**5.2 Example 2**

In this example, the Dirichlet boundary condition is given by *g* ¼ sin 2ð Þ*θ* , *θ* ∈ ½ � 0, 2*π* . We show some numerical experiments in the case of two coated inclusions using the proposed algorithm corresponding to the shape functional *K*.

**Figure 10** depicts the image of the topological gradient of the shape functional *K* and the image of temperature distribution after the optimization process.
