Optimizing Numerical Integration with CUDA: A GPU Programming Project

Optimizing Numerical Integration with CUDA: A GPU Programming Project

During our GPU programming class at ESIEA, we undertook a final project focused on optimizing numerical integration using CUDA (Compute Unified Device Architecture). This project, completed in collaboration with Samy Lateb, aimed to leverage the immense computational power of GPUs to achieve significant speedups over traditional CPU-based approaches. The project culminated in a detailed Jupyter Notebook containing our code and performance tests.

The repository for this project can be found here.

Introduction

The initial step of our project involved selecting an appropriate algorithm that was both straightforward to parallelize and complex enough to demonstrate significant performance improvements when implemented with CUDA. We decided to start with a simple yet effective method: the numerical integration of polynomials using the trapezoidal rule. This method, well-suited for parallelization, served as an excellent candidate for showcasing the advantages of GPU programming.

Project Outline

1. Classical C++ Implementation: We began by implementing a classical C++ version of our numerical integration algorithm. This version served as a baseline for performance comparison with our CUDA implementation. The C++ code illustrated the fundamental logic and sequential execution of the trapezoidal rule for numerical integration.

2. CUDA Implementation: Next, we translated our C++ code into CUDA, optimizing it to run on the GPU. CUDA allows for the execution of thousands of parallel threads, making it an ideal platform for computationally intensive tasks like numerical integration.

3. Performance Comparison: Finally, we conducted a series of speed tests to compare the execution times of our C++ and CUDA implementations. These tests highlighted the significant performance gains achieved through parallelization on the GPU.

Results

Our CUDA implementation demonstrated substantial speed improvements over the classical C++ approach. By distributing the computational workload across multiple GPU threads, we were able to achieve faster execution times, making the process of numerical integration more efficient.

Key Learnings

This project provided several valuable insights:

• Understanding CUDA: We gained a deep understanding of CUDA programming, including thread management, memory allocation, and optimization techniques.
• Parallel Computing: The project highlighted the potential of parallel computing to accelerate complex calculations, offering a practical example of how GPU resources can be utilized effectively.
• Performance Optimization: We learned to identify and address performance bottlenecks, optimizing our code to fully exploit the capabilities of the GPU.
• Algorithm Adaptation: Adapting algorithms for parallel execution requires careful consideration of data dependencies and synchronization, skills that are crucial for effective GPU programming.

Conclusion

Our GPU programming project demonstrated the powerful capabilities of CUDA for optimizing numerical computations. The significant speedups achieved underscore the potential of GPUs to revolutionize various computational tasks. This project not only enhanced our technical skills but also provided a solid foundation for future exploration in the field of parallel computing.

Thank you for reading about our project. For those interested, the full repository containing our code and detailed report can be found here.