/[escript]/trunk/doc/cookbook/example11.tex
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revision 3232 by ahallam, Fri Oct 1 02:08:38 2010 UTC revision 3308 by jfenwick, Tue Oct 26 03:24:54 2010 UTC
# Line 41  point poles. Considering our model will Line 41  point poles. Considering our model will
41  input current and approximate the current density in a volume $\Delta V$ by  input current and approximate the current density in a volume $\Delta V$ by
42  \begin{equation}  \begin{equation}
43  \nabla \vec{J} =  \nabla \vec{J} =
44  \left(\frac{I}{\Delta V} \right) \delta(x-x\hackscore{s})  \left(\frac{I}{\Delta V} \right) \delta(x-x_{s})
45                                   \delta(y-y\hackscore{s})                                   \delta(y-y_{s})
46                                   \delta(z-z\hackscore{s})                                                                   \delta(z-z_{s})
47  \end{equation}  \end{equation}
48    
49  \begin{equation}  \begin{equation}
50  -\nabla \cdot \left[ \sigma(x,y,z) \nabla \phi (x,y,z) \right] =  -\nabla \cdot \left[ \sigma(x,y,z) \nabla \phi (x,y,z) \right] =
51  \left(\frac{I}{\Delta V} \right) \delta(x-x\hackscore{s})  \left(\frac{I}{\Delta V} \right) \delta(x-x_{s})
52                                   \delta(y-y\hackscore{s})                                   \delta(y-y_{s})
53                                   \delta(z-z\hackscore{s})                                                                   \delta(z-z_{s})            
54  \end{equation}  \end{equation}
55    
56  This form is quite simple to solve in \esc.  This form is quite simple to solve in \esc.

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