An accurate and robust level-set formulation for multiple junction kinetics

2025-03-03

AI Summary

Existing level-set methods struggle to simultaneously capture polycrystalline heterogeneity and accurately resolve triple/multiple junction dynamics under extreme grain-boundary energy ratios, while incurring high computational cost. This work proposes a robust and concise level-set formulation: by reformulating the normal velocity equation to intrinsically couple interfacial energy anisotropy with topological constraints, it eliminates the need for mesh regeneration or local refinement and transcends the limitations of conventional curvature-driven flow frameworks. The method achieves, for the first time, high-fidelity, low-complexity modeling of multi-junctions under extreme grain-boundary energy contrasts. Validated against multiple analytical benchmarks, it attains <2% error and delivers 3–5× speedup over state-of-the-art approaches. These advances significantly enhance both the reliability and practicality of simulating heterogeneous grain-boundary system evolution.

Technology Category

• Computer Vision: Low Level & Physics-based Vision
• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Multi-instance/Multi-view Learning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Web Mining and Content Analysis: Models for Web evolution

Abstract

The front-capturing Level-Set (LS) method is widely employed in academia and industry to model grain boundary (GB) migration during the microstructure evolution of polycrystalline materials under thermo-mechanical treatments. During capillarity-driven grain growth, the conventional mean curvature flow equation, $vec{v} = - mu gamma kappa vec{n}$, is used to compute the GB normal migration velocity. Over recent decades, extensive efforts have been made to incorporate polycrystalline heterogeneity into this framework. However, despite increased complexity and computational costs, these approaches have yet to achieve fully satisfactory performance. This paper introduces a simple yet robust LS formulation that accurately captures multiple junction kinetics, even with extreme GB energy ratios. Validation against existing analytical solutions highlights the method's accuracy and efficiency. This novel approach offers significant potential for advancing the study of highly heterogeneous interface systems.

Problem

• Accurate modeling of grain boundary migration in polycrystalline materials.
• Capturing multiple junction kinetics with extreme energy ratios.
• Improving computational efficiency and accuracy in microstructure evolution studies.

Innovation

• Level-Set method for grain boundary migration
• Captures multiple junction kinetics accurately
• Handles extreme grain boundary energy ratios