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Efficient Fully Discrete Spectral-Galerkin Scheme for the Volume-Conserved Multi-Vesicular Phase-Field Model of Lipid Vesicles with Adhesion Potential

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Abstract

In this work, we aim to develop an effective fully discrete Spectral-Galerkin numerical scheme for the multi-vesicular phase-field model of lipid vesicles with adhesion potential. The essence of the scheme is to introduce several additional auxiliary variables and design some corresponding auxiliary ODEs to reformulate the system into an equivalent form so that the explicit discretization for the nonlinear terms can also achieve unconditional energy stability. Moreover, the scheme has a full decoupling structure and can avoid calculating variable-coefficient systems. The advantage of this scheme is its high efficiency and ease of implementation, that is, only by solving two independent linear biharmonic equations with constant coefficients for each phase-field variable, the scheme can achieve the second-order accuracy in time, spectral accuracy in space, and unconditional energy stability. We strictly prove that the fully discrete energy stability that the scheme holds and give a detailed step-by-step implementation process. Further, numerical experiments are carried out in 2D and 3D to verify the convergence rate, energy stability, and effectiveness of the developed algorithm.

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Acknowledgements

This work of C. Chen was partially supported by National Natural Science Foundation of China(11771375) and Shandong Provincial Natural Science Foundation(ZR2021ZD03, ZR2021MA010). The work of X. Yang was partially supported by National Science Foundation with grant number DMS-2012490.

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Authors and Affiliations

  1. School of Mathematics and Information Sciences, Yantai University, Yantai, 264005, People’s Republic of China

    Chuanjun Chen

  2. Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA

    Xiaofeng Yang

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  1. Chuanjun Chen
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  2. Xiaofeng Yang
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Correspondence to Xiaofeng Yang.

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Chen, C., Yang, X. Efficient Fully Discrete Spectral-Galerkin Scheme for the Volume-Conserved Multi-Vesicular Phase-Field Model of Lipid Vesicles with Adhesion Potential. Commun. Math. Stat. 12, 15–43 (2024). https://doi.org/10.1007/s40304-021-00278-z

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  • DOI: https://doi.org/10.1007/s40304-021-00278-z

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