  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.

Numerical Analysis