GPU-Accelerated Hamiltonian Integrators
Overview
This project implements GPU-accelerated numerical integrators for simulating nonlinear Hamiltonian systems, with a focus on the Hénon–Heiles system — a classical benchmark for studying chaos and long-term dynamical behavior.
The core idea is to combine:
- Mathematical structure (Hamiltonian mechanics)
- Advanced numerical methods (symplectic integrators)
- High-performance computing (CUDA on GPUs)
to simulate millions of trajectories efficiently and accurately.
Why This Project Matters
Simulating physical systems over long time horizons is fundamentally challenging:
- Standard high-order methods (e.g. RK4) introduce energy drift
- Physical systems require preservation of geometric structure
- GPUs enable massive parallel exploration of phase space
This project demonstrates that:
Structure-preserving algorithms + GPU parallelism = scalable and physically correct simulations
Project Documentation
📘 Mathematical Documentation
👉 Symplectic Integrator — Mathematical Documentation
Covers:
- Hamiltonian formulation
- Hénon–Heiles system
- Symplectic integration theory
- Energy conservation and phase-space structure
- Visual diagrams and plots
🧪 Benchmark Experiment
👉 Benchmark Experiment Documentation
Covers:
- Experimental design and methodology
- Accuracy vs stability comparison
- Energy drift analysis
- GPU vs CPU performance evaluation
- Reproducibility setup
⚙️ CUDA Implementation
👉 CUDA Implementation Documentation
Covers:
- Kernel design and parallelization strategy
- Memory layout (SoA vs AoS)
- Annotated CUDA kernels
- Performance optimization techniques
- Practical HPC considerations
Key Features
- ✅ Symplectic (Leapfrog) integrator for long-term stability
- ✅ RK4 and Euler baselines for comparison
- ✅ GPU parallelization (one trajectory per thread)
- ✅ Energy diagnostics and validation
- ✅ Visualization-ready outputs
📌 Key Insight
This project highlights a fundamental principle in scientific computing:
Numerical accuracy alone is not enough — preserving the underlying physics is essential.
👤 Author
This project is part of a portfolio exploring:
- Numerical linear algebra
- GPU programming (CUDA)
- High-performance computing systems