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For example, a line 100m long is discretised into 1m intervals or 101 nodes. If 
For example, a line 100m long is discretised into 1m intervals or 101 nodes. If 
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a wave enters with a propagation velocity of 100m/s then the travel time for 
a wave enters with a propagation velocity of 100m/s then the travel time for 
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the wave between each node will be 0.01 seconds. The time step, must therefore 
the wave between each node will be 0.01 seconds. The time step, must therefore 
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be significantly less then this. Of the order $10E4$ would be appropriate. 
be significantly less than this. Of the order $10E4$ would be appropriate. 
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This stability criterion is known as the Courant\textendash 
This stability criterion is known as the Courant\textendash 
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Friedrichs\textendash Lewy condition given by 
Friedrichs\textendash Lewy condition given by 
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\begin{equation} 
\begin{equation} 
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\end{equation} 
\end{equation} 
293 


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\subsection{Lumping} 
\subsection{Lumping} 
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For \esc, the acceleration solution is prefered as it allows the use of matrix 
For \esc, the acceleration solution is preferred as it allows the use of matrix 
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lumping. Lumping or mass lumping as it is sometimes known, is the process of 
lumping. Lumping or mass lumping as it is sometimes known, is the process of 
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aggressively approximating the density elements of a mass matrix into the main 
aggressively approximating the density elements of a mass matrix into the main 
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diagonal. The use of Lumping is motivaed by the simplicity of diagonal matrix 
diagonal. The use of Lumping is motivated by the simplicity of diagonal matrix 
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inversion. As a result, Lumping can significantly reduce the computational 
inversion. As a result, Lumping can significantly reduce the computational 
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requirements of a problem. Care should be taken however, as this 
requirements of a problem. Care should be taken however, as this 
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function can only be used when the $A$, $B$ and $C$ coefficients of the 
function can only be used when the $A$, $B$ and $C$ coefficients of the 