An Efficient Boundary Integral Scheme for the Threshold Dynamics Method II: Applications to Wetting Dynamics
- 57 Downloads
In this paper, we extend the boundary integral scheme for the threshold dynamics method to treat the case where the material interface is nonsmooth and may undergo topological changes. The scheme is then applied to study the wetting dynamics in both two and three dimensions. Numerical experiments show that the scheme is more efficient as compared with the existing method using uniform grids, making accurate simulation of wetting dynamics on a chemically patterned solid surface in three dimensions within practical reach.
KeywordsThreshold dynamics method Nonuniform FFT Heat equation Wetting
S. Jiang was supported by the National Science Foundation under Grant DMS-1720405 and by the Flatiron Institute, a division of the Simons Foundation. The work of X.P. Wang was partially supported by the Hong Kong Research Grants Council (GRF Grants 16302715, 16324416, and 16303318). Part of the work was performed when the authors were participating in the HKUST-ICERM VI-MSS program ‘Integral Equation Methods, Fast Algorithms and Their Applications to Fluid Dynamics and Materials Science’ held in 2017.
- 6.Chen, H., Leng, H., Wang, D., Wang, X.P.: An efficient threshold dynamics method for topology optimization for fluids. arXiv preprint arXiv:1812.09437 (2018)
- 20.Osting, B., Wang, D.: A diffusion generated motion for orthogonal matrix-valued fields. Math. Comp. (2019) (accepted) Google Scholar
- 23.Wang, D.: Threshold dynamics method: theories, algorithms, and applications. Ph.D. thesis, Hong Kong University of Science and Technology (2017)Google Scholar
- 26.Wang, D., Osting, B., Wang, X.P.: Interface dynamics for an Allen–Cahn-type equation governing a matrix-valued field. Multiscale Model. Sim. (2019) (accepted) Google Scholar
- 27.Wang, D., Wang, X.P.: The iterative convolution-thresholding method (ICTM) for image segmentation. arXiv preprint arXiv:1904.10917 (2019)