Application of the Monte Carlo method with meshless random walk procedure to selected scalar elliptic problems
Authors:
- S. Milewski
Abstract
The combined stochastic-deterministic approach, which may be applied to the numerical analysis of a wide range of scalar elliptic problems of civil engineering, is presented in this paper. It is based on the well-known Monte Carlo concept with a random walk procedure, in which series of random paths are constructed. Additionally, it incorporates selected features of the meshless finite difference method, especially star selection criteria and a local weighted function approximation. The approach leads to the explicit stochastic formula relating one unknown function value with all a-priori known data parameters. Therefore, it allows for a fast and effective estimation of the solution value at the selected point(s), without the necessity of generation of large systems of equations, combining all unknown values. In such a manner, the proposed approach develops and extends the original standard Monte Carlo one toward analysis of boundary value problems with more complex shape geometry, natural boundary conditions, non-homogeneous right-hand sides as well as anisotropic and non-linear material models. The paper is illustrated with numerical results of selected elliptic problems, including a torsion problem of a prismatic bar, a stationary heat flow analysis with anisotropic and non-linear material functions, as well as an inverse heat problem. Moreover, the appropriate coupling with other deterministic methods (e.g., the finite element method) is considered.
- Record ID
- CUTd8fb2ceb05a24b0fa19f16f1e1597635
- Publication categories
- ; ;
- Author
- Journal series
- Archives of Mechanics, ISSN 0373-2029
- Issue year
- 2019
- Vol
- 71
- No
- 4-5
- Pages
- 337-375
- Other elements of collation
- rys.; wykr.; Bibliografia (na s.) - 372-375; Bibliografia (liczba pozycji) - 56; Oznaczenie streszczenia - Streszcz. ang.; Numeracja w czasopiśmie - Vol. 71, No. 4-5
- Conference
- 41st Solid Mechanics Conference (SolMech 2018), 2018, 27-08-2018 - 31-08-2018, Warsaw, Polska
- Keywords in English
- Monte Carlo method, random walk procedure, meshless finite difference method, elliptic problems, method coupling, non-linear problems, inverse problems
- DOI
- DOI:10.24423/aom.3111 Opening in a new tab
- URL
- http://am.ippt.pan.pl/am/article/view/v71p337 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/CUTd8fb2ceb05a24b0fa19f16f1e1597635/
- URN
urn:pkr-prod:CUTd8fb2ceb05a24b0fa19f16f1e1597635
* 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.