Monte Carlo Increased-Radius Floating Random Walk Solution For Potential Problems

Year 2024, Volume: 8 Issue: 1, 13 - 21, 30.06.2024

Ali İhsan Çanakoğlu

https://doi.org/10.47897/bilmes.1441414

Abstract

In this paper, a new Monte Carlo walk method is introduced. The increased radius floating random walk combines of the two classical Monte Carlo methods and derived from fixed-radius floating walk method. In this paper, the method is used to solve typical Laplace’s equations in rectangular region. Also, this method is easily applied to Poisson equations. Lower walk number and hence lower computation time are obtained from new method compared with the fixed random walk, floating random walk and fixed-radius random walk methods. Analyzes were performed on an average computer and the solution time was reduced by 80%. The results are also compared with Finite Element Method. Increased radius walk method’s results are good agreement with other methods.

Keywords

Floating random walk, Laplace equations, Monte carlo method, Numerical methods, Potential problems

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