EFFICIENT COMPUTATION OF DENDRITIC MICROSTRUCTURES USING ADAPTIVE MESH REFINEMENT

We study dendritic microstructure evolution using an adaptive grid, fi nite element method applied to a phase-field model. The computational complexity of our algorithm, per unit time, scales linearly with syste m size, allowing simulations on very large lattices. a 2(17) x 2(17) l attice, but note that this is not an upper limit. Time-dependent calcu lations in two dimensions are in good agreement with the predictions o f solvability theory for high undercoolings, but predict higher values of velocity than solvability theory at low undercooling, where transi ents dominate, in accord with a heuristic criterion which we derive.