Simulation of the design activity diversification of innovative enterprise
Abstract
Simulation of the design activity diversification of innovative enterprise
Incoming article date: 08.10.2024A two-dimensional coefficient inverse problem of thermal conductivity for a finite functionally graded cylinder is investigated. The thermal conductivity coefficient is considered to be variable along the radial and axial coordinates. The direct problem of finding the temperature distribution at different moments of time with known boundary conditions and the thermal conductivity coefficient is formulated in a weak statement and solved in the FreeFem++ finite element package. The influence of various two-dimensional power laws of the thermal conductivity coefficient on additional information (the temperature of the outer surface of the cylinder) is investigated. A projection-iteration scheme is constructed to solve the inverse problem. The thermal conductivity coefficient is presented as the sum of the initial approximation and the correction function specified as an expansion in a system of polynomials. At each stage of the iteration process, the expansion coefficients are calculated from the solution of the system of algebraic equations obtained by discretizing the operator equation of the first kind. The results of computational experiments on restoring various two-dimensional laws of change in the thermal conductivity coefficient are presented.
Keywords: functionally graded cylinder, finite element package FreeFem++, identification, thermal conductivity coefficient, inverse problem, iterative-projection approach, operator equation