it is used to generate three different grid-free Monte Carlo algorithms based on different choices of the density of the radius of the balls used in Monte Carlo simulation. Only one of the generated algorithms was known before. We shall call it Sipin’s algorithm. It was proposed and studied by Sipin. The aim of this work is to study the two new algorithms proposed here and based on two other (than in Sipin’s algorithm) possible choices of the densities. The algorithms are described and analyzed. The performed numerical tests show that the efficiency of one of the new algorithms, which is based on a constant density is higher than the efficiency of Sipin’s algorithm.

Suggested Citation

  • Dimov, I.T. & Papancheva, R.Y., 2003. "Green’s function Monte Carlo algorithms for elliptic problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 63(6), pages 587-604.
    • Handle: RePEc:eee:matcom:v:63:y:2003:i:6:p:587-604
    DOI: 10.1016/S0378-4754(03)00094-6
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475403000946
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/S0378-4754(03)00094-6?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.

    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:63:y:2003:i:6:p:587-604. 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.