Shape sensitivity analysis in thermal problems using BEM

The shape design sensitivity analysis of thermal problems based on the adjoint variable method is presented. The boundary element method (BEM) is employed for the numerical evaluation of thermal responses and sensitivity of the performance functions. The adjoint variable method and the material derivative concept are utilized to obtain the sensitivity expressions. The results are verified numerically for two simple example problems using the BEM. Unlike previous studies, this approach takes into account the Dirac delta type of performance function and varying boundary temperatures. The sensitivity of the performance functions can then be evaluated more accurately at discrete points. This is achieved by an efficient application of the concentrated adjoint temperature in the boundary element framework.