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Numerics for the 2D Stochastic Allen-Cahn


In this section you can find our numerical results for the 2D stochastic Allen-Cahn equation.


Algorithm

Here you will see the details on the method we used to generate our simulations. A suitable regularisation of the white noise is introduced. Our approach is motivated by the work A finite element method via noise regularization for the stochastic Allen-Cahn problem by M. A. Katsoulakis, G.T. Kossioris, and O. Lakkis, which suggests an algorithm for the 1D equation.



Numerical experiments

We finally show and discuss some simulations carried out with our algorithm. As will be noted, the interface behaviour resembles that of motion by mean curvature, but the boundaries are here rougher and interface may move at times in the opposite direction to the one dictated by motion by mean curvature. The scheme was implemented in C++ using the DUNE numerics environment.