Code for this homework: hw05 code
And bilinear base generator code: basis_gen
With the given condition, we can first solve for the baseline condition. The figure is included below with tumor region marked as red.
We can see from the figure that heat is accumulated in the center which is the bladder and the tumor region. This treatment would work however as we treat the tumor with hyperthermia, the bladder as a critical organ is receiving even more thermo energy. However the baseline condition assumes no blood perfusion in the bladder. As the question proposed, a better treatment method can be achieved when we elevate the blood flow of bladder tissue to half of the muscle. The resulting solution map is plotted below:
As we can see, the most heated region is transferred to the tumor region now. The bladder has less heat. However, as we decreased the bladder heat, comparing to the first plot, the overall maximum heat is decreased as well.