Why does TRP exceed input power(Antenna)?

I would like to know why TRP exceed input power.

I'm working on Antenna simulation on the tutorial. Specifically, I modeled half-wave dipole antenna and found something wrong with the results when I moved on to the analysis. I ticked the box to normalize the input power and tried to check radiation report. I found TRP exceeds input power.

There is a kind of warning that says ''Total radiated (TRP) and input power values provided at the input are not accurate. TRP is greater than the input power at some frequency snapshot.''

Could anyone help me solve the problem?

I'm using FDTD on Sim4LifeLight V

Thank you very much in advance.

The TRP is computed in a different way than the input power. Both ways are mathematically correct and would both be "exact" if there were no numerical errors. In any FDTD simulation, however, there are spatial (finite grid) or temporal (finite time step) discretization error.
What you are seeing in this half-wave dipole example, is that those discretization errors are larger than the precision you would require to distinguish TRP from input power (because the radiation efficiency is very high in this case, there is almost no difference between TRP and input power).

To solve this "problem", either you accept that the simulation results are accurate enough for your needs (the warning is a simple consistency check) or you increase the precision of the simulation. You can do so by increasing the grid resolution, the overall convergence level and the resolution of the far-field sensor. This will be computationally expensive, though.

To help you understand, you could try to add some lossy media in your (coarse) simulation (e.g. place the dipole next to a phantom or any other dielectric). The simulation will not be more precise, but the numerical errors will be less "obvious" because they will be dwarfed by the losses occurring in the dielectric. The TRP will be lower than the input power and the warning will not be triggered.

I hope this helps.