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29 March 2024
 
  » arxiv » cond-mat/9710167

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Efficient Computation of Dendritic Microstructures using Adaptive Mesh Refinement
Nikolas Provatas ; Nigel Goldenfeld ; Jonathan Dantzig ;
Date 16 Oct 1997
Subject Materials Science; Pattern Formation and Solitons | cond-mat.mtrl-sci nlin.PS patt-sol
Affiliation1 and 2), Nigel Goldenfeld , and Jonathan Dantzig ( University of Illinois at Urbana-Champaign, Department of Physics, Urbana, IL University of Illinois at Urbana-Champaign, Department of Mechanical and Industrial Engineering, Urbana, IL
AbstractWe 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
Source arXiv, cond-mat/9710167
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