Parallel Heat Equation Solver

Objective: Implement a parallel solver for the heat equation using finite difference methods and OpenMP.

Description: The heat equation is a partial differential equation that describes the distribution of heat in each region over time. The goal is to use a finite difference method to solve the heat equation in parallel.

Steps:

$1.$ Implement the finite difference method to solve the heat equation in serial.

$2.$ Identify the independent computations that can be parallelized.

$3.$ Use OpenMP to parallelize these computations.

$4.$ Ensure the parallel implementation correctly handles boundary conditions.

$5.$ Test and compare the performance of the parallel solver with the serial version.

Key Learning Outcomes:

$$ Understanding and solving partial differential equations.

$$ Implementing numerical methods for PDEs.

$$ Optimizing parallel computations for large$-$scale scientific problems.