Efficient Computation of Dendritic Microstructures using Adaptive Mesh Refinement
Nikolas Provatas, Nigel Goldenfeld, Jonathan Dantzig
Abstract
We study dendritic microstructure evolution using an adaptive grid, finite element method applied to a phase-field model. The computational complexity of our algorithm, per unit time, scales linearly with system size, rather than the quadratic variation given by standard uniform mesh schemes. Time-dependent calculations in two dimensions are in good agreement with the predictions of solvability theory, and can be extended to three dimensions and small undercoolings
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