Reconstruction of multiplicative space- and time-dependent sources

This paper presents a numerical regularization approach to the simultaneous determination of multiplicative space- and time-dependent source functions in a nonlinear inverse heat conduction problem with homogeneous Neumann boundary conditions together with specified interior and final time temperature measurements. Under these conditions a unique solution is known to exist. However, the inverse prob- lem is still ill-posed since small errors in the input interior temperature data cause large errors in the output heat source solution. For the numerical discretisation, the boundary element method combined with a regularized nonlinear optimization are utilized. Results obtained from several numerical tests are provided in order to illustrate the efficiency of the adopted computational methodology.