From 9127bb5e3515b2cd8055149dc5d118d26510d291 Mon Sep 17 00:00:00 2001 From: Martin Kronbichler Date: Sun, 26 Jun 2022 21:57:53 +0200 Subject: [PATCH] Small improvements to text --- 9.4/paper.bib | 2 +- 9.4/paper.tex | 19 ++++++++++--------- 2 files changed, 11 insertions(+), 10 deletions(-) diff --git a/9.4/paper.bib b/9.4/paper.bib index 1e3e96b..7d60ca7 100644 --- a/9.4/paper.bib +++ b/9.4/paper.bib @@ -1312,7 +1312,7 @@ doi = {10.1504/IJCSE.2009.029164} } @misc{munch2022gc, - title={Efficient distributed matrix-free multigrid methods on locally refined meshes for FEM computations}, + title={Efficient distributed matrix-free multigrid methods on locally refined meshes for {FEM} computations}, author= {Munch, Peter and Heister, Timo and Prieto Saavedra, Laura and Kronbichler, Martin}, year= {2022}, url = {https://arxiv.org/abs/2203.12292} diff --git a/9.4/paper.tex b/9.4/paper.tex index f9ef67e..59b2d91 100644 --- a/9.4/paper.tex +++ b/9.4/paper.tex @@ -254,7 +254,7 @@ which we briefly outline in the remainder of this section: \texttt{FEInterfaceValues::jump\_gradient()} is now \texttt{FEInterfaceValues::jump\_in\_shape\_gradients()}. Several new functions, such as \texttt{FEInterfaceValues::get\_jump\_in\_function\_values()}, have also been added. \item The\texttt{MeshWorker::ScratchData} and \texttt{MeshWorker::CopyData} have been made $hp$-compatible, - and supports face integration where the integration rule and mapping differs on either side of an interface. + and support face integration where the integration rule and mapping differs on either side of an interface. The \texttt{MeshWorker::CopyData} class has also been made compatible with complex numbers. \item Vectors attached to \texttt{DataOut} do not need to be in ghosted state anymore. Internally, we create a copy of the vector with appropriate ghosting. \end{itemize} @@ -562,13 +562,14 @@ of cells on unstructured meshes. \item Users can now create their own cell batches, by providing \texttt{FEEvaluation::reinit()} a list of cell IDs. \texttt{FEEvaluation} accesses the appropriate data and reshuffles mapping data accordingly on the fly in order to enable vectorization over cells. The new feature is useful in several -contexts. Examples are simulations with sharp interfaces (e.g., two-phase flow +contexts, for example for sharp interfaces (e.g., two-phase flow or shock capturing), where one needs to treat cells that are ``cut'' by the interface in a special way. A challenge is that cell batches -might contain cut or non-cut cells, making the vectorization of these operations potentially more complicated. Previous functionality has provided the option of masking certain cells in cell batches, which works well if -the code paths do not diverge too much. Another way is to +might contain cut or non-cut cells, effectively counteracting the cross-cell vectorization. +Previous functionality has provided the option of masking certain cells in cell batches, which works well if +the code paths do not diverge too much, or to categorize cells during \texttt{MatrixFree::reinit()} in such a way that mixed cell batches do not occur. However, \texttt{MatrixFree::reinit()} -might be too expensive if recategorization needs to happen very frequently to follow the dynamics of a system, e.g., in each time step. Despite some overhead compared to static matrix-free loops, the new feature can be the best option in these scenarios. +might be too expensive if recategorization needs to happen very frequently to follow the dynamics of a system, e.g., in each time step. Despite some overhead compared to static matrix-free loops, the new feature can be the best option in such dynamic scenarios. \item Initial support for H(div)-conforming elements with Piola transform, based on Raviart--Thomas finite element spaces with the updated class \texttt{FE\_RaviartThomasNodal}, has been added. This feature is currently limited to meshes in standard orientation and affine geometries. Full support and performance optimizations will be provided in a future release. \item Selected matrix-free algorithms can now exploit additional data locality between the matrix-vector product and vector operations happening nearby in @@ -841,10 +842,10 @@ the \texttt{NonMatching} namespace in future releases. While our current CutFEM implementation (see Section~\ref{sec:cut}) relies on a level set description of the domain to determine the boundary and the quadrature rules, one could do that also based on non-matching overlapping grids~\cite{massing2013efficient}, for which the newly introduced, CGAL-based Boolean operations and -quadrature-generation functionality might be helpful. We would like to point out -that the functionalities are not limited to CutFEM but are also applicable +quadrature-generation functionality might be helpful. +The functionalities are applicable in a broad context of immersed problems, such as for weakly imposing boundary conditions on the interface of an immersed boundary -using Nitsche's method and coupling terms using Lagrange multipliers. +using Nitsche's method and for coupling terms using Lagrange multipliers. %These utility functions will be the building blocks for functions in the \texttt{NonMatching} namespace that will, e.g., assemble coupling terms like $(u,v)_{\Omega}$, with $\Omega$ a domain immersed in a fixed background mesh $B$ and $u,v$ finite element functions on $V_h(B)$, as needed, e.g., in %the context of CutFEM (see Section~\ref{sec:cut}) or Nitsche's method to weakly impose boundary conditions at an interface. The same applies to coupling terms of the form $(u,q)_{\Omega}$ in formulations using Lagrange multipliers, where now $q \in Q_h(\Omega)$, with $Q_h(\Omega)$ the space of the multiplier variable. @@ -998,7 +999,7 @@ future, using the interfaces now already in place. By the time of writing, \dealii uses consensus-based algorithms to determine the owners of distributed index sets (\texttt{Utilities::MPI::Partitioner}, \texttt{Utilities::MPI::Noncontiguous\allowbreak Partitioner}, \texttt{internal::MatrixFreeFunctions::VectorDataExchange}; see~\cite{dealII91}), -to setup the global-coarsening transfer operators (see~\cite{dealII92} and +to set up the global-coarsening transfer operators (see~\cite{dealII92} and Section~\ref{sec:multigrid}), to repartition distributed meshes (see Section~\ref{sec:repartitioning}), and basis coupling algorithms between non-matching meshes, based on the communication patters in \texttt{RemotePointeEvaluation} (see~\cite{dealII92}). -- 2.39.5