From: Wolfgang Bangerth Date: Thu, 28 May 2020 19:34:37 +0000 (-0600) Subject: Edit whatever text we have. X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=3cbaab24e4dd752c5c96a7385ba4d0ec33bab43b;p=release-papers.git Edit whatever text we have. --- diff --git a/9.2/paper.bib b/9.2/paper.bib index c0cc5cc..1ba7cdf 100644 --- a/9.2/paper.bib +++ b/9.2/paper.bib @@ -1029,3 +1029,16 @@ doi = {10.1016/0096-3003(82)90191-6} journal = {Geochemistry, Geophysics, Geosystems} } +@article{Brenner2005, + doi = {10.1007/s10915-004-4135-7}, + url = {https://doi.org/10.1007/s10915-004-4135-7}, + year = {2005}, + month = jun, + publisher = {Springer Science and Business Media {LLC}}, + volume = {22-23}, + number = {1-3}, + pages = {83--118}, + author = {Susanne C. Brenner and Li-Yeng Sung}, + title = {$C^0$ Interior Penalty Methods for Fourth Order Elliptic Boundary Value Problems on Polygonal Domains}, + journal = {Journal of Scientific Computing} +} diff --git a/9.2/paper.tex b/9.2/paper.tex index 332560f..91e1e68 100644 --- a/9.2/paper.tex +++ b/9.2/paper.tex @@ -606,7 +606,7 @@ BatchOptimizer for symbolic expressions %\item VectorizedArrayType %\end{itemize} -The class \texttt{VectorizedArray} is a key ingredient for the high +The class \texttt{VectorizedArray} is a key component to achieve the high node-level performance of the matrix-free algorithms in deal.II~\cite{KronbichlerKormann2012, KronbichlerKormann2019}. It is a wrapper class around a short vector of $n$ entries of type \texttt{Number} and maps arithmetic operations to appropriate single-instruction/multiple-data (SIMD) @@ -614,29 +614,26 @@ concepts by intrinsic functions. The class \texttt{VectorizedArray} has been made more user-friendly in this release by making it compatible with the STL algorithms found in the header \texttt{}. The length of the vector can now be queried by \texttt{VectorizedArray::size()} and its underlying number type by \texttt{VectorizedArray::value\_type}. -Furthermore, the \texttt{VectorizedArray} class now supports range-based iterations over its entries. +Furthermore, the \texttt{VectorizedArray} class now supports range-based iteration over its entries. -Up to release 9.1, the -vector length $n$ has been set at compile time of the library to the highest -possible value supported by the given processor architecture. +In previous \dealii{} releases, the +vector length was set at compile time of the library to match the highest +value supported by the given processor architecture. Now, a second optional template argument -\texttt{VectorizedArray} can be given with \texttt{size} explicitly controlling +can be specified as \texttt{VectorizedArray}, where \texttt{size} explicitly controls the vector length within the capabilities of a particular instruction set. -A full list of supported -vector lengths is presented in Table~\ref{tab:vectorizedarray}. - -To account for the variable-size \texttt{VectorizedArray} class, all matrix-free related classes (like \texttt{MatrixFree} and \texttt{FEEvaluation}) -have been extended with a new optional template argument specifying the -\texttt{VectorizedArrayType}. This allows users to select the vector length/ISA and, -as a consequence, the number of cells to be processed at once directly in their applications: -The deal.II-based +(A full list of supported +vector lengths is presented in Table~\ref{tab:vectorizedarray}.) +This allows users to select the vector length/ISA and, +as a consequence, the number of cells to be processed at once in matrix-free +operator evaluations. For example, the deal.II-based library \texttt{hyper.deal}~\cite{munch2020hyperdeal}, which solves the 6D Vlasov--Poisson equation with high-order discontinuous Galerkin methods (with more than a thousand degrees of freedom per cell), constructs a tensor product of two \texttt{MatrixFree} objects of different SIMD-vector length in the same application and benefits---in terms of performance---by the possibility of decreasing the number of cells processed by a single SIMD instruction. \begin{table} -\caption{Supported vector lengths of the class \texttt{VectorizedArray} and +\caption{\it Supported vector lengths of the class \texttt{VectorizedArray} and the corresponding instruction-set-architecture extensions. }\label{tab:vectorizedarray} \centering \begin{tabular}{ccc} @@ -650,7 +647,7 @@ VectorizedArray & VectorizedArray & AVX-512 \\ \bottomrule \end{tabular} -\caption{Comparison of relevant SIMD-related classes in deal.II and \texttt{C++23}.}\label{tab:simd} +\caption{\it Comparison of relevant SIMD-related classes in deal.II and \texttt{C++23}.}\label{tab:simd} \centering \begin{tabular}{cc} \toprule @@ -661,14 +658,14 @@ VectorizedArray & std::experimental::fixed\_size\_simd}. As another example, the lattice vectors in a crystal plasticity model are generally constant and known during compilation time, enabling their efficient definition as \texttt{constexpr Tensor<1, dim>}. -The capability of defining \texttt{constexpr} variables, functions, and methods -was introduced by the C++11 standard and was later expanded by the C++14 standard. -Therefore, the extent of \texttt{constexpr} support in \dealii{} depends on the C++ -standard which is used to compile the library. The next release of \dealii{} -will fully adopt the features of the C++14 standard. + +Declaring variables, functions, and methods as \texttt{constexpr} +is a C++11 feature that was later expanded by the C++14 standard. +Thus, parts of the \texttt{constexpr} support in \dealii{} depend on the C++ +standard supported by the compiler used to install the library. + +The next release of \dealii{} will require compiler support for the C++14 standard. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -769,16 +773,27 @@ all cells in this way. In addition, there are a number of new tutorial programs: \begin{itemize} -\item \texttt{step-47} solves the biharmonic equation with the - clamped boundary condition. This program is based on the $C^0$ interior - penalty method for fourth order problems. In order to overcome +\item \texttt{step-47} is a new program that solves the biharmonic + equation $\Delta^2 u = f$ with + ``clamped'' boundary condition given by $u=g, \partial u/\partial + n=h$. This program is based on the $C^0$ interior + penalty ($C^0$IP) method for fourth order problems + \cite{Brenner2005}. In order to overcome shortcomings of classical approaches, this method uses $C^0$ Lagrange finite - elements and introduces ``jump`` and ``average`` on interfaces of elements. - The resulting system is obtained through integration by parts, symmetrization, - and stabilization. Appropriate choices for the penalty parameter are - discussed based on numerical results. - - + elements and introduces ``jump'' and ``average'' operators on + interfaces of elements that penalize the jump of the gradient of the + solution in order to obtain convergence to the $H^2$-regular + solution of the equation. + + The $C^0$IP approach is a modern alternative to classical methods that + use $C^1$-conforming elements such as the Argyris + element, the Clough-Tocher element and others, all developed in the + late 1960s. From a twenty-first century perspective, they can only be + described as bizarre in their construction. They are also exceedingly + cumbersome to implement if one wants to use general meshes. As a + consequence, they have largely fallen out of favor and deal.II currently + does not contain implementations of these shape functions. + \item \texttt{step-50} \todo[inline]{Timo/Conrad/... to write} @@ -793,14 +808,15 @@ In addition, there are a number of new tutorial programs: \end{align*} augmented by appropriate initial and boundary conditions and using an appropriate form for the potential $V=V(\mathbf x)$. The - tutorial program focused on two specific aspects for which this + tutorial program focuses on two specific aspects for which this equation serves as an excellent test case: (i) Solving complex-valued problems without splitting the equation into its real and imaginary parts (as \texttt{step-29} does, for - example). (ii) Using operator splitting techniques. The equation is + example). (ii)~Using operator splitting techniques. The equation is a particularly good test case for this technique because the only nonlinear term, $\kappa |\psi|^2 \psi$, does not contain any - derivatives and consequently forms an ODE to be solved at each time + derivatives and consequently forms an ODE at each node point, to be + solved in each time step in an operator splitting scheme (for which, furthermore, there exists an analytic solution), whereas the remainder of the equation is linear and easily solved using standard finite element @@ -843,10 +859,23 @@ to the matrix-vector product to increase data locality. \label{subsec:python} \begin{figure} -\renewcommand\figurename{Listing} - \centering +\includegraphics[scale=0.5]{python_mesh.png} +\caption{\it The mesh generated by the Python code shown in the main + text. Cells are colored by material id.} +\label{fig:pymesh} +\end{figure} + +Initial support for Python has existed in \dealii{} since version +9.0. The present release significantly extends the Python +interface. Specifically, a large number of methods from classes such +as \texttt{Triangulation, CellAccessor, TriaAccessor, Mapping, + Manifold, GridTools} can now be invoked from Python. We have focused +on methods and functions that are widely used when a mesh is created +and parameters related to the boundary, manifold, and material +identifiers are assigned. The following listing gives an idea of how +such code looks: \begin{python} import PyDealII.Release as dealii @@ -867,23 +896,23 @@ for cell in triangulation.active_cells(): triangulation.execute_coarsening_and_refinement() \end{python} +The mesh that results from this code is shown in Fig.~\ref{fig:pymesh}. -\includegraphics{python_mesh.png} +All triangulations created from within Python are serial. However, +once the mesh is designed, the triangulation can be serialized along +with the auxiliary information about possible refinement, boundaries, +materials and manifolds. This object can be easily deserialized within +a C++ program for subsequent production runs. Furthermore, such a +serialized triangulation can also be used in the construction of +\texttt{parallel::shared}, \texttt{parallel::disrtibuted}, and +\texttt{parallel::fullydistributed} triangulations (see also Section~\ref{subsec:pft}). -\caption{Python code that uses \texttt{deal.II}'s Python interface to generate a mesh shown at the bottom (coloured by the cell's material id).} -\label{python_wrapper} -\end{figure} +To facilitate the illustration of the new Python bindings, tutorial programs \href{https://github.com/dealii/dealii/blob/dealii-9.2/examples/step-49/step-49.ipynb}{step-49} and \href{https://github.com/dealii/dealii/blob/dealii-9.2/examples/step-53/step-53.ipynb}{step-53} were replicated as Jupyter notebooks. - -The initial support for Python has come in \texttt{deal.II 9.0}. The present release significantly extends the Python interface. Specifically, a large number of methods from the C++ classes such as \texttt{Triangulation, CellAccessor, TriaAccessor, Mapping, Manifold, GridTools} can now be invoked from Python. The accent was made on methods and functions that are widely used at a mesh preparation stage when a mesh is created and parameters related to the boundary, manifold and material identifiers are assigned. - -A triangulation object can be read in or created using a number of simplistic geometries offered by the \texttt{GridGenerator}'s functions. Further information such as boundary, material and manifold identifiers can be assigned to cells and respective faces or edges (see Listing \ref{python_wrapper}). The introspective nature of the Python language makes it easy to infer the list of supported methods from the Python objects, for example by typing \texttt{dir(PyDealII.Release.Triangulation)}. - -All triangulations created within the Python are serial. Once the mesh is designed, triangulation can be serialized along with the auxiliary information about possible refinement, boundaries, materials and manifolds. This object can be easily deserialized within a C++ program for subsequent production runs. Although saved triangulations are serial, it is possible to use them for construction of \texttt{parallel::shared, parallel::disrtibuted, and parallel::fullydistributed} (see also Section \ref{subsec:pft}) types of triangulations respecting the refinement and all the auxiliary information. - -To facilitate the illustration of the new Python bindings, tutorial programs \href{https://github.com/dealii/dealii/blob/dealii-9.2/examples/step-49/step-49.ipynb}{step-49} and \href{https://github.com/dealii/dealii/blob/dealii-9.2/examples/step-53/step-53.ipynb}{step-53} were replicated in a form of the Jupyter notebooks. - -Note that the current Python interface does not yet provide access to the actual \texttt{deal.II}'s finite element machinery, that is classes such as \texttt{DoFHandler, FE\_*, FEValues}, etc. It is envisaged that a progress towards this will be made for the next release. +The introspective nature of the Python language makes it easy to infer +the list of supported methods from the Python objects, for example by +typing \texttt{dir(PyDealII.Release.Triangulation)}. +The current Python interface does not yet provide access to \dealii{}'s finite element machinery, i.e., classes such as \texttt{DoFHandler, FE\_*, FEValues}, etc. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Incompatible changes} @@ -904,8 +933,8 @@ applications. However, some are worth mentioning: \end{itemize} have been deprecated. As discussed in Subsection~\ref{subsec:performance}, deal.II by default no longer -stores information for all processes on all processes, but only the -local information or the locally-relevant information. On the other +stores information for all processes on all processes, but only +local or locally-relevant information. On the other hand, if necessary, global information can still be computed using, for example, calling \texttt{Utilities::MPI::Allgather(locally\_owned\_info(), comm)}. \item @@ -926,8 +955,8 @@ software, we ask that papers using the library reference one of the There are various ways to reference \dealii. To acknowledge the use of the current version of the library, \textbf{please reference the present -document}. For up to date information and a bibtex entry for this document -see: +document}. For up to date information and a bibtex entry +see \begin{center} \url{https://www.dealii.org/publications.html} \end{center} @@ -936,7 +965,9 @@ The original \texttt{\dealii} paper containing an overview of its architecture is \cite{BangerthHartmannKanschat2007}. If you rely on specific features of the library, please consider citing any of the following: -\begin{itemize} +\begin{multicols}{2} + \vspace*{-36pt} + \begin{itemize} \item For geometric multigrid: \cite{Kanschat2004,JanssenKanschat2011,ClevengerHeisterKanschatKronbichler2019}; \item For distributed parallel computing: \cite{BangerthBursteddeHeisterKronbichler11}; \item For $hp$~adaptivity: \cite{BangerthKayserHerold2007}; @@ -948,6 +979,7 @@ following: \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: @@ -956,12 +988,15 @@ following: \cite{MaierBardelloniHeltai-2016-a,MaierBardelloniHeltai-2016-b}; \item For uses of the \texttt{WorkStream} interface: \cite{TKB16}; - \item For uses of the \texttt{ParameterAcceptor} concept, the - \texttt{MeshWorker::ScratchData} base class, and the - \texttt{ParsedConvergenceTable} class: - \cite{SartoriGiulianiBardelloni-2018-a}; - \item For uses of the particle functionality in \dealii{}: \cite{GLHPB18}. + \item For uses of the \texttt{ParameterAcceptor} concept, the + \texttt{MeshWorker::ScratchData} base class, and the + \texttt{ParsedConvergenceTable} class: + \cite{SartoriGiulianiBardelloni-2018-a}; + \item For uses of the particle functionality in \dealii{}: + \cite{GLHPB18}. + \vfill\null \end{itemize} +\end{multicols} \dealii can interface with many other libraries: \todo[inline]{We picked up gingko. Anything else?}