 # Diff of /branches/doubleplusgood/doc/cookbook/example07.tex

revision 4344 by jfenwick, Wed Feb 27 03:42:40 2013 UTC revision 4345 by jfenwick, Fri Mar 29 07:09:41 2013 UTC
# Line 119  is able to, and in general, needs to be Line 119  is able to, and in general, needs to be
119  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
120  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
121  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
122  be significantly less then this. Of the order $10E-4$ would be appropriate.  be significantly less than this. Of the order $10E-4$ would be appropriate.
123  This stability criterion is known as the Courant\textendash  This stability criterion is known as the Courant\textendash
124  Friedrichs\textendash Lewy condition given by  Friedrichs\textendash Lewy condition given by
125  \begin{equation}  \begin{equation}
# Line 292  After each iteration the displacement is Line 292  After each iteration the displacement is
292  \end{equation}  \end{equation}
293
294  \subsection{Lumping}  \subsection{Lumping}
295  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
296  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
297  aggressively approximating the density elements of a mass matrix into the main  aggressively approximating the density elements of a mass matrix into the main
298  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
299   inversion. As a result, Lumping can significantly reduce the computational   inversion. As a result, Lumping can significantly reduce the computational
300  requirements of a problem. Care should be taken however, as this  requirements of a problem. Care should be taken however, as this
301  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

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