Virginie Bonnaillie-Noël, Monique Dauge, Grégory Vial
 

Square domain

The magnetic potential corresponds to a constant field.

The square is  [-1,1] x [-1,1] . The potential is   (y, -x) / 2 .

Computations done with the FEM library  Mélina. Tensor product mesh, degree Q10.

A. View the real parts of the first 8 eigenmodes, and their moduli.

Classified versus h:

h = 0.1   h = 0.09   h = 0.08   h = 0.07   h = 0.06   h = 0.05   h = 0.04   h = 0.03   h = 0.02   h = 0.014   h = 0.01 .

The up and down arrows allow a quick navigation between different values of h, increasing or decreasing its value.
This can be done either with the real part, or with the modulus.

Each figure can be seen in its original twice larger format by simply clicking on it.

B. Follow eigenmodes along analytic curves of eigenvalues.

Organized versus  k = 1/h  and their initial rank  R  at  h = 1.

R = 1    R = 2    R = 5

The increment of k is set to 0.5. k goes from 1 to 48.
Each figure can be seen in its original format by simply clicking on it.