What is the purpose of an inboard aileron?
As far as I know, the inboard ailerons are used for high speed maneuvering.
The rolling moment induced by the ailerons is linearly dependent with the distance to the center of gravity (e.g. the farther out, the stronger the moment, the harder the roll).
As the aileron is an aerodynamic surface, the force induces is equal to:
$$F_{aileron} = c_l(\alpha) \frac{1}{2} \rho V^2 S_{aileron} $$.
The moment induced is equal to this force, multiplied by the distance to the c.o.g.:
$$M_{aileron} = y_{aileron} \cdot c_l(\alpha) \frac{1}{2} \rho V^2 S_{aileron} $$
If you're flying in cruise , and you want to make a smooth turn, you need a relatively small $M_{aileron}$.

However, the $V^2$ term, is already very large. So we want to make the rest of the terms relatively small.

We could do this with outboard ailerons: Use the outboard aileron with a large $y_{aileron}$, combined with a small $c_l(\alpha)$, usually the outboard $S_{aileron}$ is fixed by the low speed control requirements.
However, you can provide $M_{aileron}$ more accurate if you use the inboard ailerons (with a small $y _{aileron}$). The smaller distance makes the moment a bit smaller, and less susceptible to small deviations.

I think the Airbus A330 &amp; A340 use their spoilers to maneuver at high speeds. They simply extend their spoilers -which are usually also reasonably close to the c.o.g.- a tiny bit, this changes the lift distribution, also causing a rolling moment. I did not research this fact, so I'm not 100% sure this is the reason the A330 and A340 do not have inboard ailerons, but I do know some aircraft use this method for high speed maneuvering.