Different solution values for different dolfinx version

[dokken]

It seems like you are ignoring the key takeaway message of my post above. To make it possible for other people to help you, it would be good if you could generate two codes that are as equal as possible. As pygmsh is not a dependency of dolfinx, you should use the same version and same mesh in both problems (preferrably the newest version with occ).
Additionally, you should use the same variable names in both codes, as:

@wwshunan

a = 1/theta_sqr*(inner(curl(u), curl(v)) - k0_sqr*e_r*inner(u, v))*dx 
b = inner(grad(p), v)*dx + inner(u, v)*dx + inner(grad(p), grad(q))*dx + inner(u, grad(q))*dx - k0_sqr*e_r*inner(p, q)*dx
c = b + a 

#%%

S = assemble_matrix(b, [bc])
T = assemble_matrix(c, [bc])

@wwshunan

    a = inner(grad(p), v)*dx + inner(u, v)*dx + inner(grad(p), grad(q))*dx + inner(u, grad(q))*dx - k0_sqr*e_r*inner(p, q)*dx
    b = a + 1/theta_sqr*(inner(curl(u), curl(v)) - k0_sqr*e_r*inner(u, v))*dx


    # In[11]:


    # TODO: requires fork. If you want to use master dolfinx, you should throw away Dirichlet BCs
    # using a petsc4py submatrix, see e.g. https://github.com/michalhabera/dolfiny/blob/master/dolfiny/restriction.py#L69
    #A = assemble_matrix(a, bcs=[], restriction=(restriction_W_Gamma, restriction_W_Gamma))
    A = assemble_matrix(a, bcs=[bc])
    A.assemble()
    B = assemble_matrix(b, bcs=[bc])
    #B = assemble_matrix(b, bcs=[], restriction=(restriction_W_Gamma, restriction_W_Gamma))
    B.assemble()

are assembling different structures into matrix A and B than into S and T, and you should therefore get different results.

You also use different solver options:

@wwshunan

es = SLEPc.EPS(which='LR').create(comm=MPI.comm_world)
es.setDimensions(10)
es.setOperators(S, T)
es.setFromOptions()
es.solve()

@wwshunan

    # Solve
    eps = SLEPc.EPS().create()
    eps.setOperators(A, B)
    eps.setProblemType(SLEPc.EPS.ProblemType.GNHEP)
    eps.setDimensions(1, PETSc.DECIDE, PETSc.DECIDE)
    eps.setWhichEigenpairs(SLEPc.EPS.Which.LARGEST_REAL)
    eps.getST().getKSP().setType("preonly")
    eps.getST().getKSP().getPC().setType("lu")
    eps.getST().getKSP().getPC().setFactorSolverType("mumps")
    eps.solve()
    assert eps.getConverged() >= 1

which could influence the answer.

When you present your codes as this, it is hard for someone to give you assistance, as it is not clear what the codes should actually do, and what should compare to what.