Hierarchical Tree Methods
Using adaptive octree structures to group distant bodies and approximate their collective influence, reducing computational complexity from O(n²) to O(n log n).
Featured Project · Physics
Inertial Field Solver
Fast, stable numerical solvers for multi-body gravitational and inertial fields. Achieving sub-millisecond precision in complex orbital scenarios.
Overview
The Inertial Field Solver is a high-performance computational framework for simulating gravitational and inertial interactions in multi-body systems. Traditional N-body solvers suffer from computational complexity that scales poorly with the number of bodies. Our approach leverages novel mathematical techniques and optimized numerical methods to achieve near-linear scaling while maintaining accuracy.
This work has applications in orbital mechanics, spacecraft trajectory planning, and astrophysical simulations where real-time or near-real-time computation is essential.
Technical Approach
Symplectic Integration
Energy-preserving integration schemes that maintain long-term stability of orbital trajectories without artificial damping or energy drift.
Parallel Computing
GPU-accelerated force calculations and CPU-based tree construction, achieving optimal load balancing across heterogeneous compute resources.
Adaptive Time-Stepping
Dynamic adjustment of integration timesteps based on local error estimates, ensuring accuracy while minimizing unnecessary computation.
Performance Metrics
- 10,000+ bodies.Real-time simulation of complex multi-body systems with sub-millisecond timesteps.
- 1e-12 energy conservation.Maintains energy conservation to machine precision over long integration periods.
- 100x speedup.Compared to traditional direct summation methods for systems with >1000 bodies.
- GPU acceleration.Seamless scaling to multi-GPU systems with near-linear speedup.
Use Cases
Spacecraft Trajectory Planning
Real-time computation of optimal trajectories accounting for gravitational influences from multiple bodies.
Asteroid Belt Simulation
Long-term stability analysis of asteroid orbits for planetary defense and resource exploration.
Satellite Constellation Design
Optimizing orbital parameters for large satellite constellations while avoiding collisions.
Access & Collaboration
Interested in using our solver?
We offer commercial licenses and research partnerships. Academic researchers can request free access for non-commercial use.