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This is a non-linear eigenvalue problem example. It consists in a spherical
electromagnetic cavity. The wall conductivity is modelled by a Leontovich
surface impedance boundary condition (SIBC). Simply run:
make
to test cim.py.
The Makefile will first mesh the geometry square.geo by calling Gmsh.
Afterwards, cim.py is called. The GetDP formulation is located in sphere.pro.
In the GetDP formulation, the variables:
angularFreqRe
angularFreqIm
x()
b()
imposeRHS
doPostpro
doApply
fileName
are reserved for cim.py. The parts of the GetDP code related to cim.py are
located in cimParameters.pro and cimResolution.pro.
For the default parameters:
radius = 150e-6 m
conductivity = 1e15 S/m
the analytical resonance angular frequency for the fundamental mode should be:
5.48362e12+4.24068e05j
where j is the imaginary unit. This analytical result comes from the reference:
S. Papantonis and S. Lucyszyn, "Lossy spherical cavity resonators for
stress-testing arbitrary 3D eigenmode solvers," Progress In Electromagnetics
Research, vol. 151, pp. 151-167, 2015.