Mathematical modeling of the gettering process for a cylindrical region

Abstract

Abstract The paper considers a mathematical model of the technical process of external gettering of silicon rods. The purpose of this process is to remove unwanted impurities from silicon. The model of this process is an initial-boundary value problem for a linear partial differential equation of parabolic type. A feature of this problem is the presence of a nonlocal in time boundary condition, which reflects the law of conservation of mass (matter). For numerical modeling, an algorithm based on difference approximations of differential operators of the 1st and 2nd order is proposed. The classical sweep method is used to find a solution to a discrete problem.