Shape identification problem in estimating geometry of multiple cavities

A shape identification problem (or an inverse geometry heat conduction problem) is solved to detect the unknown shape of multiple cavities by using the steepest descent method (SDM). One of the advantages of using the SDM lies in that it easily can handle problems having a large number of unknown parameters. The boundary element method is used to calculate the direct as well as the sensitivity and adjoint problems because of its characteristic of easily handling the problem considered here. Results obtained by using the SDM to solve the inverse problems are verified based on the numerical experiments. One concludes that the SDM is applied successfully in estimating the arbitrary shape of cavities, and the rate of convergence is also very fast. Moreover, the accuracy of the inverse solutions depends on the positions of the sensors. When the sensors are arranged closer to the cavities, the estimated results are more accurate. Finally, the effects of the measurement errors on the inverse solutions are discussed.