systems over long physical times.

Recent advances have led to powerful general purpose codes such as Gerris [@Popinet2003] and BLUE [@shin2017solver]. It is with the multiphase code BLUE, which is based on recently developed hybrid front-tracking/level-set interface methods implemented on parallel computer architectures, that we conduct the current study. We have previously used this code to study large-scale square patterns of Faraday waves [@Lyes]. Here, we use BLUE to carry out the first numerical investigation of the Faraday problem on a sphere.

One of the most appealing aspects of the Faraday instability is that the pattern length scale is not set by the geometry, but by the imposed forcing frequency. (It is this feature which has allowed the generation of quasipatterns and superlattices, since multiple length scales can be excited simultaneously over the entire domain by superposing different frequencies.) This means that for a drop with a fixed radius ${R}$, patterns can be created with any wavenumber $\ell$, where the interface is described via its spherical harmonic decomposition $$\zeta(t,\theta,\phi) = \sum_{\ell=0}^\infty \sum_{m=-\ell}^{m=\ell} \zeta_\ell^m(t)Y_\ell^m(\theta,\phi)
\label{eq:defint_intro}$$ For fixed ${R}$, the length scale associated with $\ell$ is ${R}/\ell$. More importantly, $\ell$ is associated with a set of allowed patterns; each value of $\ell$ 