Estimation of heat sources and temperature distribution by boundary integral method

A simple evaluation of boundary integral in the inverse problem of the steady state heat conduction system is proposed. The boundary values of temperature and its gradient are computated from the direct analysis using FDM and the results of inverse analysis from these boundary values are compared with the given FDM parameters to give the reasonable estimation of boundary integrals. We show that the temperature gradient has some leaks from Dirichlet boundary region by the incomplete derivation of temperature gradient on the boundary surface. The 0.5 mesh extrapolation of temperature gradient from Dirichlet boundary region is also shown to give the accurate boundary integrals in the case of relatively coarse data points of boundary values. This 0.5 mesh extrapolation method is applicable to the actual inverse analysis of three dimensional system