NUMERICAL SOLUTION OF THE INVERSE PROBLEM OF HEATING OF A SOLID BODY BY LASER RADIATION

A study has been made of the process of heating of an inhomogeneous solid body by laser radiation, that is described by a one-dimensional parabolic equation with a volume heat source. The inverse problem of determining the law of variation in the density of laser-radiation power with the depth of the solid body has been posed. The temperature distribution through the body′s depth at a certain fi xed instant of time was used as the supplementary condition. A discrete analog of the posed problem has been constructed with fi nite-diff erence approximations. To solve the obtained diff erence problem, a special representation was proposed which allows splitting this problem into two mutually independent diff erence problems. As a result, an explicit formula has been obtained from which the law of variation in the density of laser-radiation power with the depth of the solid body is restored
A study has been made of the process of heating of an inhomogeneous solid body by laser radiation, that is described by a one-dimensional parabolic equation with a volume heat source. The inverse problem of determining the law of variation in the density of laser-radiation power with the depth of the solid body has been posed. The temperature distribution through the body′s depth at a certain fi xed instant of time was used as the supplementary condition. A discrete analog of the posed problem has been constructed with fi nite-diff erence approximations. To solve the obtained diff erence problem, a special representation was proposed which allows splitting this problem into two mutually independent diff erence problems. As a result, an explicit formula has been obtained from which the law of variation in the density of laser-radiation power with the depth of the solid body is restored
Author:  Kh. M. Gamzaev
Keywords:  solid body, laser radiation, volume heat source, radiation-power density, diff erence problem, inverse problem
Page:  1128