Solving the Heat Equation

The actual solving of the equation is done on different contexts in different phases with increasing complexity and dimension. Serial implementations were done in order to understand the solving of the heat equations, and parallel implementation explores the splitting up the problem into managable pieces, and actually implementing a parallel algorithm with the use of MPI. Table 3.1 shows the summary of these variations.

Table 3.1: Table of different domains, dimensions with which the heat equation is solved.

Serial/Parallel	FD/FE	(Dimension/Shape)	Discretization	Trans/SS
Serial	FD	1-D Rod	Intervals	Transient
Serial	FD	1-D Ring	Intervals	Transient
Serial	FD	2-D Square	Mesh	Transient
Parallel	FD	2-D Square	Mesh	Transient