Application of the Monte Carlo method with meshless random walk procedure to selected scalar elliptic problems

• Autorzy: Milewski S.

Identyfikatory

DOI

10.24423/aom.3111

• Konferencja: Solid Mechanics Conference (SolMech 2018) (41 ; 27–31.08. 2018 ; Warsaw, Poland)
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Monte Carlo method; random walk procedure; meshless finite differences method; elliptic problems; method coupling; non-linear problems; inverse problems

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2019
• Tom: Vol. 71, nr 4-5
• Strony: 337–--375
• Opis fizyczny: Bibliogr. 56 poz., rys. kolor.

Twórcy

autor

Milewski S.

• Cracow University of Technology, Department of Civil Engineering, Institute for Computational Civil Engineering, Warszawska 24, 31-155 Cracow, Poland

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Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).