  This paper is concerned with a practical inverse problem of simultaneously
reconstructing the surface heat flux and the thickness of a solid structure
from the associated ultrasonic measurements. In a thermoacoustic coupling
model, the thermal boundary condition and the thickness of a solid structure
are both unknown, while the measurements of the propagation time by ultrasonic
sensors are given. We reformulate the inverse problem as a PDE-constrained
optimization problem by constructing a proper objective functional. We then
develop an alternating iteration scheme which combines the conjugate gradient
method and the deepest decent method to solve the optimization problem.
Rigorous convergence analysis is provided for the proposed numerical scheme. By
using experimental real data from the lab, we conduct extensive numerical
experiments to verify several promising features of the newly developed method.
