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A Matlab software for approximate solution of 2D elliptic problems by means of the meshless Monte Carlo random walk method. (English) Zbl 1507.65014

Summary: 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.

MSC:

65C05 Monte Carlo methods
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
60G50 Sums of independent random variables; random walks
65-04 Software, source code, etc. for problems pertaining to numerical analysis

Software:

Matlab; Mfree2D; MFDMtool
PDFBibTeX XMLCite
Full Text: DOI

References:

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