update the results on M matrix in the two-hole example to match with the meshes used.

Author: dnpham23

docs/src/examples/circular_hole.md

@@ -287,35 +287,44 @@ matrix from the stored magnetic energy:
 M_{ij} = \frac{\mathbf{A}_j^T K \mathbf{A}_i}{\Phi_i \Phi_j},
 ```
 
-where ``K`` is the curl-curl stiffness matrix. The off-diagonal entries ``M_{ij}``
-(``i \neq j``) represent the mutual inductance between loops, quantifying their magnetic
-coupling. For the two-hole configuration on a shared plate, the computed inductance matrix
-is:
+where ``K`` is the curl-curl stiffness matrix. The diagonal entries ``M_{ii}`` give the
+self-inductance of each flux loop, which is the energy cost of trapping one flux quantum in hole
+``i``. The off-diagonal entries ``M_{ij}`` (``i \neq j``) give the mutual
+inductance, which captures how the magnetic field generated by a flux quantum in one hole
+influences the other.
+
+For the two-hole configuration on a shared plate, the computed inductance matrix is:
 
 ```math
 M = \begin{pmatrix}
-2.8076 & 0.4654 \\
-0.4654 & 2.8080
+1.909 & -1.405 \times 10^{-5} \\
+-1.405 \times 10^{-5} & 1.909
 \end{pmatrix} \text{pH}
 ```
 
-The nearly equal self-inductances reflect the geometric symmetry, while the mutual
-inductance (about 17% of the self-inductance) indicates moderate magnetic coupling at this
-hole separation.
+The equal self-inductances reflect the geometric symmetry of the two holes. The mutual
+inductance is five orders of magnitude
+smaller than the self-inductance, indicating that despite being on the same plate, the two
+holes are magnetically nearly independent at this separation: a flux quantum trapped in one
+hole has negligible influence on the shielding currents around the other.
 
 ### Two holes on separate planes
 
-For the configuration with holes on spatially separated plates, the inductance matrix is:
+When the two holes are placed on spatially separated plates, the inductance matrix is:
 
 ```math
 M = \begin{pmatrix}
-2.9989 & -0.0510 \\
--0.0510 & 2.9988
+1.839 & -1.134 \times 10^{-5}\\
+-1.134 \times 10^{-5} & 1.829
 \end{pmatrix} \text{pH}
 ```
 
-The mutual inductance is an order of magnitude smaller than in the shared-plate case, despite
-the same center-to-center separation between holes. This reduction arises because the
-surface currents generated by each trapped flux are confined to their respective plates and
-cannot overlap with the other hole's current distribution, greatly suppressing the inductive
-coupling.
+The self-inductances are slightly smaller than in the shared-plate case because the
+surrounding metal no longer extends as far, reducing the flux return path. The mutual
+inductance is comparable in magnitude to the shared-plate result, which may be
+counterintuitive. The key reason is that mutual inductance in this geometry is dominated
+by the far-field magnetic interaction between the two holes, which depends mainly on their
+center-to-center separation -- not on whether they share a plate. The shielding currents
+flowing around each hole are confined to their own plate and cannot cross over to the other,
+but the magnetic field itself still permeates the surrounding space and couples the two
+loops at long range.