Efficient Computation of Dendritic Microstructures using Adaptive Mesh Refinement
Nikolas Provatas (1, 2), Nigel Goldenfeld (1), and Jonathan Dantzig, (2) ((1) University of Illinois at Urbana-Champaign, Department of Physics,, Urbana, IL (2) University of Illinois at Urbana-Champaign, Department of, Mechanical, Industrial Engineering, Urbana, IL)
TL;DR
This paper presents an adaptive mesh finite element method for simulating dendritic microstructures, achieving linear computational complexity and validating results against theoretical predictions in two dimensions, with extensions to 3D.
Contribution
It introduces an efficient adaptive mesh approach that reduces computational complexity from quadratic to linear for dendritic microstructure simulations.
Findings
Computational complexity scales linearly with system size.
Results agree with solvability theory in 2D.
Method extends to 3D and small undercoolings.
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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Taxonomy
TopicsSolidification and crystal growth phenomena · Theoretical and Computational Physics · Block Copolymer Self-Assembly