Performance Analysis of Parallel N-Body Simulation Using CPU and GPU Acceleration

Submitted under: CDAC CINE, IIT Guwahati Campus
Contributors: Partha Pratim Das, Manash Das

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Project Overview

This project implements a classic N-Body gravitational simulation to demonstrate the power of High Performance Computing (HPC) using GPU acceleration. We compare a baseline sequential CPU implementation (NumPy) against a parallel GPU implementation (CuPy) to measure speedup and scalability.

This work addresses the $O(N^2)$ computational complexity of the N-Body problem and answers the question: When does GPU acceleration become beneficial?

Key Features

• Scientific Correctness: Uses Newton's Law of Gravitation with softening.
• Dual Implementation:
  • CPU: Sequential, vectorized implementation using NumPy.
  • GPU: Massive parallel implementation using CuPy (CUDA).
• Benchmarking: Rigorous performance analysis across varying particle counts ($N$).
• Visualization: Speedup curves, scalability plots, and particle animations.
• Portability: Designed to run seamlessly on Google Colab and local implementations with NVIDIA GPUs.

HPC Concepts Demonstrated

• Data Parallelism: Distributing particle force calculations across thousands of GPU cores.
• Memory Bandwidth vs. Compute Bound: Analyzing the transfer overhead vs. computational gain.
• Amdahl's Law: Understanding the limits of parallel speedup.
• Vectorization: Efficient array operations in Python.

Folder Structure

HPC-NBody-Simulation/
├── notebooks/          # Main logical notebook for benchmarking & visualization
├── src/                # Python source modules for N-Body logic
│   ├── cpu_nbody.py    # NumPy implementation
│   └── gpu_nbody.py    # CuPy implementation
├── data/               # Directory for initial conditions (auto-generated)
├── results/            # Generated plots and animations
├── report/             # Project report and documentation
└── requirements.txt    # Python dependencies

How to Run

Option 1: Google Colab (Recommended)

1. Upload the entire HPC-NBody-Simulation folder to your Google Drive.
2. Open notebooks/nbody_cpu_vs_gpu.ipynb in Google Colab.
3. Mount Google Drive.
4. Change the runtime type to GPU.
5. Run all cells to execute benchmarks and generate results.

Option 2: Local Execution

Prerequisites: NVIDIA GPU, CUDA Toolkit installed.

1. Clone the repository:

   git clone <repository-url>
   cd HPC-NBody-Simulation

2. Create a virtual environment (optional but recommended):

   python -m venv venv
   source venv/bin/activate  # On Windows: venv\Scripts\activate

3. Install dependencies:

   pip install -r requirements.txt

   Note: You may need to install the specific CuPy version for your CUDA toolkit (e.g., pip install cupy-cuda12x).

4. detailed steps are in the notebook.

Expected Outputs

• Console output showing execution times for different $N$.
• Plots in results/:
  • cpu_time_vs_particles.png
  • gpu_time_vs_particles.png
  • speedup_curve.png
• nbody_simulation.gif: Animation of the planetary motion.

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Developed for academic evaluation.