VoxEl-based boundary inClination smooThing AlgORithms

This project provides four smoothing algorithms to get the inclination of each voxel on the 2D and 3D sharp boundary: Vertex smoothing algorithm, Allen-Cahn smoothing algorithm, Level-Set smoothing algorithm and Bilinear smoothing algorithm.

All smoothing algorithms can work in parallel and are integrated with comprehensive analysis tools for materials science applications, particularly grain growth simulation and grain boundary characterization.

VECTOR/
├── Core Algorithm Files
│   ├── myInput.py                       # Input utilities and data processing functions
│   ├── post_processing.py               # Post-processing and analysis utilities
│   └── PACKAGE_MP_*.py                  # Core smoothing algorithm implementations
├── Algorithm Packages
│   ├── PACKAGE_MP_Vertex.py             # 2D Vertex smoothing algorithm
│   ├── PACKAGE_MP_Linear.py             # 2D Bilinear smoothing algorithm
│   ├── PACKAGE_MP_AllenCahn.py          # 2D Allen-Cahn smoothing algorithm
│   ├── PACKAGE_MP_LevelSet.py           # 2D Level-Set smoothing algorithm
│   ├── PACKAGE_MP_3DVertex.py           # 3D Vertex smoothing algorithm
│   ├── PACKAGE_MP_3DLinear.py           # 3D Bilinear smoothing algorithm
│   ├── PACKAGE_MP_3DAllenCahn.py        # 3D Allen-Cahn smoothing algorithm
│   └── PACKAGE_MP_3DLevelSet.py         # 3D Level-Set smoothing algorithm
├── Application Examples
│   ├── examples/                        # Comprehensive application examples
│   └── verification/                    # Algorithm verification and testing
└── Documentation and Metadata
    ├── README.md                        # This documentation
    ├── CITATION.cff                     # Citation information
    └── __init__.py                      # Python package initialization

Purpose: Comprehensive input utilities and data processing functions

• Core Functions:
  • Input file processing from various formats (SPPARKS, DREAM.3D, custom formats)
  • Microstructure data handling and conversion utilities
  • Periodic boundary condition management
  • Geometric utility functions for 2D and 3D systems
  • Data validation and preprocessing tools
• Key Applications: Interface between simulation data and VECTOR algorithms

Purpose: Extensive post-processing and analysis utilities

• Core Functions:
  • Grain boundary analysis and characterization
  • Curvature calculation and validation
  • Statistical analysis tools for microstructure evolution
  • Visualization utilities for 2D and 3D data
  • Integration with SPPARKS simulation framework
  • Energy function analysis and grain growth metrics
• Key Applications: Scientific analysis and result interpretation

• Algorithm: Vertex-based boundary smoothing for 2D grain boundary inclination calculation
• Key Features: Vertex identification, geometric smoothing, parallel processing
• Applications: Grain boundary inclination calculation and analysis

• Algorithm: Bilinear smoothing for 2D grain boundary inclination calculation
• Key Features: Linear interpolation, gradient calculation, parallel implementation
• Applications: Grain boundary inclination calculation and analysis

• Algorithm: Allen-Cahn equation-based smoothing for 2D grain boundary inclination calculation
• Key Features: Phase field methodology, diffuse interface modeling
• Applications: Grain boundary inclination calculation and analysis

• Algorithm: Level-Set method for 2D grain boundary inclination calculation
• Key Features: Level-set smoothing method
• Applications: Grain boundary inclination calculation and analysis

• Algorithm: 3D vertex-based boundary smoothing
• Key Features: 3D vertex identification, volumetric smoothing, enhanced parallel processing
• Applications: 3D grain boundary inclination calculation and analysis

• Algorithm: 3D bilinear smoothing for grain boundary analysis
• Key Features: 3D gradient calculation, mean curvature computation, parallel 3D processing
• Applications: 3D grain boundary characterization and curvature analysis

• Algorithm: 3D Allen-Cahn equation-based smoothing
• Key Features: 3D phase field smoothing method
• Applications: 3D grain boundary characterization and curvature analysis

• Algorithm: 3D Level-Set method for boundary smoothing
• Key Features: 3D level-set smoothing method
• Applications: 3D grain boundary characterization and curvature analysis

Purpose: Grain boundary velocity and anti-curvature analysis

• Content: 23 Jupyter notebooks for comprehensive grain boundary dynamics analysis
• Key Features: 2D/3D analysis, energy function comparison, anti-curvature detection
• Applications: Understanding counter-intuitive grain boundary motion patterns

Purpose: Energy function verification through statistical analysis

• Content: 6 analysis tools (Python scripts and Jupyter notebooks)
• Key Features: Grain size distribution analysis, misorientation distribution characterization
• Applications: Energy function validation and comparative analysis

Purpose: SPPARKS preprocessing utilities

• Content: 5 specialized tools for simulation data processing
• Key Features: Microstructure generation, data conversion, neighbor connectivity
• Applications: Bridge between simulation preparation and execution

Purpose: Grain boundary inclination calculation and validation

• Content: PRIMME-based inclination calculation tools and basic example script (calculate_inclination_example.py)
• Key Features: High-performance inclination computation, HiPerGator integration, educational example workflow
• Applications: Large-scale crystallographic analysis, algorithm demonstration and learning

Purpose: Tangent vector calculation for grain boundaries

• Content: Triple junction analysis and tangent vector computation
• Key Features: Dihedral angle calculation, tangent vector analysis
• Applications: Triple junction characterization and geometric analysis

Purpose: Comprehensive curvature calculation and validation

• Content: Multiple curvature analysis tools and validation datasets
• Key Features: Algorithm comparison, geometric validation, 3D curvature analysis
• Applications: Curvature algorithm development and verification

Purpose: Microstructure visualization and analysis

• Content: Visualization tools for various microstructure types
• Key Features: 2D/3D plotting, statistical analysis, publication-quality figures
• Applications: Microstructure characterization and visual analysis

Purpose: Grain growth property analysis and visualization

• Content: Comprehensive grain growth analysis tools
• Key Features: Statistical analysis, temporal evolution, energy analysis
• Applications: Grain growth kinetics and microstructure evolution studies

Purpose: Triple junction site energy calculation

• Content: Energy calculation tools for triple junction analysis
• Key Features: Site-specific energy analysis, junction characterization
• Applications: Triple junction energy analysis and materials design

Purpose: Normal vector and triple junction angle analysis

• Content: Geometric analysis tools for complex junction systems
• Key Features: Normal vector calculation, angle analysis
• Applications: Advanced geometric characterization of grain boundaries

Purpose: Comprehensive algorithm verification and testing suite

• Content:
  • run_tests.py: Automated testing framework
  • test_config.py: Test configuration management
  • test_cases/: Comprehensive test case library
  • output/: Verification results and benchmarks
• Key Features: Algorithm accuracy validation, performance benchmarking, regression testing
• Applications: Quality assurance and algorithm development validation

• Algorithm Development: Development and validation of new smoothing algorithms for inclination and curvature calculation
• Simulation Integration: Interface with Monte Carlo simulations
• Performance Optimization: Parallel processing and computational efficiency
• Method Validation: Comprehensive testing and verification frameworks
• Grain Growth Studies: Comprehensive analysis of grain growth kinetics and mechanisms
• Energy Function Development: Validation and optimization of grain boundary energy models
• Crystallographic Analysis: Advanced texture and orientation analysis

• Materials Design: Microstructure-property relationship analysis
• Processing Optimization: Understanding processing-microstructure connections
• Quality Control: Microstructure characterization for manufacturing
• Property Prediction: Computational prediction of material properties

• Parallel Processing: All algorithms support multicore parallel execution
• Scalability: Designed for large-scale 3D microstructures (up to 1000³ voxels)
• Memory Efficiency: Optimized data structures for large dataset processing

• SPPARKS: Native integration with SPPARKS simulation output
• DREAM.3D: Support for experimental microstructure data
• HDF5: High-performance scientific data format support
• NumPy: Efficient numerical array processing
• Custom Formats: Flexible input/output for various data types

• 2D Systems: Optimized for high-resolution 2D microstructure analysis
• 3D Systems: Advanced 3D algorithms with enhanced computational efficiency
• Accuracy: Validated against analytical solutions and experimental data
• Robustness: Comprehensive error handling and validation

pip install numpy matplotlib scipy tqdm numba
pip install h5py multiprocess

pip install jupyter ipywidgets  # For interactive notebooks
pip install plotly  # For advanced 3D visualization
pip install torch  # For GPU-accelerated processing

# Execute VECTOR smoothing analysis using example script
python examples/calculate_inclination/calculate_inclination_example.py

# Use Jupyter notebooks for interactive analysis
jupyter notebook examples/GB_velocity/3D_GB_velocity_analysis.ipynb

Primary Citation: https://www.sciencedirect.com/science/article/pii/S1359646222002925

Lin Yang
Email: [email protected]/[email protected]

For detailed documentation of specific components, refer to the README.md files in individual example directories and the comprehensive inline documentation within each module.