## 3 Results and Discussion  
Using the described optimization procedure, the input power levels (\(P_{i}\)) together with the phases of the dipole antennas (\(\phi_{i}\)) for individual applicators were successfully determined. It should be emphasized that the values for optimal \(P_{i}\) and \(\phi_{i}\) parameters are summarized in Table 2 for different tumor radii \(r\) growing incrementally from 2 mm to 12 mm, in steps of 2 mm. Moreover, the total MW power of all the antennas was found to be 8 W, which directly translates into the expected breast cancer temperature of about 42 \({}^{\circ}\)C. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Tumor Size**} & \multicolumn{3}{c}{**Tumor Size**} \\  & \multicolumn{2}{c}{\(r\) = 2 mm} & \multicolumn{3}{c}{**\(r\) = 4 mm**} \\ \hline \multirow{2}{*}{**Antenna No.**} & **Power** & **Phase** & \multirow{2}{*}{**Antenna No.**} & **Power** & **Phase** \\  & \(P_{i}\) (W) & & & & \(P_{i}\) (W) & \(\phi_{i}\) (\({}^{\circ}\)) \\ \hline
1 & 0.3113 & 9.1212 & 1 & 0.3202 & 9.8917 \\
2 & 2.8172 & \(-\)55.0652 & 2 & 2.8224 & \(-\)53.5573 \\
3 & 3.1238 & 7.5346 & 3 & 3.1074 & 8.0062 \\
4 & 0.7207 & 122.8282 & 4 & 0.6914 & 124.1266 \\
5 & 0.0015 & 155.1581 & 5 & 0.0014 & 159.7430 \\
6 & 0.0252 & 82.6938 & 6 & 0.0257 & 77.6330 \\
7 & 0.3572 & 30.1722 & 7 & 0.3668 & 28.1556 \\
8 & 0.6431 & 0 & 8 & 0.6647 & 0 \\ \hline \hline \multicolumn{3}{c}{**Tumor Size**} & \multicolumn{3}{c}{**Tumor Size**} \\  & \multicolumn{2}{c}{\(r\) = 6 mm} & \multicolumn{3}{c}{**\(r\) = 8 mm**} \\ \hline \multirow{2}{*}{**Antenna No.**} & **Power** & **Phase** & \multirow{2}{*}{**Antenna No.**} & **Power** & **Phase** \\  & \(P_{i}\) (W) & & & \(P_{i}\) (W) & \(\phi_{i}\) (\({}^{\circ}\)) \\ \hline
1 & 0.3491 & 12.0320 & 1 & 0.3932 & 12.6731 \\
2 & 2.8912 & \(-\)51.2217 & 2 & 3.2524 & \(-\)53.2903 \\
3 & 2.9268 & 10.5009 & 3 & 2.6419 & 9.9976 \\
4 & 0.6478 & 128.7051 & 4 & 0.5701 & 135.6660 \\
5 & 0.0011 & 179.4337 & 5 & 0.0020 & \(-\)147.9632 \\
6 & 0.0243 & 70.5049 & 6 & 0.0105 & 61.6180 \\
7 & 0.3954 & 25.5423 & 7 & 0.3104 & 26.5520 \\
8 & 0.7643 & 0 & 8 & 0.8195 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The optimized parameters of an eight-dipole antenna array for various breast tumor sizes. Figure 5: The computing speed (**a**) and iteration completion time (**b**) as function of iterations number for the thermal solver. The convergence was obtained after 1911 iterations. In the last part of this paper, the optimal parameters, gathered in Table 2, were used to specify the SAR distributions as well as the radius-dependent thermal profiles of spherical breast cancers. In this case, Figure 6 shows the normalized SAR distributions in the \(xy\) plane for steady state inside the breast models with various tumor diameters surrounded by the matrix of dipole antennas working at optimal \(P_{i}\) and \(\phi_{i}\) parameters (sum \(P_{i}\) = 8 W). All the distributions were normalized to the maximum SAR value and were expressed on a decibel scale. As can be seen, the maximum SAR value in the tumor increased as its size increased, reaching values of SAR\({}_{\max}\) = 1.41, 1.51, 1.71, 1.79, and 1.86 kW/kg for tumor radii \(r\) = 4, 6, 8, 10, and 12 mm, respectively.