1D Heat Equation Solver

A parallel explicit finite-difference solver for the one-dimensional heat equation, provided with 13 different implementations:

• 3 serial kernels
• 4 OpenMP kernels (half-domain, loop unrolling, SIMD-aligned, collapse, swap)
• 5 MPI kernels (blocking point-to-point, non-blocking halo exchange, broadcast, scatter)

This repository includes a reproducible test suite, a performance driver, and post-processing scripts. You can compare speed-up and efficiency on both a local multicore machine and a PBS-managed HPC cluster.

---

Table of Contents

• Prerequisites
• Quick Start
• Quick Start Cluster
• Usage
• Output Files
• Project Structure

---

Prerequisites

• Compiler & MPI
  • mpicc from GCC ≥ 9 with OpenMP support
  • MPICH ≥ 3.2 or equivalent MPI library
• PBS job scheduler (for cluster runs)

---

Quick Start

1. Clone the repository

   git clone https://github.com/SaraFrancavilla/1D_Heat_Equation.git
   cd 1D_Heat_Equation

2. Compile

   mpicc -O2 -march=native -fopenmp all_implementation.h grouping_functions.c main.c matrix_config.c mpi.c parallel.c sequential.c write_to_file.c -lm

3. Run

   mpirun -np <num_processes≤64> ./a.out

Quick Start Cluster

1. Access and clone

   ssh [email protected]
   git clone https://github.com/SaraFrancavilla/1D_Heat_Equation.git
   cd 1D_Heat_Equation

2. Start an interactive session and load the modules

   qsub -I -q short_cpuQ -l select=1:ncpus=64:mpiprocs=64
   module load gcc91 mpich-3.2.1--gcc-9.1.0

3. Compile and launch the program

   mpicc -O2 -march=native -fopenmp all_implementation.h grouping_functions.c main.c matrix_config.c mpi.c     parallel.c sequential.c write_to_file.c -lm
   mpirun -np <max_processes64> ./a.out

Usage

After launching ./a.out, select one of the available menu options:

1. Correctness
   Validate all 13 kernels and write the final temperature profile to Results_comparison.txt.
2. Strong Scaling Fix problem sizes from the configuration matrix, test 2–64 OpenMP threads and 2–32 MPI ranks, and record wall-time, speed-up, and efficiency in Execution_times.txt.
3. Weak Scaling & Best Configuration Double mesh size with proportional resources, then log execution time, weak-scaling ratio, and the optimal configuration in Optimal_configurations_study.txt.

Output Files

1. Results_comparison.txt — Final temperature columns for correctness checks

2. Execution_times.txt — Timings, speed-up, and efficiency for strong-scaling studies

3. Optimal_configurations_study.txt — Times, weak-scaling ratios, and best thread/rank settings

Project Structure

 .
├── all_implementation.h     # Prototypes and common definitions  
├── grouping_functions.c     # Utility routines  
├── main.c                   # Driver and menu handling  
├── matrix_config.c          # Configuration matrix loader  
├── mpi.c                    # MPI-specific kernels and wrappers  
├── parallel.c               # OpenMP and hybrid implementations  
├── sequential.c             # Baseline serial implementation  
├── write_to_file.c          # Logging and output routines  
└── README.md                # This file