Boundary element methods for solving inverse boundary conditions identification problems

This thesis explores various features of the boundary element method (BEM) used in solving heat transfer boundary conditions identification problems. In particular, we present boundary integral equation (BIE) formulations and procedures of the numerical computation for the approximation of the boundary temperatures, heat fluxes and space, time or temperature dependent heat transfer coefficients. There are many practical heat transfer situations where such problems occur, for example in
high temperature regions or hostile environments, such as in combustion chambers, steel cooling
processes, etc., in which the actual method of heat transfer on the surface is unknown. In such
situations the boundary condition relating the heat flux to the difference between the boundary
temperature and that of the surrounding fluid is represented by an unknown function which may
depend on space, time, or temperature.
In these inverse heat conduction problems (IHCP), the BEM is formulated as a minimization
of some functional that measures the discrepancy between the measured data, say the average
temperature on a portion of the boundary or at an instant over the whole domain. The
minimization provides solutions that are consistent with the data. This indicates that the BEM
algorithms for the IRCP are robust, stable and predict reliable results.
When the input data is noisy, we have used the truncated singular value decomposition and
the Tikhonov regularisation methods to stabilise the solution of the IRCI' boundary conditions
identification. Numerical approximations have been obtained and, where possible, the results
obtained are compared to the analytical solutions.