From: Marco Feder Date: Tue, 21 Jun 2022 18:49:16 +0000 (+0200) Subject: Improve CGAL section X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=refs%2Fpull%2F79%2Fhead;p=release-papers.git Improve CGAL section --- diff --git a/9.4/paper.tex b/9.4/paper.tex index 5a37d7b..9c6934c 100644 --- a/9.4/paper.tex +++ b/9.4/paper.tex @@ -729,12 +729,6 @@ GridGenerator::implicit_function(tria, implicit_function, data, {0, 0, 0}, 10.0); \end{c++} -\begin{figure} - \centering - \includegraphics[width=.6\paperwidth]{png/heart_implicit.png} - \caption{\it \texttt{Triangulation<3>} of a heart surface starting from an implicit function $f$. \label{fig:heart_tria}} -\end{figure} - A related function is \texttt{GridGenerator::surface\_mesh\_to\_volumetric\_mesh()}, which computes a tetrahedral volume triangulation \texttt{Triangulation<3>}, based on a @@ -775,19 +769,23 @@ A possible workflow is the following: the same mesh has been remeshed. \begin{figure} \centering - \begin{subfigure}[b]{0.4\textwidth} + \begin{subfigure}[b]{0.3\textwidth} \centering - \includegraphics[height=.2\paperheight]{png/intersection_cube_sphere_mesh.png} + \includegraphics[width=.2\paperwidth]{png/heart_implicit.png} + \caption{\label{fig:heart_tria}} + \end{subfigure} + \begin{subfigure}[b]{0.3\textwidth} + \centering + \includegraphics[height=.14\paperheight]{png/intersection_cube_sphere_mesh.png} \caption{\label{fig:corefinement}} \end{subfigure} \qquad - \begin{subfigure}[b]{0.5\textwidth} + \begin{subfigure}[b]{0.3\textwidth} \centering - \includegraphics[height=.2\paperheight]{png/cube_sphere_remeshed.png} + \includegraphics[height=.14\paperheight]{png/cube_sphere_remeshed.png} \caption{ \label{fig:corefinement_remeshed}} \end{subfigure} - \caption{\it (a) Union of the unit cube with an hyper ball. Notice - how the corefinement around the intersection results in badly shaped elements. (b) The remeshed \dealii{} Triangulation.} + \caption{\it (a) \texttt{Triangulation<3>} of a heart surface starting from an implicit function $f$. (b) Union of the unit cube with an hyper ball. Notice how the corefinement around the intersection gives badly shaped elements. (c) The remeshed \dealii{} 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. @@ -796,6 +794,8 @@ collecting all of the rules together, giving a \texttt{Quadrature<3>} formula on These utilities will be the building blocks for adding functions to the \texttt{NonMatching} namespace that will assemble coupling terms like $(u,v)_{B}$, with $B$ a domain immersed in a fixed background mesh $\Omega$ and $u,v$ finite element functions on $V_h(\Omega)$, as usually happens using Nitsche's method to weakly impose boundary conditions at an interface. The same applies to coupling terms of the form $(u,q)_B$ in formulations using Lagrange multipliers, where now $q \in Q_h(B)$, with $Q_h(B)$ the space of the multiplier variable. +Notice that the most relevant difference with the quadrature rules provided by cutFEM support in \texttt{QuadratureGenerator} is that \texttt{Quadrature} objects are not created using a level-set approach, as described in the previous section, but directly with the two overlapped grids. + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -1080,8 +1080,6 @@ Their contributions are much appreciated! \dealii{} and its developers are financially supported through a variety of funding sources: -\todo[inline]{Update. In particular make sure that we list how Marco - Feder is supported.} D.~Arndt and B.~Turcksin: Research sponsored by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory, managed by UT-Battelle,