PDE Solvers: High-Performance Numerical Solvers for Heat and Wave Equations

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Project Overview

This project implements parallelized 3D solvers for:

• Heat Equation (Diffusion equation)
• Wave Equation (Hyperbolic PDE)

Features:

• OpenMP parallelization for multi-core CPUs
• Optimized memory access patterns
• Physical boundary conditions
• Detailed visualization tools

Requirements

• C++17 compatible compiler (GCC, Clang, MSVC)
• CMake (≥ 3.10)
• Python 3 (for visualization)
• OpenMP (usually included with compiler)

Python visualization packages:

pip install numpy matplotlib scikit-image

Installation & Building

git clone https://github.com/sowmya8900/HPCProject.git
cd PDE_Solvers
mkdir build && cd build
cmake .. -DCMAKE_BUILD_TYPE=Release
make -j4

Running the Solvers

Heat Equation

# Serial version
./heat_solver

# Parallel version (4 threads)
export OMP_NUM_THREADS=4
./heat_solver

Wave Equation

# Serial version
./wave_solver

# Parallel version (4 threads)
export OMP_NUM_THREADS=4
./wave_solver

Output Files

Both solvers generate:

• Final state: data/heat_final.txt or data/wave_final.txt
• Time steps: data/heat_step_*.txt and data/wave_step_*.txt

Visualization

Python Scripts

# Heat equation visualizations
python visualize_heat.py

# Wave equation visualizations
python visualize_wave.py

Generated visualizations:

• 2D Slices (*_slices.png)
• 3D Isosurfaces (*_3d.png)
• Time Animations (*_diffusion.gif, *_propagation.gif)

Configuration Options

Modify these in the source files:

• Grid size (grid_size)
• Physical parameters (alpha, c)
• Time steps (dt, total iterations)
• Initial conditions

Performance Tuning

• Adjust OMP_NUM_THREADS for your CPU cores
• Try different grid sizes (powers of 2 often perform better)

Future Work

• Add MPI parallelization
• Implement adaptive mesh refinement
• Add GUI controls via web interface
• Machine learning for parameter optimization