A methodology for the solution of nonlinear two-point boundary value inverse problems in physics and engineering

This dissertation focuses on the development of a new methodology for the solution of two-point boundary value inverse problems and on its application to solve inverse problems in science and engineering. The new methodology, derived from the parallel shooting method, attempts to improve the performance time of the original method by modifying the convergence iteration procedure. In an effort to further improve the speed of the calculation, the algorithm was also implemented on a shared memory parallel computer. The new methodology is used to solve inverse problems in (a) optimal control, to calculate the xenon concentration buildup in a nuclear reactor, the optimal fuel distribution in a slab reactor and to solve the stationary Schrodinger equation, (b) computer simulation, to determine the heat transfer coefficients in a sodium to water heat exchanger, and (c) applied quantum physics, to design semiconductor devices. The results demonstrate that the new methodology achieves a much faster performance time compared to the one of the traditional parallel shooting method. Also, the new methodology shows to be very reliable, since highly nonlinear two-point boundary value inverse problems could be quite easily solved.