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A Matlab software for approximate solution of 2D elliptic problems by means of the meshless Monte Carlo random walk method

  • Sławomir Milewski
Open Access
Original Paper
  • 62 Downloads

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.

Keywords

Monte Carlo method Random walk technique Meshless methods Elliptic problems Finite difference method Implementation in Matlab 

Notes

Funding information

This research was supported by the National Science Centre, Poland, under the scientific project 2015/19/D/ST8/00816 (Computational coupled FEM / meshless FDM analysis dedicated to engineering non-stationary thermo-elastic and thermoplastic problems).

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Copyright information

© The Author(s) 2019

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Civil Engineering DepartmentCracow University of TechnologyKrakówPoland

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