Linear Numerical Schemes for a $\textbfQ$-Tensor System for Nematic Liquid Crystals
<|reference_start|>Linear Numerical Schemes for a $\textbfQ$-Tensor System for Nematic Liquid Crystals: In this work, we present three linear numerical schemes to model nematic liquid crystals using the Landau-de Gennes $\textbf{Q}$-tensor theory. The first scheme is based on using a truncation procedure of the energy, which allows for an unconditionally energy stable first order accurate decoupled scheme. The second scheme uses a modified second order accurate optimal dissipation algorithm, which gives a second order accurate coupled scheme. Finally, the third scheme uses a new idea to decouple the unknowns from the second scheme which allows us to obtain accurate dynamics while improving computational efficiency. We present several numerical experiments to offer a comparative study of the accuracy, efficiency and the ability of the numerical schemes to represent realistic dynamics.<|reference_end|>
@article{swain2024linear,
    title={Linear Numerical Schemes for a $\textbf{Q}$-Tensor System for Nematic
  Liquid Crystals},
    author={Justin Swain and Giordano Tierra},
    journal={arXiv preprint arXiv:2403.17289},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.17289},
    primaryClass={math.NA cs.NA}
}