Efficient simulation of Bose-Einstein condensates in nontrivial topologies

Bubble-shaped Bose-Einstein condensates (BECs) constitute a unique class of quantum fluids with a hollow, thin-shell geometry that supports a wide variety of phenomena distinct from those of compact condensates. Numerical simulation of such systems is particularly challenging due to their inherently three-dimensional structure and extreme aspect ratios. We present an efficient finite-difference simulation framework for solving partial differential equations in nontrivial topologies, with a focus on the static and dynamical modeling of bubble-shaped BECs. By employing selective spatial sampling on a semistructured grid, our method substantially reduces memory usage and achieves more than an order-of-magnitude improvement in computational performance compared with conventional split-step Fourier solvers. The algorithm is naturally extendable to highly parallel execution on graphics processing units (GPUs), enabling large-scale, time-dependent simulations of thin-shell condensates. We apply this framework to simulate the formation of bubble BECs through a controlled hollowing-out protocol using trapping potentials relevant to the Cold Atom Laboratory aboard the International Space Station. From these simulations, we identify characteristic timescales and parameter ramps required to achieve adiabatic evolution, thereby assessing the feasibility of experimentally realizing bubble-shaped condensates in microgravity environments.