  The granulation of red supergiants (RSGs) in the Magellanic Clouds are
systematically investigated by combining the latest RSGs samples and light
curves from the Optical Gravitational Lensing Experiment and the All-Sky
Automated Survey for Supernovae. The present RSGs samples are firstly examined
for foreground stars and possible misidentified sources, and the light curves
are sequentially checked to remove the outliers by white noise and photometric
quality. The Gaussian Process regression is used to model the granulation, and
the Markov Chain Monte Carlo is applied to derive the granulation amplitude
$\sigma$ and the period of the undamped oscillator $\rho$, as well as the
damping timescale $\tau$. The dimensionless quality factor $Q$ is then
calculated through $Q=\pi \tau/\rho$. RSGs around $Q = 1/\sqrt{2}$ are
considered to have significant granulation signals and are used for further
analysis. Combining granulation parameters with stellar parameters, robust
scaling relations for the timescale $\rho$ are established, while the scaling
relations for amplitude $\sigma$ are represented by a piecewise function,
possibly related to the tendency of amplitudes in faint RSGs to converge
towards a certain value. Comparing results between the SMC and LMC confirms
that amplitudes and timescales become larger with metallicity. In examining the
scaling relations between the two galaxies, it is found that $\rho$ is nearly
independent of metallicity, whereas $\sigma$ is more significantly affected by
metallicity. The Gaussian Process method is compared with the periodogram
fitting of the granulations, and the advantages of either are discussed.
