/[escript]/trunk/doc/cookbook/einsteinETA.tex
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revision 2632 by ahallam, Wed Aug 26 22:18:19 2009 UTC revision 2775 by ahallam, Wed Nov 25 05:01:43 2009 UTC
# Line 13  Line 13 
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14  \section{The Einstein Summation Convention}  \section{The Einstein Summation Convention}
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16  The Einstein Summation Convention (ESC) is a notational convention that is prefered by the \ESCRIPT developers. It is a condensed and practical way to deal with multi-dimensional and convoluted PDEs. By suppressing the need to write out the many terms of each problem it is possible to increase efficiency and reduce the number of errors created through poor working. According to the convention, when an index variable appears twice in a single term, it implies that we are summing over all of its possible values.  The Einstein Summation Convention (ESC) is a notational convention that is prefered by the \esc developers. It is a condensed and practical way to deal with multi-dimensional and convoluted PDEs. By suppressing the need to write out the many terms of each problem it is possible to increase efficiency and reduce the number of errors created through poor working. According to the convention, when an index variable appears twice in a single term, it implies that we are summing over all of its possible values.
17  So we have;  So we have;
18  \begin{equation}  \begin{equation}
19  a_1\frac{\partial^2 f}{\partial x_1^2} + a_2\frac{\partial^2 f}{\partial x_2^2} = a_i\frac{\partial^2 f}{\partial x_i^2}  a_1\frac{\partial^2 f}{\partial x_1^2} + a_2\frac{\partial^2 f}{\partial x_2^2} = a_i\frac{\partial^2 f}{\partial x_i^2}

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