and analysis of hydrodynamic quasipatterns [@EF1994; @Rucklidge2015], superlattices [@KPG1998; @Silber1998; @Arbell2002], supersquares [@Douady1990; @Lyes] and other exotic patterns [@Perinet2012; @Rajchenbach2011].

Here, we consider a spherical analogue to the Faraday instability, a fluid drop subjected to a time-periodic radial body force. The study of such problems therefore relies particularly on numerical simulation.

Numerical studies of axisymmetric oscillating viscous drops have been carried out by [@LM1988] via a boundary-integral method, by [@Patz1991] and [@Meradji2001] via a Galerkin/finite-element method, and by [@Bas1992] via a marker-in-cell initial-value problem. [@TB1983] used a Poincare-Lindstedt expansion method, to calculate the shapes of axisymmetric inviscid drops subjected to moderate amplitude oscillations for the three lowest capillary modes (see ). They were unable to confirm mathematically the existence of an asymptotic finite-amplitude motion; this can be verified only by means of numerical calculations. Indeed, the problem of axisymmetric ellipsoidal drop oscillation and decay has now come to be seen as a routine validation test case for numerical codes and interface methods for multiphase flows. However, the full non-linear problem is non-axisymmetric and requires three-dimensional numerical simulation with interface algorithms that ensure volume conservation and precise calculation of capillary forces as well as the ability to integrate highly spatially resolved 