$H^2$ gradient method for the coefficient identification problem in a partial differential equation

Abstract

A numerical method is considered herein for solving the problem of coefficient identification in a linear partial differential equation used to detect damages in steel-concrete composite beams. To identify the numerically unknown coefficient, an iterating algorithm based on the adjoint method is presented. The $H^1$ gradient method is applied to set the search direction in our algorithm. The search direction is selected based on the solution to the weak equation with a bilinear form in the $H^2$ Sobolev space. The effectiveness of our method is confirmed via numerical experiments.