Multi-scale modelling using 3-dimensional adaptive meshing with an implicit, multigrid solver: A crystallization example

We review the application of advanced numerical techniques such as adaptive mesh refinement, implicit time-stepping, multigrid solvers and massively parallel implementations as a route to obtaining solutions to the 3-dimensional phase-field problem with a domain size and interface resolution previously possible only in 2-dimensions. Using such techniques it is shown that such models are tractable even as the interface width approaches the solute capillary length.