TY - JOUR
T1 - Simulations of singularity dynamics in liquid crystal flows
T2 - A C0 finite element approach
AU - Lin, Ping
AU - Liu, Chun
N1 - Funding Information:
P. Lin is partially supported by Singapore Academic Research Grant No. R-146-000-033-112. C. Liu is partially supported by NSF Grant DMS-0405850. This work has begun when C. Liu was visiting the National University of Singapore in the winter of 2004. He wants to thank the hospitality and the assistance provided by the Department of Mathematics and Institute for Mathematical Sciences in NUS. P. Lin wants to thank Olivier Pironneau for his help with Freefem++ and for his valuable discussion on the algorithm.
PY - 2006/6/10
Y1 - 2006/6/10
N2 - In this paper, we present a C0 finite element method for a 2D hydrodynamic liquid crystal model which is simpler than existing C1 element methods and mixed element formulation. The energy law is formally justified and the energy decay is used as a validation tool for our numerical computation. A splitting method combined with only a few fixed point iteration for the penalty term of the director field is applied to reduce the size of the stiffness matrix and to keep the stiffness matrix time-independent. The latter avoids solving a linear system at every time step and largely reduces the computational time, especially when direct linear system solvers are used. Our approach is verified by comparing its computational results with those obtained by C1 elements and by mixed formulation. Through numerical experiments of a few other splittings and explicit-implicit strategies, we recommend a fast and reliable algorithm for this model. A number of examples are computed to demonstrate the algorithm.
AB - In this paper, we present a C0 finite element method for a 2D hydrodynamic liquid crystal model which is simpler than existing C1 element methods and mixed element formulation. The energy law is formally justified and the energy decay is used as a validation tool for our numerical computation. A splitting method combined with only a few fixed point iteration for the penalty term of the director field is applied to reduce the size of the stiffness matrix and to keep the stiffness matrix time-independent. The latter avoids solving a linear system at every time step and largely reduces the computational time, especially when direct linear system solvers are used. Our approach is verified by comparing its computational results with those obtained by C1 elements and by mixed formulation. Through numerical experiments of a few other splittings and explicit-implicit strategies, we recommend a fast and reliable algorithm for this model. A number of examples are computed to demonstrate the algorithm.
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U2 - 10.1016/j.jcp.2005.10.027
DO - 10.1016/j.jcp.2005.10.027
M3 - Article
AN - SCOPUS:33645888383
SN - 0021-9991
VL - 215
SP - 348
EP - 362
JO - Journal of Computational Physics
JF - Journal of Computational Physics
IS - 1
ER -