A simplified threshold dynamics algorithm for isotropic surface energies
This work provides a more efficient and simpler algorithm for simulating multiphase networks with arbitrary surface tensions and mobilities, which is relevant to computational materials science.
The paper presents a simplified threshold dynamics algorithm for isotropic surface energies that avoids retardation functions by using linear combinations of Gaussians, maintaining efficiency with only two distinct Gaussians. The algorithm is shown to converge for common cases like the Read & Shockley model, though counterexamples of non-convergence are also discussed.
We present a simplified version of the threshold dynamics algorithm given in the work of Esedoglu and Otto (2015). The new version still allows specifying N-choose-2 possibly distinct surface tensions and N-choose-2 possibly distinct mobilities for a network with N phases, but achieves this level of generality without the use of retardation functions. Instead, it employs linear combinations of Gaussians in the convolution step of the algorithm. Convolutions with only two distinct Gaussians is enough for the entire network, maintaining the efficiency of the original thresholding scheme. We discuss stability and convergence of the new algorithm, including some counterexamples in which convergence fails. The apparently convergent cases include unequal surface tensions given by the Read \& Shockley model and its three dimensional extensions, along with equal mobilities, that are a very common choice in computational materials science.