From: Simon Sticko Date: Thu, 23 Jun 2022 14:06:46 +0000 (+0200) Subject: Slightly weaken statement on exact integration. X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=bbb6d55a595363d15f4c9e534eeab95712d4a768;p=release-papers.git Slightly weaken statement on exact integration. --- diff --git a/9.4/paper.tex b/9.4/paper.tex index 40e3a08..a7df516 100644 --- a/9.4/paper.tex +++ b/9.4/paper.tex @@ -828,7 +828,7 @@ the same mesh has been remeshed. \caption{\it (a) Triangulation created by filling a heart-shaped surface implicitly described by a function $f$. (b) Union of a cube with a sphere with badly shaped cells at the intersection. (c) Remeshed version of the same triangulation.} \end{figure} -\texttt{CGALWrappers::compute\_quadrature\_on\_boolean\_operation()} returns a \texttt{Quadrature<3>} that allows exact integration on polyhedral elements coming out of a \texttt{BooleanOperation} between \dealii cells. +\texttt{CGALWrappers::compute\_quadrature\_on\_boolean\_operation()} returns a \texttt{Quadrature<3>} that allows exact integration of polynomials on polyhedral elements coming out of a \texttt{BooleanOperation} between \dealii cells. The quadrature rule is built by meshing the polyhedral region with tetrahedra, computing on each tetrahedron a \texttt{QGaussSimplex<3>} quadrature rule by using \texttt{QSimplex<3>::\allowbreak{}compute\_affine\_transformation()}, and finally collecting all of the rules together, giving a \texttt{Quadrature<3>} formula on the \emph{physical} element.