Resolving the final time singularity in gradient methods for inverse heat conduction problems

This work investigates overall performance of the modification techniques for resolving the singularity at the final time in the gradient method for the inverse heat conduction problem. Four representative methods are selected based on the literature and analyzed for the same case. They are the regularization term method, the differential equation method, the gradient integration method, and the sequential gradient method. All four methods are reproduced and tested for the same test case. Based on the test results, a two-step method that can both alleviate the systematic bias and at the same time resolve the singularity is proposed.