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diff --git a/doc/documentation.tex b/doc/documentation.tex index 5cefc97..6299ed7 100644 --- a/doc/documentation.tex +++ b/doc/documentation.tex @@ -27,8 +27,37 @@ grid functions with the standard names {\tt x}, {\tt y}, and from {\tt grid}. The coordinates are registered with the flesh using the same names "x", "y" and "z". In addition a grid function {\tt r} (registered as -"r") is provided, containing the radius from the origin. +"r") is provided, containing the radial coordinate from +the origin where +$$ +r = \sqrt{x^2+y^2+z^2} +$$ +{\tt CartGrid3D} registers the lower and upper range of each coordinate +with the flesh. + +\subsection{Symmetries} + +If your problem and initial data allow it, {\tt CartGrid3D} +allows you to enforce either an even or odd parity +symmetry condition for any grid functions at each +coordinate axes. For a function $\phi(x,y,z)$, +even parity symmetry on the $x$-axis means +$$ +\phi(-x,y,z) = \phi(x,y,z) +$$ +while odd parity symmetry means +$$ +\phi(-x,y,z) = -\phi(x,y,z) +$$ + +Note that the symmetries will only be enforced if a +symmetry domain is chosen (that is, if +{\tt domain} is {\tt octant}, {\tt quadrant} or {\tt bitant}). + +\subsection{Registering Symmetry Behaviour} + +Each grid function can register how it behaves under a coordinate change % Automatically created from the ccl files by using gmake thorndoc |