2D-Heat-Equation_OpenMP

Introduction

2D Heat Equation for a Square Plate. Solution found by Iterating through the System Algebraic Equations via the OpenMP API.

Scenario

The north (top) plate has a temperature of 0 deg. celsius. The rest of the plate-sides have temperatures of 100 deg. celsius

                        I = 0
                        
           [0][0]------------------[0][N-1]
                |                  |
         J = 0  |                  |  J = N-1
                |                  |
         [M-1][0]------------------[M-1][N-1]
          
                        I = M-1

This diagram will prove very useful so refer to it. Solution to the heat-equation:

  w(Central) = (1/4)*([w(North] + w[South] + w[East] + w[West])

Operating System

Ubuntu 20.04

Text Editor

Any Text Editor will do but I've used Visual Studio Code. Vim, gedit, Emacs etc.

Compiler

gcc/g++ 9.4.0

OpenMP API

OpenMP is typically used for loop-level parallelism, but it also supports function-level parallelism. In this project, OpenMP is used to parallelise the iterator. By using multithreading, we are able to achive faster speeds while iterating through the loop structures, thus obtain a solution/heat distribution of a plate more quickly than we would via sequential programming. OpenMP comes with gcc/g++ and gfortran so there is no need to install anything.

Running the Application

• $ git clone http://github/MRLintern/2D-Heat-Equation_OpenMP.git
• $ make
• $ ./2D_Heat

Additions

Added some data and plots showing speed-up and efficiency of code. Also, data and plot added to investigate how different optimisation flags effect the speed-up.