The numerical solution of the Dirichlet generalized and classical harmonic problems for irregular n-sided pyramidal domains by the method of probabilistic solutions - Zakradze, Mamuli; Tabagari, Zaza; Koblishvili, Nana; Davitashvili, Tinatin; Sánchez-Sáez, José María; Criado-Aldeanueva, Francisco (AIMS Press, 2025)
This paper describes the application of the method of probabilistic solutions (MPS) to numerically solve the Dirichlet generalized and classical harmonic problems for irregular -sided pyramidal domains. Here, "generalized" means that the boundary function has a finite number of first-kind discontinuity curves, with the pyramid edges acting as these curves. The pyramid's base is a convex polygon, and its vertex projection lies within the base. The proposed algorithm for solving boundary problems numerically includes the following steps: a) applying MPS, which relies on computer modeling of the Wiener process; b) determining the intersection point between the simulated Wiener process path and the pyramid surface; c) developing a code for numerical implementation and verifying the accuracy of the results; d) calculating the desired function's value at any chosen point. Two examples are provided for illustration, and the results of the numerical experiments are presented and discussed.
Keywords: Wiener, Integrales de; Probabilidades; Dirichlet, Problema de; Dirichlet generalized and classical harmonic problems; Wiener process; Pyramidal domain; Method of probabilistic solution