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A Matlab software for approximate solution of 2D elliptic problems by means of the meshless Monte Carlo random walk method
- Source :
- Numerical Algorithms. 83:565-591
- Publication Year :
- 2019
- Publisher :
- Springer Science and Business Media LLC, 2019.
-
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.
- Subjects :
- Discretization
business.industry
Applied Mathematics
Numerical analysis
Monte Carlo method
010103 numerical & computational mathematics
System of linear equations
Random walk
01 natural sciences
010101 applied mathematics
Software
Applied mathematics
Meshfree methods
Boundary value problem
0101 mathematics
business
Mathematics
Subjects
Details
- ISSN :
- 15729265 and 10171398
- Volume :
- 83
- Database :
- OpenAIRE
- Journal :
- Numerical Algorithms
- Accession number :
- edsair.doi...........de2e66fcf775081e2971f16ec0454d87