\subsection{Advances in the particle infrastructure}
\label{subsec:particles}
-TODO
+\todo[inline]{TODO}
+
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Advances in the multigrid infrastructure}
\label{subsec:mg}
-Until now, \dealii has only supported local smoothing multigrid
-algorithms~\citep{ClevengerHeisterKanschatKronbichler2019}; in local
-smoothing algorithms, smoothers only act on the cells of a given refinement level,
-skipping those parts of the mesh that are not adaptively refined to that level.
-The current release now also has support for global coarsening~\citep{becker2000multigrid, sundar2012parallel} when
+Until now, \dealii has only supported ``local smoothing'' multigrid
+algorithms~\citep{ClevengerHeisterKanschatKronbichler2019} wherein
+smoothers only act on the cells of a given refinement level,
+skipping those parts of the mesh that have not been adaptively refined
+to that level. This approach guarantees that the work done summed up
+over all levels is proportional to the number of unknowns, and is
+consequently necessary so that the overall multigrid preconditioner
+can have a complexity of ${\cal O}(N)$.
+
+In contrast, the current release now also supports ``global
+coarsening'' algorithms \citep{becker2000multigrid, sundar2012parallel} when
using continuous (\texttt{FE\_Q}, \texttt{FE\_SimplexP}) and
discontinuous (\texttt{FE\_DGQ}, \texttt{FE\_SimplexDGP})
elements. Global coarsening builds multigrid levels for the entire
work per iteration overall.
The transfer operators between two levels have been implemented in the new class \texttt{MGTwoLevel\allowbreak Transfer}, which can be set up via the functions \texttt{MGTwoLevel\allowbreak Transfer::\allowbreak reinit\_\allowbreak geometric\_\allowbreak transfer()} or \texttt{MGTwo\allowbreak LevelTransfer::\allowbreak reinit\_\allowbreak polynomial\_\allowbreak transfer()} for given
-\texttt{DoFHandler} and \texttt{AffineConstraint} classes of two levels. The resulting transfer operators
+\texttt{DoFHandler} and \texttt{AffineConstraint} objects
+corresponding to the two levels. The resulting transfer operators
can then be collected in a single
\texttt{MGTransfer\allowbreak GlobalCoarsening} object that can be used just as the previous workhorse \texttt{MGTransferMatrixFree} within the \texttt{Multigrid}
algorithm.
\subsection{Advances in the matrix-free infrastructure}
\label{subsec:mf}
+\dealii{}'s matrix-free framework enables high-throughput operations
+for applications in which only the availability of the \textit{action}
+of a matrix, but not the entries of the matrix, are necessary. This
+framework has been substantially extended in the current release.
+
+
\subsubsection{Precompilation of evaluation kernels}
-The classes \texttt{FEEvaluation} and \texttt{FEFaceEvaluation} use template parameters for
+The \texttt{FEEvaluation} and \texttt{FEFaceEvaluation} classes use template parameters for
the polynomial degree of the finite element $k$ and the number of the 1D quadrature points $q$
to generate near-optimal code for these operations.
For application codes that rely on operators of many different degrees (e.g., because
In the current release, specializations of these classes that do
not rely on the template parameters $k$ and $q$ (expressed in the code
-with ``-1'' and ``0'') have been added. For example:
+using special values ``-1'' and ``0'') have been added. For example:
\begin{c++}
FEEvaluation<dim, -1, 0, n_components, Number, VectorizedArrayType>
phi(range, dofhandler_index, quadrature_index, first_selected_component);
\subsubsection{Parallel matrix-free $hp$-implementation}\label{subsubsection:mf:hp}
-With release 9.1 \cite{dealII91}, large parts of the $hp$-algorithms in \dealii were parallelized, enabling
-parallel matrix-based simulations with the $hp$-infrastructure. In the present
+With release 9.1, large parts of the $hp$-algorithms
+in \dealii were ported to a model that allows for
+parallel matrix-based simulations \cite{dealII91}. In the present
release, the parallel $hp$ support was extended to \texttt{MatrixFree}.
-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.
+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.}
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
\subsection{MPI-3.0 shared-memory support}\label{subsec:sm}
-In many large computations, certain pieces of data are computed once
-and then treated as read-only. If this information is needed by more
+In many large computations, certain pieces of data are computed
+(or read from disk) once and then treated as read-only. If this information is needed by more
than one MPI process, it is more efficient to store this information only
once in shared memory among all processes located on a multicore
node. MPI supports the creation of such shared memory windows since
version 3.0, and deal.II can now use this in the
\texttt{AlignedVector} and \texttt{Table} classes that are often used
-for large lookup tables.
+for large lookup tables for classes such as \texttt{InterpolatedTensorProductGridData}.
-The feature is also used in the \texttt{MatrixFree} and
+Shared memory storage is also used in the \texttt{MatrixFree} and
\texttt{LinearAlgebra::\allowbreak distributed::\allowbreak Vector} classes. If \texttt{MatrixFree} has been configured by setting
-\texttt{MatrixFree::AdditionalData::communicator\_sm} appropriately, then
+\texttt{MatrixFree::\allowbreak AdditionalData::\allowbreak communicator\_sm} appropriately, then
\texttt{MatrixFree::create\_dof\_vector()} creates vectors that share
information among all processes on one node. As a consequence, the
\texttt{FEEvaluation} classes can access vector elements owned by
\subsection{Evaluation and integration at arbitrary points}
\label{subsec:fepointvalues}
-In a number of circumstances, finite element solutions need to be evaluated on
+In a number of circumstances, finite element solutions need to be evaluated at
arbitrary reference points that change from one element to next. Two important
examples are particle simulations coupled to a finite element solution, or
algorithms on non-matching grids. The existing \texttt{FEValues} class is a poor
-fit for this task, as it relies on tabulating all information before its usage,
-necessitating a separate setup for every cell. The new class
-\texttt{FEPointEvaluation} provides a more convenient interface for this
-task. For tensor product finite elements (\texttt{FE\_Q}, \texttt{FE\_DGQ})
+fit for this task, as it is based on the assumption that evaluation of
+shape functions and their derivatives happens at the same quadrature
+points on every cell, and that consequently expensive computations can
+be done once and results re-used for many subsequent cells. The new class
+\texttt{FEPointEvaluation} provides a more convenient interface for
+cases where the evaluation on different cells does not happen at the
+same points mapped from the reference cell.
+For tensor product finite elements (\texttt{FE\_Q}, \texttt{FE\_DGQ})
and tensor product mappings (\texttt{MappingQGeneric} and derived classes),
the new approach is also very fast, as it can use some of the matrix-free
infrastructure and vectorization facilities.
To give an example of the new features, let us consider the evaluation of a
surface tension force in the context of sharp-interface methods, whose
contribution is added to a fluid solver by multiplication with test function
-and addition over quadrature points:
+and addition over quadrature points located at the interface section
+$\Gamma_K=\Gamma \cup K$ located on the current cell $K$ and that is,
+in general, located differently within $K$ than for any other cell:
\begin{align*}
-\left(\vec{v}, \kappa \, \vec{n}\right)_\Gamma
+\left(\mathbf{v}, \kappa \, \mathbf{n}\right)_\Gamma
\approx
-\sum_q\left(\vec{v}, \kappa(\vec{p}_q) \, \vec{n}(\vec{p}_q) (JxW)_q\right).
+\sum_q \mathbf{v}(\mathbf{x}_q) \cdot \left(\kappa(\mathbf{x}_q) \, \mathbf{n}(\mathbf{x}_q)\right) (JxW)_q.
\end{align*}
In \dealii{}, this can now be conveniently written as
\begin{c++}
phi_normal.get_value(q) * JxW[q], q);
phi_force.integrate(force_values, EvaluationFlags::values);
\end{c++}
-The quadrature points (at reference positions - \texttt{reference\_points}) and the related \texttt{JxW} value can, e.g., come from
-a mesh of codimension one. Determining to which \texttt{cell} a quadrature
-point belongs to on the background mesh, including the reference-cell
-coordinates \texttt{reference\_points}, can be determined with functions like
+The quadrature points (at reference positions
+\texttt{reference\_points}) and the related \texttt{JxW} value can,
+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
functions have been available in \dealii{} previously, their performance has
been considerably enhanced with the aforementioned more optimized code paths
for selected mappings.
While \texttt{FEPointEvaluation} assumes that evaluation points are already sorted according to
-the owning cells and such can concentrate on cell-local operations, the new class
-\texttt{RemovePointEvaluation} is responsible to determine the owning cells in a distributed
+the owning cells and thus can focus on cell-local operations, the new class
+\texttt{RemotePointEvaluation} is responsible for determine the owning cells in a distributed
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 \texttt{VectorTools::evaluate\_at\_points()}).
+solution vector at arbitrary points (see also the
+\texttt{VectorTools::evaluate\_at\_points()} function).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\label{subsec:steps}
Many of the \dealii{} tutorial programs were revised in a variety of
-ways as part of this release. TODO
-
-In addition, there are a number of new tutorial programs:
+ways as part of this release. In addition, there are a number of new tutorial programs:
\begin{itemize}
\item \texttt{step-19} is an introductory demonstration of \dealii{}'s
particle functionality. It solves the coupled problem of
charged particles and an electric field, using a cathode tube as an
example.
-\item \texttt{step-68} TODO
-
+\item \texttt{step-68} \todo[inline]{TODO}
+
\item \texttt{step-71} focuses on automatic and symbolic
differentiation (AD and SD, in short) as a tool to make solvers for complex,
nonlinear problems possible. To this end, \dealii{} can interface to a number
compressible Euler equations discretized with a high-order discontinuous
Galerkin (DG) scheme, using the matrix-free infrastructure just as \texttt{step-67} does.
The tutorial presents advanced topics, like the usage of cell-centric loops and
- the new MPI-3.0 shared-memory capabilities of \texttt{MatrixFree} tor each high
+ the new MPI-3.0 shared-memory capabilities of \texttt{MatrixFree} to reach high
throughput. Furthermore, the utilization of the template parameter
- \texttt{VectorizedArrayType} and the application of lambdas to capture cell and face
+ \texttt{VectorizedArrayType} and the application of lambda functions to describe cell and face
integrals are discussed.
-\item \texttt{step-77} is a program that illustrate \texttt{dealii}'s
+\item \texttt{step-77} is a program that illustrate \dealii{}'s
interfaces to the SUNDIALS library \cite{sundials}, and specifically
the KINSOL nonlinear solver. Like the \texttt{step-72} program
mentioned above, it is a variation of the minimal surface solver
wheel but instead building on an existing and well-tuned software
such as KINSOL.
- \dealii{}'s interfaces were also updated to the latest SUNDIALS release, 5.7.
+ \dealii{}'s interfaces to the various SUNDIALS sub-packages were also updated to the latest SUNDIALS release, 5.7.
-\item \texttt{step-78} TODO
+\item \texttt{step-78} \todo[inline]{TODO}
-\item \texttt{step-79} TODO
+\item \texttt{step-79} \todo[inline]{TODO}
\end{itemize}
There is also a new program in the code gallery (a collection of
than tutorial programs, and intended as starting points for further
research rather than as teaching tools):
\begin{itemize}
- \item preCICE: TODO
+ \item preCICE: \todo[inline]{TODO}
\end{itemize}
and classes like \texttt{DataOut} or \texttt{SolutionTransfer} for example
no longer require them. If you rely on these template arguments, an interim
namespace \texttt{Legacy} has been introduced that provides all affected
- classes with the old interface for the transition phase.
+ classes with the old interface for a transition period.
\end{itemize}
+\todo[inline]{Check whether there are other things worth listing.}
+
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
In order to justify the work the developers of \dealii{} put into this
software, we ask that papers using the library reference one of the
-\dealii{} papers. This helps us justify the effort we put into it.
+\dealii{} papers. This helps us justify the effort we put into this library.
There are various ways to reference \dealii{}. To acknowledge the use of
the current version of the library, \textbf{please reference the present
\end{center}
The original \dealii{} paper containing an overview of its
-architecture is \cite{BangerthHartmannKanschat2007}. If you rely on
+architecture is \cite{BangerthHartmannKanschat2007}, and a more recent
+publication documenting \dealii{}'s design decisions is available as \cite{dealII2020design}. If you rely on
specific features of the library, please consider citing any of the
following:
\begin{multicols}{2}
\item For geometric multigrid: \cite{Kanschat2004,JanssenKanschat2011,ClevengerHeisterKanschatKronbichler2019};
\item For distributed parallel computing: \cite{BangerthBursteddeHeisterKronbichler11};
\item For $hp$-adaptivity: \cite{BangerthKayserHerold2007};
- \item For partition-of-unity (PUM) and enrichment methods of the
- finite element space: \cite{Davydov2016};
+ \item For partition-of-unity (PUM) and finite element enrichment methods:
+ \cite{Davydov2016};
\item For matrix-free and fast assembly techniques:
\cite{KronbichlerKormann2012,KronbichlerKormann2019};
\item For computations on lower-dimensional manifolds:
\cite{DeSimoneHeltaiManigrasso2009};
\item For curved geometry representations and manifolds:
\cite{HeltaiBangerthKronbichlerMola2019};
- \vfill\null \columnbreak
\item For integration with CAD files and tools:
\cite{HeltaiMola2015};
\item For boundary element computations:
\cite{GiulianiMolaHeltai-2018-a};
- \item For \texttt{LinearOperator} and \texttt{PackagedOperation} facilities:
+ \item For the \texttt{LinearOperator} and
+ \texttt{Packaged\-Operation} facilities:
\cite{MaierBardelloniHeltai-2016-a,MaierBardelloniHeltai-2016-b};
\item For uses of the \texttt{WorkStream} interface:
\cite{TKB16};
% we should make sure he's listed.
%
% 9.3: updated 5/08/2021 PM
-Alexander Grayver,
-Andrew Davis,
+% sorted by WB 5/28
+Pasquale Africa,
+Tyler Anderson,
+Mathias Anselmann,
Arpit Babbar,
+Maximilian Bergbauer,
+Nicolas Barnafi,
Bruno Blais,
-Bruno Turcksin,
-Ce Qin,
-Christoph Kammer,
+Michele Bucelli,
+Marcus Calhoun-Lopez,
+Praveen Chandrashekar,
Conrad Clevenger,
-Dominic Soldner,
-Daniel Arndt,
-Daniel Garcia-Sanchez,
-Daniel Paukner,
David F. Castellanos,
-David Wells,
-Doug Shi-Dong,
-David Schneider,
+Andrew Davis,
Elias Dejene,
-Graham Harper,
-Ignacio Tomas,
-Ivan Fumagalli,
-Jake Harmon,
-Jean-Paul Pelteret,
-Jiaqi Zhang,
-Julian Roth,
-Katharina Kormann,
-Konrad Simon,
-Krishnakumar Gopalakrishnan,
-Laura Prieto Saavedra,
-Lei Qiao,
-Luca Heltai,
-Magdalena Schreter,
-Malhar Tidke,
-Marc Fehling,
-Marcus Calhoun-Lopez,
-Martin Kronbichler ,
-Mathias Anselmann,
-Matthias Maier,
-Maximilian Bergbauer,
+Niklas Fehn,
Menno Fraters,
-Michele Bucelli,
+Ivan Fumagalli,
+Daniel Garcia-Sanchez,
+Rene Gassmoeller,
Nicola Giuliani,
-Nicolas Barnafi,
-Niklas Fehn,
-Nils Much,
+Krishnakumar Gopalakrishnan,
+Alexander Grayver,
Olivier Guevremont,
-Pasquale Africa,
-Peter Munch,
-Peter Westerbaan,
+Jake Harmon,
+Graham Harper,
+Uwe K\"ocher,
+Katharina Kormann,
+Christoph Kammer,
+Wenyu Lei,
+Zhou Lei,
Phillip Mobley,
+Nils Much,
Pratik Nayak,
-Praveen Chandrashekar,
-Rene Gassmoeller,
+Toni El Geitani Nehme,
+Justin O'Connor,
+Daniel Paukner,
+Sebastian Proell,
+Lei Qiao,
+Ce Qin,
Reza Rastak,
+Julian Roth,
+Laura Prieto Saavedra,
+Doug Shi-Dong,
+David Schneider,
+Magdalena Schreter,
Richard Schussnig,
-Sebastian Proell,
+Konrad Simon,
+Dominic Soldner,
Simon Sticko,
-Timo Heister,
-Toni El Geitani Nehme,
-Wenyu Lei,
-Wolfgang Bangerth,
-Zhou Lei
+Malhar Tidke,
+Ignacio Tomas,
+Peter Westerbaan,
+Jiaqi Zhang.
+\todo[inline]{Remove everyone who may end up being a co-author.}
Their contributions are much appreciated!
Development Program of Oak Ridge National Laboratory, managed by UT-Battelle,
LLC, for the U. S. Department of Energy.
-W.~Bangerth, T.~C.~Clevenger, and T.~Heister were partially
+W.~Bangerth and T.~Heister were partially
supported by the Computational Infrastructure
in Geodynamics initiative (CIG), through the National Science
Foundation under Award No.~EAR-1550901 and The
program, DMS-1821210,
and EAR-1925595.
-%D.~Davydov was supported by the German Research Foundation (DFG), grant DA
-%1664/2-1 and the Bayerisches Kompetenznetzwerk
-%f\"ur Technisch-Wissenschaftliches Hoch- und H\"ochstleistungsrechnen
-%(KONWIHR).
-
-B.~Blais was partially supported by the National Science and Engineering Research Council of Canada(NSERC) through the RGPIN-2020-04510 Discovery Grant
-
-T.~C.~Clevenger was also partially supported EAR-1925575 and OAC-2015848.
-
-A.~V.~Grayver was partially supported by the European Space Agency
-Swarm DISC program.
-
Timo Heister was also partially supported by the National Science Foundation (NSF)
Award DMS-2028346, OAC-2015848, EAR-1925575, and by
Technical Data Analysis, Inc. through US Navy STTR Contract N68335-18-C-0011.
D.~Wells was supported by the National Science Foundation (NSF) through Grant
DMS-1344962.
-Z.~Wang was partially
-supported by the National Science Foundation under award OAC-1835673.
-
The Interdisciplinary Center for Scientific Computing (IWR) at Heidelberg
University has provided hosting services for the \dealii{} web page.
-
-The authors acknowledge the Texas Advanced Computing Center (TACC) at The
-University of Texas at Austin for providing access to HPC resources that have
-contributed to the research results reported within this paper.
-
-Clemson University is acknowledged for generous allotment of compute time on
-the Palmetto cluster.
-
+\todo[inline]{Everyone update. Add support for any additional authors.}
\bibliography{paper}{}
\bibliographystyle{abbrv}
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