Abstract
Liquid crystal elastomers (LCEs) are soft complex materials of potential technological importance because of their remarkable responsiveness to excitations. In the previous work (Zhu et al. Phys. Rev. E 83, 051703 2011), we proposed a non-local continuum model to explore the dynamical behaviors of LCEs. The preliminary simulation demonstrated that the model can successfully capture the shape changing phenomena and other features of LCEs that were observed in real experiments (Camacho-Lopez et al. Nat. Mat. 3, 307–310 2004). However, due to the complexity of the governing equations, especially the velocity equation, the simulation is very time-consuming and thus efficient methods are imperatively needed. In this work, we propose a novel preconditioner for solving the velocity equation using Chebyshev spectral collocation method. Different from the well-known finite difference preconditioning (Orszag J. Comput. Phys. 37, 70–92 1980), the proposed preconditioner is constructed directly from the coefficient matrix of solving the velocity equation, without resorting to other operators such as the finite difference operator. With this preconditioner, very few inner iterations are needed when solving the resulting large scale linear system using GMRES method (Saad and Schultz SIAM J. Sci. STAT. Comput. 7(3), 856–869 1986). The experiments validate the efficiency of the proposed preconditioner.
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Communicated by: Silas Alben
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Zhu, W. Simulation of liquid crystal elastomers using Chebyshev spectral method with a new preconditioner. Adv Comput Math 41, 853–879 (2015). https://doi.org/10.1007/s10444-014-9389-5
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DOI: https://doi.org/10.1007/s10444-014-9389-5