پرویز ملک زاده

In the present research, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to estimate the unknown location and time-wise varing strength of the point and distributed heat source of a functionally graded rectangular plate from the knowledge of temperature measurements taken on the boundaries of plate. It is assumed that no prior information is available on the functional form of time-wise variation of the heat source strength so estimation process starts with an arbitrary initial guess. The temperature data obtained from the direct problem are used to simulate the temperature measurements. The conjugate gradient method (CGM) is employed for optimization process and the finite element method (FEM) is applied to solve the governing differential equations. The reliability and robustness of the presented approach is demonstrated by simulating the exact and noisy data through different examples. Results show that the estimation of location and strength of point heat source can be obtained with any arbitrary initial guesses.The approach presented in this paper, can be used as a scientific reference for estimation of unknown parameters whenever measuring them are either more complicated or need the expensive instruments. Also the results can be used as a reference for future studies on inverse algorithm.