The method of probabilistic solution for the dirichlet generalized harmonic problem in irregular pyramidal domains

The Dirichlet generalized harmonic problem for irregular n-sided pyramidal domains is considered. The term "generalized" indicates that a boundary function has a finite number of first kind discontinuity curves. In the case under consideration, the pyramid edges appear in the role of the mentioned curves. The algorithm for a numerical solution of boundary problems consists of the following main steps: a) application of the method of probabilistic solution (MPS), which is in its turn based on a computer modeling of the Wiener process; b) finding the intersection point of the path of Wiener process simulation and the pyramid surface; c) development of a code for the numerical realization and checking the accuracy of calculated results; d) calculating the meaning of sought for function at any chosen point. For illustration two examples are considered. Numerical results are presented and discussed.