From fb60c96e70c172f835966722b59c4ba3fdd8730c Mon Sep 17 00:00:00 2001 From: Luca Heltai Date: Sat, 18 Mar 2017 19:09:06 +0100 Subject: [PATCH] Added draft blurp on MappingManifold --- 8.5/paper.tex | 19 ++++++++++++++++++- 1 file changed, 18 insertions(+), 1 deletion(-) diff --git a/8.5/paper.tex b/8.5/paper.tex index 414fdc3..4f7c616 100644 --- a/8.5/paper.tex +++ b/8.5/paper.tex @@ -219,7 +219,24 @@ points, but it also ships the data automatically between MPI processes. \subsection{The \texttt{MappingManifold} class} -TODO: Luca +The \texttt{MappingManifold} class implements the same functionality +of the \texttt{Mapping} class for \emph{manifold conforming} +mappings. This class computes the transformation between the +reference and real cell by exploiting the geometrical information +coming from the underlying \texttt{Manifold} object. + +Quadrature points computed using this mapping lie on the exact +geometrical objects, and tangent and normal vectors computed using +this class are tangent and normal to the underlying geometry. This is +in constrast with the \texttt{MappingQ} and \texttt{MappingQGeneric} +classes, which approximate the geometry using a polynomial of some +order, and then compute the normals and tangents using the +approximated surface. + +Currently only first order transformations are implemented, and an +assertion is thrown if the user requests any higher order +transformations, for example, the hessian of the mapping. + \subsection{Extension of the \texttt{LinearOperator} class} -- 2.39.5