Parallel Numerical Solution of 2-D Heat Equation

In this paper, we will discuss the numerical solution of the two dimensional Heat Equation. An approximation to the solution function is calculated at discrete spatial mesh points, proceeding in discrete time steps. The starting values are given by an initial value condition. We will first explain how to transform the differential equation into a finite difference equation, respectively a set of finite difference equations, that can be used to compute the approximate solution. We will then modify this algorithm in order to parallelize this task on multiple processors. Special focus is given on the performance respectively performance improvement of a parallelized algorithm on different hardware platforms. Additionally we will run the implemented algorithm on two different clusters and calculate speedup based on the execution time of 1 to 32 CPUs.