A challenging problem in materials science are problems like solidification, melting or the kinetics also of more general phase transformation processes. One of the major difficulties is the motion of phase boundaries, which separate domains with very different physical behavior like different diffusivities, heat transport, elastic response etc.. Furthermore, e.g. during solidification latent heat is released at the moving fronts, therefore heating up the system. As the arising interface morphologies are very complex (for example dendrites), the tracking of the interfaces during a numerical simulation is challenging.
Here, phase field methods are a convenient way to overcome this difficulty, as they avoid this tracking procedure. Instead, an order parameter discriminates between the different phases - it can for example be 1 in the solid and 0 in the liquid phase. At the interface, this quantity smoothly interpolates between these bulk values. The major advantage is now that the evolution of this order parameter can be described by partial differential equations, which are supplemented by other equations e.g. for the solute diffusion or elastic equilibria. A tracking of the interfaces is no longer needed. Nevertheless, the interface locations can a posteriori be reproduced from the phase field evolution.
On the computational level the phase field equations can efficiently be parallelized e.g. using the message passing interface (MPI). Alternatively, a numerical solution using graphic cards is possible. In contrast to CPU parallelization we typically use one thread per lattice point of the simulation, thus leading to a large number of parallel executions. For an efficient treatment it is important to keep all data entirely on the graphics card, in order to avoid time-consuming memory transfer to the CPU. This allows to perform simulations with reasonable system sizes on consumer graphics cards.