## 5 Numerical Tests
### Performance of the DLMU Scheme  
This section discusses the performance of the DLMU scheme in the five test-examples, for the five fully refined discretizations considered, i.e., [75,000, 100,000, 150,000, 200,000]. For each test example, the performance of the DLMU scheme is compared with the corresponding implementation of SIMP, with respect to the time and number of iterations required for the fully refined discretization, as well as the solution quality, as inferred by the objective function value. For the finer discretization with 200,000 FEs, a comparative evaluation of the DLMU scheme and the DLTOP methodology is further conducted. The computing effort required by DLMU refers to the time needed for implementing Steps 1, 2 and 3 of the scheme. All recorded data for test example A are given in Table 1. DLMU achieved a maximum reduction of computational time equal to 80.64% for the case of 200,000 FEs in \(D_{(0)}^{f}\) with respect to SIMP, while the objective function value slightly increased by 0.73%. The final optimized topologies generated by SIMP and DLMU for the finer discretization with 200,000 FEs are shown in Figure 5a,b, respectively. Accordingly, all recorded data for test example B are given in Table 2. Similar to the previous case, DLMU achieved a maximum reduction of computational time equal to 56.91% for the case of 200,000 FEs in \(D_{(0)}^{f}\) with respect to SIMP, while a decreased objective function value by 0.58% was achieved. The final optimized topologies generated by SIMP and DLMU for the finer discretization with 200,000 FEs are shown in Figure 6a,b, respectively. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**ne**} & \multicolumn{3}{c}{**SIMP**} & \multicolumn{3}{c}{**DLMU**} & \multirow{2}{*}{**Acceleration (\%)**} & \multirow{2}{*}{**Reduction (\%)**} \\ \cline{2-2} \cline{5-8}  & **Iterations** & **Objective** & **Time (s)** & **Iterations** & **Objective** & **Time (s)** \\ \hline
75,000 & 251 & 248.41 & 404.89 & 80 & 249.40 & 219.40 & 45.87 & \(-\)0.40 \\
100,000 & 331 & 246.46 & 736.53 & 61 & 247.37 & 224.06 & 69.58 & \(-\)0.37 \\
150,000 & 340 & 243.52 & 1203.95 & 72 & 245.15 & 337.66 & 71.95 & \(-\)0.67 \\
200,000 & 521 & 242.62 & 2559.05 & 86 & 244.39 & 495.55 & 80.64 & \(-\)0.73 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Test example A—Performance of the DLMU scheme. Figure 5: Optimized domain for test example A for the case of 200,000 FEs discretization: (**a**) SIMP output and (**b**) DL-SCALE output. Subsequently, all recorded data for test example C are given in Table 3. Similar to the previous cases, DLMU achieved a maximum reduction of computational time equal to 78.69% for the case of 200,000 FEs in \(D^{f}_{(0)}\) with respect to SIMP, while the objective function value slightly increased by 0.11%. The final optimized topologies generated by SIMP and DLMU for the finer discretization with 200,000 FEs are shown in Figure 7a,b, respectively. All recorded data for test example D are given in Table 4. Similar to the previous cases, DLMU achieved a maximum reduction of computational time equal to 60.58% for the case of 200,000 FEs in \(D^{f}_{(0)}\) with respect to SIMP, while the objective function value is almost the same with that achieved by SIMP. The final optimized topologies generated by SIMP and DLMU for the finer discretization with 200,000 FEs are shown in Figure 8a,b, respectively.