METHODS FOR SOLVING APPLIED PROBLEMS IN MATHEMATICAL PHYSICS

Abstract

The article proposes methods for solving applied problems for optimizing the parameters of the laser embryo division process. The spherical shape of the embryo, its three-layer internal structure, and laser action modes are taken into account. It is shown that the computational mathematical model of the laser action process is based on a nonlocal boundary value problem of a system of multidimensional, nonstationary differential heat conduction equations with boundary conditions of the third kind and Dirichlet boundary conditions. These boundary conditions are formed taking into account the permissible temperatures of laser action on the embryo, based on expert assessment of the technical parameters of laser emitters. Due to the peculiarities of the embryo and the technical characteristics of laser emitters, significant computer time is required to implement the procedure for solving boundary value problems and to ensure the iterative process of searching for the optimal technical parameters of laser emitters. Therefore, the author proposes to perform this procedure on specialized grid processors. This will increase the accuracy of solving the entire problem of finding the optimal technical parameters of lasers.

The correctness of the boundary value problem presented in the article is justified using specialized methods and estimates of the fundamental function of solutions over the space of generalized functions. Taking into account the peculiarities of the embryo structure and the technical characteristics of laser emitters, a method for solving the boundary value problem for the process of laser action on the embryo was chosen. To control the trauma of the embryo, the author proposes to use an integral criterion for assessing material damage. The quality of embryo division is determined by the ratio of the volumes of the segment of injured embryo embryos to the entire layer of embryos. This will increase the accuracy of laser embryo division and reduce the energy consumption of laser emitters.