A Rust implementation of Direct Parameterization of Invariant Manifolds (DPIM) for Model Order Reduction to Spectral Submanifolds (SSMs), with applications in structural dynamics and finite element analysis.

• Efficient computation of invariant manifolds for high-dimensional mechanical systems
• Spectral Submanifold (SSM) based model order reduction
• Rust-native performance for large-scale FEM problems
• Parallelized computations using Rayon
• Serde support for configuration serialization
• Customizable nonlinearity handlers
• Integration with popular FEM data formats

The tool implements the parameterization method for invariant manifolds as described in:

Haller, G. et al. (2020). "Nonlinear model reduction to spectral submanifolds". Journal of Sound and Vibration.

The method enables the reduction of high-dimensional FEM models to low-dimensional invariant manifolds while preserving nonlinear dynamics.

Add to your Cargo.toml:

[dependencies]
dpim = { git = "https://github.com/yourusername/dpim-rs" }

Or install via cargo:

cargo add dpim --git https://github.com/yourusername/dpim-rs

use dpim::core::System;
use dpim::reduction::SSMReducer;
use dpim::fem::FEModel;

fn main() {
    // Load FEM model
    let model = FEModel::from_file("beam_model.vtk")?;
    
    // Create dynamical system representation
    let system = System::from_fem(model, 
        Nonlinearity::Cubic, 
        Damping::Rayleigh(0.01, 0.001));
    
    // Perform SSM reduction
    let reducer = SSMReducer::new(system);
    let reduced = reducer.reduce_to_ssm(2, 3)?; // 2 modes, order 3
    
    // Use reduced model for simulation
    let trajectory = reduced.simulate(initial_conditions, time_steps);
}

Full API documentation is available at: docs.rs/dpim

The package includes a CLI for processing FEM models:

dpim-cli --model beam_fem.h5 --modes 3 --order 2 --output reduced_model.json

Performance compared to MATLAB reference implementation:

Contributions are welcome! Please see CONTRIBUTING.md for guidelines.

MIT License - see LICENSE for details.

dpim-rs/
├── Cargo.toml
├── README.md
├── src/
│   ├── lib.rs          # Main library
│   ├── core/           # Core dynamical systems
│   ├── reduction/      # SSM reduction algorithms  
│   ├── fem/            # FEM-specific functionality
│   ├── nonlinearities/ # Nonlinearity handlers
│   └── utils/          # Math utilities
├── examples/           # Usage examples
├── benches/            # Performance benchmarks
└── tests/              # Unit tests

Would you like me to:

1. Add more mathematical details about the implementation?
2. Include specific FEM format support details?
3. Add more usage examples?
4. Customize any section further?