Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 228, Issue 21, Pages 8015-8033Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2009.07.020
Keywords
Diffusion-generated motion; Mean curvature flow; Grain growth
Funding
- NSF [DMS-0748333, DMS-0810113]
- Alfred P. Sloan Foundation fellowship
- Direct For Mathematical & Physical Scien [0810113] Funding Source: National Science Foundation
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0748333] Funding Source: National Science Foundation
- Division Of Mathematical Sciences [0810113] Funding Source: National Science Foundation
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An efficient algorithm for accurately simulating curvature flow for large networks of curves in two dimensions and surfaces in three dimensions on uniform grids is proposed. This motion arises in the technologically important problem of simulating grain boundary motion in polycrystalline materials. In this formulation grain boundaries are zero-level sets of signed distance functions. Curvature motion is achieved by first diffusing locally maintained signed distance functions followed by a reinitialization step. A technique is devised to allow a single signed distance function to represent a large subset of spatially separated grains. Hundreds of thousands of grains can be simulated using a small number of signed distance functions (in this work, 32 in two dimensions and 64 in three dimensions are more than sufficient) using modest computational hardware. (C) 2009 Elsevier Inc. All rights reserved.
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