HomerReid
commented
8 years ago Thanks for your interest in SCUFF-EM and for filing this thorough report.
I'm not sure what is responsible for the 25% errors you are seeing. I understand the low-frequency errors as arising from large numerical cancellations in the method used to compute the power at low frequencies: the normal Poynting vector is nonzero everywhere over the surface of the sphere, but it integrates to something very small at low frequencies (almost all of the flux on any portion of the surface is cancelled by the flux on other portions), so there is an inherent numerical difficulty at low frequencies. However, this doesn't explain the 25% errors you see across a wide frequency range.
I am just in the process of preparing an updated version of SCUFF-NEQ that implements some new techniques for computing power, force and torque, which will hopefully yield better results. I will notify you when that is ready, hopefully later this month sometime.
In the meantime, the existing version of SCUFF-NEQ already offers some options for selecting the method used to compute the power, force, and torque (PFT). I suggest re-running your calculations with these options:
--ForceDSI --DSIRadius 1.0 --DSIPoints 302
This will use the "displaced-surface integral" technique for computing the PFT, with the Poynting-vector integral performed over a sphere of radius 1.0 with 302 cubature points. Try varying the radius of the integration sphere and the number of cubature points to see how that affects the accuracy. (Type scuff-neq --help to see a list of the allowed values of --DSIPoints.)
Also, it would be interesting to see how the errors depend on material properties and sphere radius. The Kruger formulas are themselves approximations (assuming you truncate the sum at a finite number of spherical multipoles, i.e. L=1 or 2) and the various approximations are more accurate for certain materials and frequencies than for others (see e.g. Table 1 in the paper you cited).
To your questions:
- I don't think the difficulty lies with the discretization or the BEM method, but rather with the technique used to compute the power, and specifically with cancellations in the Poynting-vector integral.
- It is true that errors can arise when the frequency is large (wavelength is small) compared to the size of the triangles, and that should be evident if you carry your calculations out to higher frequencies, but this is not the origin of the low-frequency errors.
Note that these calculations can also be performed, using a different numerical method, by my BUFF-EM code.
klnguyen
ZhihaoJia16
If you know the reason,please tell me.
best
thank you in advance.
Hi,
I am using scuff-neq to compute the temperature-independant spectral flux radiated flux by a single SiC sphere and transferred between two SiC spheres (center-center distance = 10 micrometer).
The SiC permeability Mu and permittivity Eps are Mu(w)= 1 and Eps(w) = EpsInf_(1+(wL^2-wT^2)/(wT^2-w^2-i_Gamma*w)) where EpsInf = 6.7, wL = 1.825e14 rad/s, wT = 1.494e14 rad/s and Gamma = 8.966e11 rad/s. The first four figures represent the spectral flux tau_rad, radiated by a signle sphere and the relative errors. N denotes the edge number of FE mesh. The black continuous curves are analytical results shown by equation (124) in Ref. [Kruger2012]. [Kruger2012] M. Krüger, G. Bimonte, T. Emig, and M. Kardar. Trace formulas for non equilibrium Casimir interactions, heat radiation, and heat transfer for arbitrary objects. Physical Review B 86, 115423 (2012)
Following these figures, we can observe that :
The second four figures represent the spectral flux tau_transfer, exchanged by two spheres and the relative errors. The black continuous curves are reference results given by equation (137) in Ref.[Kruger2012]. We also have the relative errors around 25% in the whole frequency range (The ratio between numerical and reference results is about pi/4. For a small sphere (R = 0.0125 micrometer), the transfered flux computed by scuff-neq is in good consistence with the reference results, especially for low frequencies, contrary to the computation of radiated flux.
We haven't understood the reason for these phenomena yet. We have the following questions :
If you know the reason for these phenomena, please tell me. Thank you very much. Kind regards
