I'm currently attempting a 3D FDTD simulation where I'm modeling a plasma as a dielectric tensor based off a frequency dependent Appleton Hartree dispersion relation. The inversion of the dielectric tensor is symmetric positive definite (SPD) when my propagation frequency (f0) is less than the plasma frequency (fpe), when f = fpe the inversion of the dielectric tensor is not possible, and when f < fpe, the inversion of the dielectric matrix is not SPD.
This causes my simulations to blow up in the regions where f
If the matrix is SPD then you have real eigenvalues. If the matrix is not symmetric positive definite, then you have complex eigenvalues. With complex eigenvalues x, e^(i*x) has a real part that goes to infinity when f
Correct, that is what I'm seeing. So I was wondering if there is some way to treat this or if I am able to use some other SPD when f
When the refractive index eigenvalue is complex
x= a+ib,
b is the absoption coefficient in that material, a is the index of refraction.
Read this please
https://en.wikipedia.org/wiki/Refractive_index#Complex_refractive_index
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