Numerical solution and parameter estimation of multi-interface heat conduction models

Abstract:

This paper mainly studies the numerical solution and parameter estimation of a multi-interface heat conduction equation. Firstly, the heat conduction equation and interface conditions are discretized to tridiagonal linear equations by using the finite difference method. Then a chasing algorithm is used to obtain the numerical solution. Furthermore, an adaptive Particle Swarm Optimization (PSO) algorithm is proposed for the parameter estimation. This algorithm adopts an adaptive nonlinear decreasing adjustment strategy for the inertia factor in order not to sink into the local extreme values prematurely and thus improve the optimization accuracy. Finally, the performance of the proposed algorithm is compared to the standard PSO algorithm and some classical nonlinear optimization algorithms such as Active Set ( AS ), Interior Point ( IP ) and SQP by using a numerical example.