Combination of the meshless finite difference approach with the Monte Carlo random walk technique for solution of elliptic problems
Authors:
- Sławomir Milewski
Abstract
This paper proposes a stochastic approach for the fast and effective numerical analysis of the second order elliptic differential equations. It is based upon the well-known Monte Carlo (MC) method with a random walk (RW) technique, carried out on the grid of points. This method allows for accurate estimation of the solution of the differential equation at selected point(s) of the domain and/or its boundary. It extends the standard formulation of the Monte Carlo–random walk (MC–RW) approach by means of its appropriate combination with the meshless version of the finite difference method. In this manner, the proposed approach may deal with elliptic equations in more general non-homogeneous form as well as boundary conditions of both essential and natural types. Moreover, arbitrarily irregular clouds of nodes may be used, with no a-priori imposed nodes structure. Therefore, the meshless MC/RW approach may be applied to the significantly wider class of problems with more complex geometry. This concept was examined on variety of 2D boundary value problems. Selected numerical results are presented and discussed. A simple Matlab code is included as well.
- Record ID
- CUT5b9ee0e46c4c426193ee4ae605694304
- Publication categories
- ;
- Author
- Journal series
- Computers & Mathematics With Applications, ISSN 0898-1221, e-ISSN 1873-7668
- Issue year
- 2018
- Vol
- 76
- No
- 4
- Pages
- 854-876
- Other elements of collation
- il. (w tym kolor.); Bibliografia (na s.) - 875-876; Bibliografia (liczba pozycji) - 50; Oznaczenie streszczenia - Abstr.; Data udostępnienia on-line - 2018-06-19; Numeracja w czasopiśmie - Vol. 76, Iss. 4
- Keywords in English
- Monte Carlo method, random walk technique, finite difference method, meshless methods, elliptic problems
- DOI
- DOI:10.1016/j.camwa.2018.05.025 Opening in a new tab
- URL
- https://www.sciencedirect.com/science/article/pii/S0898122118302931 Opening in a new tab
- Related project
- Komputerowa analiza inżynierskich nieustalonych zagadnień termosprężystych i termoplastycznych za pomocą sprzężonej MES / bezsiatkowej MRS. . Project leader at PK: , ,
Projects financed by NSC [Projekty finansowane przez NCN] - Language
- eng (en) English
- Score (nominal)
- 40
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUT5b9ee0e46c4c426193ee4ae605694304/
- URN
urn:pkr-prod:CUT5b9ee0e46c4c426193ee4ae605694304
* presented citation count is obtained through Internet information analysis, and it is close to the number calculated by the Publish or PerishOpening in a new tab system.