Landau-de Gennes numerical simulation of nematic liquid crystals utilizing radial basis functions

Numerical simulations based on radial basis functions have been developed for systems with complex geometries and have been successfully applied across various fields, including seismology, coastal hydrodynamics, and biology. However, examples in liquid crystal modeling are limited. In this study, we present a Landau-de Gennes numerical simulation of nematic liquid crystals utilizing radial basis functions, emphasizing its advantages over traditional cubic grid calculations, such as enhanced geometric flexibility and improved computational efficiency. Through simulations of liquid crystal-colloid systems with diverse geometries, we demonstrate that our approach effectively captures the essential topological and energetic features of liquid crystal equilibrium structures. Additionally, we introduce an adaptive node refinement scheme that is crucial for resolving the fine structure of singular defects in nematic liquid crystals.