In this post I report of the results of TE noise simulated by COMSOL for the TE noise of Infinite test masses.
The aim was to follow the procedure by Liu and Thorne in their analytic calculations so that the same model could be used for the other
The simulation is done in a different way than the TR simulations. It was observed that the output given by COMSOL by the use of commands
like mphinterp() or taking an export resulted in certain discrepancies between the results computed in COMSOL and that read by MATLAB.
Thus, the volume integration of the temperature gradient is performed in COMSOL itself and the results of the integration for each time
are sent to files. Matlab read these values and time averages them to get the result as in the paper (Sec. 2 of Liu and Thorne).
The errors expected are
> Fourier analysis is not done at all. This would have involved exporting data which, as mentioned before is giving errors
> The numerical errors by COMSOL are therefore not filtered off.
> The plot differs from the analytic solution for larger frequencies over 3000 Hz.
> It is to be noted from the paper by Liu and Thorne that the TE noise for the finite and infinite case are not very different. In
fact the correction factor goes as O(1). Thus, differences between finite and inifinte cases are unlikely to be prominent
in the log scale plots
The codes are put as a zip file. Corrections made to the codes will be uploaded as a reply.
Here is another plot with a mesh size slightly finer than the default Extra fine mesh in COMSOL.
One may notice that the value for the final frequency i.e. 10000Hz is different from the previous plot.
It maybe that the error for the higher frequencies is a result of the FEA. However, it may also be that
the appropriate boundary conditions required for an infinite model break down at high frequencies.