## 3 Numeric Experiments and Results Discussion
Problem 3: Investigation of the Influence of the Boundary Conditions of the Thermal Problem on the Identification of 18 Inclusions in the Form of Rectangles Rotated by 90 Degrees Compared to Problem 2  
Table 4 shows the heat flux distribution, as well as the results of a study of the impact of the boundary conditions of the thermal problem on the identification of 18 rectangular shaped inclusions, rotated by 90 degrees compared to problem 2. With impact of the heat flux only on the left boundary of the plate (boundary condition (10) (Table 4a)), the left and central columns are identified (Table 4d). In the case of impact of heat flux on the left and upper boundaries of the plate (boundary condition (11), (Table 4b)) inclusions 15, 17 and 18 (Table 4e) were not identified. In the case of heat flux impact on the left, upper and lower boundaries of the plate (boundary condition (12), (Table 4c)), all inclusions were identified (Table 4f). The results show that, as in the previous case (Table 3), when changing the direction of the inclusions. the best identification occurs when using the boundary condition (12). Problem 4: Investigation of the Influence of the Boundary Conditions of the Thermal Problem on the Identification of 18 Inclusions in the Form of Rectangles Rotated by 45 Degrees Compared to Problem 3  
Let us consider the case when the plate contains 18 rectangular-shaped inclusions rotated by 45 degrees, compared to problem 3. Upon impact of heat flux only on the left border of the plate (boundary condition (10), (Table 5a)), the left and central columns were identified, except for two inclusions in column number 3 (Table 5d). In the case of impact of heat flux on the left and top plate boundary (boundary condition (11), (Table 5b)), inclusions 12, 15 and 18 (Table 5e) were not identified. In the case where heat flux impacted on the left, top and bottom of the plate (boundary condition (12), (Table 5c)), all inclusions were identified (Table 5f). The best identification occurred for the boundary condition (12), as well as for the examples given in Tables 3 and 4. Based on the examples above, it should be concluded that the angle of rotation of rectangular inclusions relative to the Y-axis does not affect the identification of the boundary conditions (12). Problem 5: Identification of the 18 Rhombuses Inclusions, under the Influence of Temperature and Heat Fluxes  
Further, consider a problem with 18 inclusions in the shape of a rhombus with a side size of 0.05 m along the plate. The coordinates of the centers of these inclusions coincide with the coordinates of the rectangles (Table 1). The boundary conditions and the form of temperature and heat fluxes are the same as in Problem 2. The convergence of FEM when solving the direct problem of revealing of rhomboidal inclusions is presented in Table 6. The boundary conditions and the location of inclusions are presented in Table 7. \begin{table}
\begin{tabular}{c c c} \hline \hline N & 643 & 1222 \\ FE number & 643 & 1222 \\ \hline \(\delta\) & 1.612 & 0.5142 \\ (in percent) & 1.612 & 0.5142 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Investigation of convergence of FEM with different numbers of finite elements (FEs)—problem 5. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Type of Boundary Conditions (10)–(12)** & \
\begin{tabular}{c} **Temperature** \\ **Distribution** \\ \end{tabular} &
\begin{tabular}{c} **Results of the** \\ **Topological Optimization** \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Distribution of the thermal field and identification results for rectangular-shaped inclusions (18 elements) rotated by 45 degrees—Problem 4; \(\Omega_{n}=\left\{a=1\cdot 1^{-1},b=2\cdot 10^{-2}\right\}\). With the influence of heat flux on the left and top of the plate (boundary condition (11), (Table 7b)), unlike in the first case, almost all inclusions were identified except for the bottom one in the third column (Table 7e).