Reproducing Stable and unstable finite elements for the Maxwell eigenvalue problem in Fenicsx

[CastriMik]

@philippweder

1. When I comment out the lines

solver.setWhichEigenpairs(SLEPc.EPS.Which.TARGET_MAGNITUDE)
solver.setTarget(5.5)

I get the 12 eigenvalues with the largest magnitude as expected. However, when I include the lines, no eigenvalue converges. What could be the cause of this?

As far as I know, setWhichEigenpairs and setTarget are useful when using spectral transformation in SLEPc, which you are not using here. To do that, add the following lines to your code:

solver = SLEPc.EPS()
solver.create()
solver.setOperators(A, B)

# Add this #
solver.setType(SLEPc.EPS.Type.KRYLOVSCHUR)
st = solver.getST()
st.setType(SLEPc.ST.Type.SINVERT)
############

solver.setProblemType(SLEPc.EPS.ProblemType.GHEP)
solver.setWhichEigenpairs(SLEPc.EPS.Which.TARGET_MAGNITUDE)
solver.setTarget(5.5)
neigs = 12
solver.setDimensions(nev=neigs, ncv=2*neigs)
solver.setFromOptions()

Also, this post may be useful:

Waveguide number of eigenmodes

For completeness sake. Wave equation \nabla^2\vec{E}+k^2\vec{E}=0 has an infinite number of solutions which do not satisfy divergence equation \nabla\cdot\vec{E}=0. \nabla\times\nabla\times\vec{E}-k^2\vec{E}=0 on the other hand satisfy divergence-free condition automatically (as explained here). There’s not mathematically intensive explanation in Computational electromagnetics by David Davidson, chapter “The null space of the curl operator and spurious modes”. PS code in the question is not en…