Dr. Rodal - I'm still wondering about ratio-ing Ag/CU * copper conductivity to obtain a valid Ag conductivity, but in the mean time, I have a new question for you, and all. meep is converging nicely now to positive Q values but they are still unreal. I just completed a run of the NSF-1701A model and meep calculated Q as 328,441. That's nice but it seems to me that it is about an order of magnitude to large.
Is it possible that you or DeltaMass misplaced a decimal point giving conductivity off by a factor of 10? I doubt that you did because in following the symbolic math you provided, I calculated the same number that you did. But we both started with the number for sigma, CU-sigmaSI 3.25E+8. Perhaps that should have been 10^+7 instead.
Does that seem reasonable?
As explained in
http://forum.nasaspaceflight.com/index.php?topic=38577.msg1453093#msg1453093
3.25E+8 was not the conductivity.
3.25E+8 is the number in SI units that corresponds to the expression used in Meep: it is not the conductivity, it is instead the imaginary part of the relative complex permittivity
Therefore 3.25E+8 corresponds instead to epsilon"/epsilon_o = 0.00288/epsilon_o
According to the exact solutions and to the COMSOL and FEKO runs, these copper cavities, for these dimensions ( ~0.3 m) can have theoretical Q's of 70,000 to 95,000.
So, a calculated Meep Q of 328,441 is about 3 to 4 times larger than what is supposed to be.
This factor of 3 to 4 may be due to the numerical method used in Meep to calculate Q's. If interested in studying this, I suggest to study the numerical convergence:
* Output Q's for the same problem, everything else being the same, with the mesh progressively refined such that the distance between nodes is cut by 1/2, (the purpose here being to study the behavior of the calculated Q vs space discretization):
Q for N number of nodes
Q for 2*N nodes
Q for 4*N nodes
Q for 8*N nodes
etc
==> Plot Q vs number of nodes
* Output Q's for the same problem with the same mesh, everything else being the same, with the deltaT of the central difference time discretization solution (the purpose here being to study the behavior of the calculated Q vs time discretization)
Q for deltaT = t
Q for deltaT = t/2
Q for deltaT = t/4
Q for deltaT = t/8
etc
==> Plot Q vs deltaT
* Output Q's for the same problem with the same mesh and same deltaT, everything else being the same, vs. the final termination time T (the purpose here being to study the behavior of the calculated Q vs the transient solution, as Q determined from too early a time maybe erroneous)
Q for T
Q for 2*T
Q for 4*T
Q for 8*T
etc
==> Plot Q vs final time T (fractions of a second)
_________________
Don't use the same discretization used in COMSOL Finite Element or FEKO Boundary Element methods: the finite difference scheme used in Meep (central difference method) requires a larger number of nodes to achieve similar convergence as COMSOL or FEKO or ANSYS. COMSOL or FEKO or ANSYS have higher rates of convergence because Finite Element methods and Boundary Element Methods are higher order and hence converge faster to a solution than the low order finite difference method used in Meep. For example, Finite Element Methods use polynomial interpolation functions between nodes and the Finite Element Method is based on a variational principle that ensures higher rate of convergence (for the same number of nodes) than the finite difference method.
The finite difference method implementation in Meep is optimized for solutions of optical frequency nonlinear problems, not for solution of microwave frequency linear problems.Meep is efficient for optical frequency nonlinear problems. It may be inefficient (compared to FEKO or COMSOL) when applied to microwave frequency, linear problems that can be handled more optimally with methods like FEM or BEM.
