From 7eefa8e41f034468412ce66ab8c79f5faeb51752 Mon Sep 17 00:00:00 2001 From: Wolfgang Bangerth Date: Tue, 24 Sep 2024 09:02:16 -0600 Subject: [PATCH] Minor edits. --- 9.6/paper.tex | 44 +++++++++++++++++++++----------------------- 1 file changed, 21 insertions(+), 23 deletions(-) diff --git a/9.6/paper.tex b/9.6/paper.tex index 573703f..88f17c2 100644 --- a/9.6/paper.tex +++ b/9.6/paper.tex @@ -296,17 +296,16 @@ which we briefly outline in the remainder of this section: \item The \texttt{FE\_NedelecSZ} class that contains our implementation of the N\'ed\'elec element using the orientation scheme of \cite{Zag06} now supports the computation of hanging - node constraints for locally refined \todo[inline]{hexahedral?} meshes. - Therefore, the sign-conflict that arises for hp quadrilateral and - hexahedral N\'ed\'elec elements in the presence of hanging edges - and hanging faces was addressed for the implementation details; - we refer to \cite{Kinnewig2024}. - The \texttt{FE\_NedelecSZ} class and the hanging node constraints - automatically account for the presence of hanging edges and hanging - faces; therefore, there is no difference for the user when using - \texttt{FE\_NedelecSZ} as finite elements compared to other finite - element classes when used on triangulations with hanging nodes. - Note that the special case where, in 3D, more than four cells with + node constraints for locally refined, hexahedral meshes. + That is, the implementation of hanging node constraints now + correctly addresses the sign-conflict that arises for $hp$ quadrilateral and + hexahedral N\'ed\'elec elements; + see \cite{Kinnewig2024} for details. + The other implementation of N\'ed\'elec elements, in the \texttt{FE\_NedelecSZ} class, already + implements hanging node constraints; therefore, there is no longer + a difference for the user between the two classes as far as + constraints are concerned. + However, the special case where, in 3D, more than four cells with different refinement levels share a common edge is not covered yet. \item The \texttt{AffineConstraints} class stores and processes constraints on degrees of freedom in \dealii{}. Such constraints @@ -413,8 +412,8 @@ infrastructure in \dealii. These changes include: evaluators as well as the evaluators for simplex elements. This speeds up the operator evaluation in several scenarios, especially for simplices (around two times higher throughput for operator evaluation) and - multi-component systems. The restructuring made to enable these optimizations - also reduces the compile times and the size of the generated code slightly. + multi-component systems. The restructuring that led to these optimizations + also reduced the compile times and the size of the generated code slightly. \item In addition, we performed substantial improvements to the global-coarsening multigrid infrastructure: \texttt{MGTransferMF} (previously: @@ -429,9 +428,6 @@ infrastructure in \dealii. These changes include: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Advances in non-matching support}\label{sec:nonmatching} -%\todo[inline]{All: If you contributed to this functionality, please -% help flesh out this section.} - In the non-matching infrastructure of \dealii, we made the following improvements: \begin{itemize} @@ -453,19 +449,21 @@ Tutorial \step{89} has been added to present its usage in the context of the application to acoustic conservation equations~\cite{heinz2023high}. \item The \texttt{FECouplingValues} class provides a powerful tool for - integrating finite element data between two different objects, even if they + computing + integrals of functions that contain finite element fields defined on + different objects, for example if these fields live on separate grids or have different topological dimensions (e.g., cells, faces, edges). This is particularly useful in the following scenarios: \begin{itemize} - \item Non-local Differential Operators: Evaluating fractional laplacian or + \item Non-local differential operators: Evaluating fractional Laplacian or boundary element methods. - \item Non-matching Discretizations: Integrating data between two independent - discretization schemes that overlap on some areas. - \item Bulk-surface Coupling: Combining data from a bulk discretization and - surface discretization. + \item Non-matching discretizations: Integrating data between two independent + discretization schemes that overlap in some areas. + \item Bulk-surface coupling: Combining data from a bulk discretization and + a surface discretization. \end{itemize} -This class enables the combination of degrees of freedom indices, shape +The new class enables the combination of degrees of freedom indices, shape functions, and quadrature points from two existing \texttt{FEValuesBase} objects. The way this combination is performed is controlled by user-provided \texttt{DoFCouplingType} and \texttt{QuadratureCouplingType} objects, which -- 2.39.5