Error Estimation and Optimization of the Direct Simulation Monte Carlo Method Taking into Account Spatial Regularization

M. Yu. Plotnikov; Плотников М. Ю.; E. V. Shkarupa; Шкарупа Е. В.

doi:10.31857/S0044466923070128

Error Estimation and Optimization of the Direct Simulation Monte Carlo Method Taking into Account Spatial Regularization

Autores: Plotnikov M.Y.¹, Shkarupa E.V.²
Afiliações:
1. Kutateladze Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences
2. Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences
Edição: Volume 63, Nº 8 (2023)
Páginas: 1367-1379
Seção: Mathematical physics
URL: https://rjonco.com/0044-4669/article/view/665003
DOI: https://doi.org/10.31857/S0044466923070128
EDN: https://elibrary.ru/ZXWLAB
ID: 665003

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Resumo

The direct simulation Monte Carlo method is widely used for solving rarefied gas dynamics problems. The focus in this paper is on the study of the error introduced by spatial regularization of the interaction between two particles. Two approaches to spatial regularization and three direct simulation Monte Carlo algorithms implementing these approaches are considered. An upper bound on the error of these algorithms in the metric of the space of continuous functions is constructed, and conditionally optimal parameters that guarantee a prescribed error level in probability are obtained. Using the classical Fourier problem as an example, the error introduced by regularization is numerically investigated, and the constructed conditionally optimal parameters are tested.

Palavras-chave

Direct simulation Monte Carlo method, error, optimization, regularization

Sobre autores

M. Plotnikov

Kutateladze Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences

Email: plotnikov@itp.nsc.ru
630090, Novosibirsk, Russia

E. Shkarupa

Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences

Autor responsável pela correspondência
Email: sev@osmf.sscc.ru
630090, Novosibirsk, Russia

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