  We analyze and compare different methods for handling the mutual coupling in
RIS-aided communication systems. A new mutual coupling aware algorithm is
derived where the reactance of each element is updated successively with a
closed-form solution. In comparison to existing element-wise methods, this
approach leads to a considerably reduced computational complexity. Furthermore,
we introduce decoupling networks for the RIS array as a potential solution for
handling mutual coupling. With these networks, the system model reduces to the
same structure as when no mutual coupling were present. Including decoupling
networks, we can optimize the channel gain of a RIS-aided SISO system in
closed-form which allows to analyze the scenario under mutual coupling
analytically and to draw connections to the conventional transmit array gain.
In particular, a super-quadratic channel gain can be achieved which scales as
N^4 where N is the number of RIS elements.
