2D Heat Plate Simulation on GPU

This project implements a GPU-accelerated simulation of heat distribution on a 2D metal plate using the Jacobi iterative method.

The serial implementation is based on the OpenACC Training Materials provided by OpenACC.org
This repository extends the original tutorial by adding a CUDA version for GPU acceleration.

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Problem Description

Heat diffusion on a 2D plate is modeled by solving the Laplace equation iteratively:

$$ A_{j,i}^{\text{new}} = \tfrac{1}{4}\Big( A_{j,i+1} + A_{j,i-1} + A_{j-1,i} + A_{j+1,i} \Big) $$

• Boundary conditions:

  • Top row fixed at 1.0 (heat source).
  • Other boundaries fixed at 0.0.

• Convergence: Iteration stops when the maximum difference between iterations falls below a tolerance, or after a maximum number of iterations.

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Project Structure

• serial/ – serial implementation in C.

• cuda/ – GPU implementation in CUDA.

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Performance

Grid Size	Serial	CUDA	Speedup
1024 x 1024	6.6511 s	0.0757 s	88x
2048 x 2048	26.7749 s	0.4801 s	55x
4096 x 4096	154.8857 s	2.4873 s	62x
8192 x 8192	437.6124 s	7.7569 s	56x

Environment

• CPU: AMD Ryzen 7 5800X 8-Core Processor
• GPU: NVIDIA GeForce RTX 4070 Ti
• Ubuntu 22.04.1

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Build & Run

Requirements

• gcc compiler for serial version.

• NVIDIA CUDA Toolkit - nvcc compiler for CUDA version.

• Linux environment recommended.

Serial version

cd serial
make
./jacobi

CUDA version

cd cuda
make
./jacobi

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