A user-focused summary of information around simplex and mixed mesh
support is also available on the new module page at
- \url{https://www.dealii.org/current/doxygen/deal.II/group__simplex.html}
+ \url{https://www.dealii.org/current/doxygen/deal.II/group__simplex.html}.
In particular, it shows how to solve a simple Poisson problem like in
the \texttt{step-3} tutorial program
on simplex and mixed meshes, with a focus on the necessary changes to
\coordinate (12) at (0.5, 0.0, 1.5);
\coordinate (13) at (0.0, 0.5, 1.5);
\coordinate (14) at (0.5, 0.5, 1.5);
+
+ \coordinate (15) at (0,0,0.75);
+ \coordinate (16) at (1,0,0.75);
+ \coordinate (17) at (0.0,1.0,0.75);
\foreach \i in {0,1,2,3,4,5}
\draw[blue,fill=blue] (\i) circle (1.5pt) node [below] {};
- \foreach \i in {6,7,8,9,10,11,12,13,14}
+ \foreach \i in {6,7,8,9,10,11,12,13,14,15,16,17}
\draw (\i) node[cross, draw=red, rotate=-20] {};
(tetrahedron, pyramid, wedge, hexahedron) with the support points
indicated both for linear ({\color{blue}$\bullet$}) and quadratic
({\color{red}$\times$}) shape functions.
- \todo[inline]{The pyramid is missing red crosses. The wedge is
- missing them on three edges.}}
+ %\todo[inline]{The pyramid is missing red crosses. The wedge is
+ % missing them on three edges.}
+ % PM: we only have linear pyramids for now.
+ }
\label{fig:simplex}
\end{figure}
FEValues<dim, spacedim> fe_values(mapping, fe, quad, flags);
\end{c++}
The list of currently supported finite-element classes is provided in Table~\ref{tab:simplex:fe}. Currently,
-only linear iso-parametric mappings (via the \texttt{MappingFE} and
-\texttt{MappingFEField} classes) are available.
-\todo[inline]{I don't understand the previous sentence. "linear" means
- p=1, but isoparametric means that it has the same p as the finite
- element. It can't be both.}
-For quadrature, the classes \texttt{QDuffy}, \texttt{QGaussSimplex}, \texttt{QWitherdenVincentSimplex},
+only linear and quadratic mappings via the \texttt{MappingFE} and
+\texttt{MappingFEField} classes built around the listed nodal elements are available.
+%\todo[inline]{I don't understand the previous sentence. "linear" means
+% p=1, but isoparametric means that it has the same p as the finite
+% element. It can't be both.}
+For quadrature, the classes \texttt{QDuffy}, \texttt{QGaussSimplex}, \texttt{QWitherdenVincentSimplex} \cite{schloemer21, witherden2015identification},
\texttt{QGaussPyamid}, and \texttt{QGaussWedge} are
available.
for(const auto & cell : tria.active_cell_iterators())
{
hp_fe_values.reinit(cell);
- local_rhs.resize(cell->get_fe().dofs_per_cell);
+ local_rhs.resize(cell->get_fe().n_dofs_per_cell());
}
\end{c++}
elements. Global coarsening builds multigrid levels for the entire
domain, coarsening \textit{all} cells of a triangulation regardless of
how many times they have been refined. In addition, the framework now available in
-\dealii{} in not only applicable to geometric coarsening, but can also
+\dealii{} is not only applicable to geometric coarsening, but can also
perform coarsening by reducing the polynomial degree ($p$-multigrid,
see~\cite{Fehn2020}), for example
to support $hp$-adaptive meshes.
These classes select at runtime -- for common low and medium
polynomial degree/quadrature combinations ($k\le 6$ and $q\in\{ k+1,
k+2, \left\lfloor (3k)/2 \right\rfloor \}$) -- efficient precompiled implementations and default to non-templated
-evaluation kernels else.
+evaluation kernels else (see also \texttt{FEEvaluation::fast\_evaluation\_\allowbreak supported()}).
In the case that even higher polynomial degrees are needed, one can precompile the
relevant internal classes
DEAL_II_NAMESPACE_OPEN
template struct dealii::internal::FEEvaluationFactory
<dim, VectorizedArrayType::value_type, VectorizedArrayType>;
+// same for FEFaceEvaluationFactory and CellwiseInverseMassFactory (skipped)
DEAL_II_NAMESPACE_CLOSE
\end{c++}
Until now, the \texttt{FEEvaluation} classes used the template
parameters $k$ and $q$ to select the correct active FE and quadrature
-index and cumbersome detection of subranges of the same degree.
-\todo{I don't understand what ``detection of subranges of the same
- degree'' refers to. Please clarify. In particular, I don't know what
-``subranges'' mean in this paragraph.}
+index and users were responsible for the cumbersome detection of
+subranges of the same $k$ and $q$ within the cell ranges returned by the
+matrix-free loops.
+%\todo{I don't understand what ``detection of subranges of the same
+% degree'' refers to. Please clarify. In particular, I don't know what
+%``subranges'' mean in this paragraph.}
The creation of subranges is now performed internally, and the non-templated versions
of the \texttt{FEEvaluation} classes have been extended for the $hp$-case. To determine
the desired FE and quadrature index of a subrange, the current cell/face range has to be provided
for example, come from
a mesh of lower dimension. Determining to which \texttt{cell} a quadrature
point belongs to on the background mesh, including the reference cell
-coordinates \texttt{reference\_points}, is aided by functions like
-\texttt{GridTools::find\_all\_active\_cells\_around\_point()}. While these
+coordinates \texttt{reference\_\allowbreak points}, is aided by functions like
+\texttt{find\_active\_cell\_around\_point()}
+\texttt{find\_all\_active\_cells\_\allowbreak around\_\allowbreak point()} from the \texttt{GridTools} namespace. While these
functions have been available in \dealii{} previously, their performance has
been considerably enhanced with the aforementioned more optimized code paths
for selected mappings.
context and for providing efficient communication patterns for the data exchange. In \texttt{deal.II},
the class has been successfully applied together with \texttt{FEPointEvaluation} to evaluate a distributed
solution vector at arbitrary points (see also the
-\texttt{VectorTools::evaluate\_at\_points()} function).
+\texttt{VectorTools::point\_values()} function).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\cite{Bartlett2006a}, ADOL-C \cite{Griewank1996a}, and
SymEngine \cite{symengine-web-page}. The tutorial
illustrates how these techniques can be used to compute derivatives
- of first a rather simple function, and then of the much more complex
+ first of a rather simple function, and then of the much more complex
energy functions of two magnetoelastic and magneto-viscoelastic
material formulations in which just the scalar energy functional
takes up the better part of a page, and even first derivatives can
projects / release-papers.git / commitdiff