I have read that the total magnetic field of a ferromagnet, $\vec{B} = \mu_0\vec{H}+\mu_0\vec{M}$ where $\vec{H}$ is an external magnetic field and $\vec{M}$ is the magnetic field of the ferromagnet due to the alignment of its dipoles to $\vec{H}$.
On the other hand, I have read that ferromagnetic materials tend to "channel" and "concentrate" field lines. See, for example, the image below. With the solenoid alone, the shape of the magnetic field would be very different than the shape with the magnet included. The magnet has "channeled" the magnetic field lines of the solenoid.
What explains this "channeling" behavior of ferromagnetic materials? In other words, is this explainable using the normal methods for magnetic field calculations such as Biot-Savart and treating the ferromagnet as consisting of infinitesimal dipoles or does the dynamic process of domain alignment need to be considered in calculating the final magnetic field?
Edit: In order to explain myself better, I have included two simulations from FEMM. One is a selenoid wrapped around an iron core which has geometry chosen to emphasis the channeling behavior I mention above. The second is identical to the first, with iron replaced with air. From the equation $\vec{B} = \mu_0\vec{H}+\mu_0\vec{M}$ I would expect the two simulations to have magnetic fields that have identical directions $(\vec{B_{iron}}/|\vec{B_{iron}}| = \vec{B_{air}}/|\vec{B_{air}}|)$ but these simulations show they do not. Why is this?
Note the simulations are axisymmetric which means that they are treated as if the entire configuration is rotated around the left axis to form a three-dimensional problem.