Shape optimizations of inhomogeneities of two dimensional (2D) and three dimensional (3D) steady state heat conduction problems by the boundary element method

The shape optimizations of inhomogeneities for 2D and 3D steady state heat conductions in an infinite medium are respectively studied by the boundary element method (BEM). Interest in the shape optimization by the BEM is mainly due to its high computation accuracy and simplicity in meshing. The boundary integral equations and the heat energy formulations in this paper only contain the temperature on each inhomogeneity–matrix interface. The heat energy increment in the inhomogeneous medium is taken as the objective function. The method of moving asymptotes (MMA) is adopted to carry out numerical implementation of the shape optimizations of 2D and 3D inhomogeneities.