A Matlab software for approximate solution of 2D elliptic problems by means of the meshless Monte Carlo random walk method
Authors:
- Sławomir Milewski
Abstract
This paper is devoted to the development of an innovative Matlab software, dedicated to the numerical analysis of two-dimensional elliptic problems, by means of the probabilistic approach. This approach combines features of the Monte Carlo random walk method with discretization and approximation techniques, typical for meshless methods. It allows for determination of an approximate solution of elliptic equations at the specified point (or group of points), without a necessity to generate large system of equations for the entire problem domain. While the procedure is simple and fast, the final solution may suffer from both stochastic and discretization errors. The attached Matlab software is based on several original author’s concepts. It permits the use of arbitrarily irregular clouds of nodes, non-homogeneous right-hand side functions, mixed type of boundary conditions as well as variable material coefficients (of anisotropic materials). The paper is illustrated with results of analysis of selected elliptic problems, obtained by means of this software.
- Record ID
- CUT9ae4076c6901473695625a22cea71a49
- Publication categories
- ;
- Author
- Journal series
- Numerical Algorithms, ISSN 1017-1398, e-ISSN 1572-9265
- Issue year
- 2020
- Vol
- 83
- No
- 2
- Pages
- 565-591
- Other elements of collation
- schem.; wykr.; Bibliografia (na s.) - 589-591; Bibliografia (liczba pozycji) - 53; Oznaczenie streszczenia - Abstr.; Data udostępnienia on-line - 2019-04-11; Numeracja w czasopiśmie - Vol. 83, Iss. 2
- Keywords in English
- thod, random walk technique, Meshless methods, elliptic problems, finite difference method, implementation in Matlab
- DOI
- DOI:10.1007/s11075-019-00694-x Opening in a new tab
- URL
- https://link.springer.com/article/10.1007/s11075-019-00694-x 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
- License
- Score (nominal)
- 100
- Additional fields
- Indeksowana w: Web of Science, Scopus
- Uniform Resource Identifier
- https://cris.pk.edu.pl/info/article/CUT9ae4076c6901473695625a22cea71a49/
- URN
urn:pkr-prod:CUT9ae4076c6901473695625a22cea71a49
* 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.