From 166ac2e5df849c9d512930fa9f15628ec000df8f Mon Sep 17 00:00:00 2001 From: Peter Munch Date: Mon, 22 May 2023 09:37:51 +0200 Subject: [PATCH] Write text (Augsburg/Munich) --- 9.5/paper.bib | 107 ++++++++++++++++ 9.5/paper.tex | 346 ++++++++++++++++++++++++++++++++++++++++++++------ 2 files changed, 415 insertions(+), 38 deletions(-) diff --git a/9.5/paper.bib b/9.5/paper.bib index de140f5..8c8be2a 100644 --- a/9.5/paper.bib +++ b/9.5/paper.bib @@ -1451,3 +1451,110 @@ See: https://doc.cgal.org/latest/Manual/how_to_cite_cgal.html year={2013}, publisher={SIAM} } + +@article{heinz2023high, + title={High-order non-conforming discontinuous Galerkin methods for the acoustic conservation equations}, + author={Heinz, Johannes and Munch, Peter and Kaltenbacher, Manfred}, + journal={International Journal for Numerical Methods in Engineering}, + volume={124}, + number={9}, + pages={2034--2049}, + year={2023}, + publisher={Wiley Online Library} +} + +@article{adams2002evaluation, + title={Evaluation of three unstructured multigrid methods on 3D finite element problems in solid mechanics}, + author={Adams, Mark}, + journal={International Journal for Numerical Methods in Engineering}, + volume={55}, + number={5}, + pages={519--534}, + year={2002}, + publisher={Wiley Online Library} +} + +@article{bittencourt2001nonnested, + title={Nonnested multigrid methods for linear problems}, + author={Bittencourt, Marco L. and Douglas, Craig C. and Feij{\'o}o, Ra{\'u}l A.}, + journal={Numerical Methods for Partial Differential Equations: An International Journal}, + volume={17}, + number={4}, + pages={313--331}, + year={2001}, + publisher={Wiley Online Library} +} + +@article{bramble1991analysis, + title={The analysis of multigrid algorithms with nonnested spaces or noninherited quadratic forms}, + author={Bramble, James H. and Pasciak, Joseph E. and Xu, Jinchao}, + journal={Mathematics of Computation}, + volume={56}, + number={193}, + pages={1--34}, + year={1991} +} + +@article{proell2023highly, + title={A highly efficient computational framework for fast scan-resolved simulations of metal additive manufacturing processes on the scale of real parts}, + author={Proell, Sebastian D and Munch, Peter and Kronbichler, Martin and Wall, Wolfgang A and Meier, Christoph}, + journal={arXiv preprint arXiv:2302.05164}, + year={2023} +} + +@article{lottes2022optimal, + title={Optimal polynomial smoothers for multigrid V-cycles}, + author={Lottes, James}, + journal={arXiv preprint arXiv:2202.08830}, + year={2022} +} + +@article{phillips2022optimal, + title={Optimal Chebyshev Smoothers and One-sided V-cycles}, + author={Phillips, Malachi and Fischer, Paul}, + journal={arXiv preprint arXiv:2210.03179}, + year={2022} +} + +@article{lynch1964direct, + title={Direct solution of partial difference equations by tensor product methods}, + author={Lynch, Robert E and Rice, John R and Thomas, Donald H}, + journal={Numerische Mathematik}, + volume={6}, + number={1}, + pages={185--199}, + year={1964}, + publisher={Springer} +} + +@article{kronbichler2019hermite, + title={A Hermite-like basis for faster matrix-free evaluation of interior penalty discontinuous Galerkin operators}, + author={Kronbichler, Martin and Kormann, Katharina and Fehn, Niklas and Munch, Peter and Witte, Julius}, + journal={arXiv preprint arXiv:1907.08492}, + year={2019} +} + +@article{witte2021fast, + title={Fast tensor product Schwarz smoothers for high-order discontinuous Galerkin methods}, + author={Witte, Julius and Arndt, Daniel and Kanschat, Guido}, + journal={Computational Methods in Applied Mathematics}, + volume={21}, + number={3}, + pages={709--728}, + year={2021}, + publisher={De Gruyter} +} + +@article{phillips2021auto, + title={Auto-Tuned Preconditioners for the Spectral Element Method on GPUs}, + author={Phillips, Malachi and Kerkemeier, Stefan and Fischer, Paul}, + year={2021} +} + +@techreport{couzy1995spectral, + title={Spectral element discretization of the unsteady Navier-Stokes equations and its iterative solution on parallel computers}, + author={Couzy, Wouter}, + year={1995}, + institution={EPFL} +} + diff --git a/9.5/paper.tex b/9.5/paper.tex index 0ef3933..be46c1f 100644 --- a/9.5/paper.tex +++ b/9.5/paper.tex @@ -23,7 +23,10 @@ \usepackage{booktabs} -%\renewcommand{\baselinestretch}{2.0} +%\renewcommand{\baselinestretch}{2.0} +%\usepackage{lineno} +%\renewcommand\linenumberfont{\normalfont\tiny} +%\linenumbers \graphicspath{{svg/}} @@ -113,7 +116,7 @@ cross/.default={2pt}} \affil[6]{Institute of Mathematics, University of Augsburg, Universit\"atsstr.~12a, 86159 Augsburg, Germany. - {\texttt{martin.kronbichler@uni-a.de}}} + {\texttt{martin.kronbichler/peter.muench@uni-a.de}}} \author[7]{Matthias~Maier} \affil[7]{Department of Mathematics, @@ -125,8 +128,7 @@ cross/.default={2pt}} \author[6,8]{Peter Munch} \affil[8]{Institute of Material Systems Modeling, Helmholtz-Zentrum Hereon, - Max-Planck-Str. 1, 21502 Geesthacht, Germany. - {\texttt{peter.muench@hereon.de}}} + Max-Planck-Str. 1, 21502 Geesthacht, Germany} \author[9]{Jean-Paul~Pelteret} @@ -188,8 +190,8 @@ The major changes of this release are: \item Update to and extension of the \texttt{PETSc} wrappers (see Section~\ref{sec:petsc}); \item Addition of new \texttt{Trilinos} wrappers (see Section~\ref{sec:trilinos}); \item Advances in matrix-free infrastructure (see Section~\ref{sec:mf}); - \item Advance in non-matching support (see Section~\ref{sec:nonmatching}); - \item New liner algebra features (see Section~\ref{sec:lac})l + \item Advances in non-matching support (see Section~\ref{sec:nonmatching}); + \item New features related to liner algebra (see Section~\ref{sec:lac}) \item C++ language modernization (see Section~\ref{sec:language}). \end{itemize} % @@ -200,7 +202,18 @@ are a number of other noteworthy changes in the current \dealii release, which we briefly outline in the remainder of this section: % \begin{itemize} - \item The \texttt{CellAccessor::as\_dof\_handler\_iterator()} + \item The new function \texttt{CellAccessor::as\_dof\_handler\_iterator()} + simplifies the conversion from a \texttt{Cell\-Accessor} to a \texttt{DoF\-Cell\-Accessor}. + The old way +\begin{c++} +const auto cell_dof = typename DoFHandler:: + active_cell_iterator(&dof_handler.get_triangulation(), + cell->level(), cell->index(), &dof_handler); +\end{c++} +was lengthy and error-prone. In contrast, the new way: +\begin{c++} +const auto cell_dof = cell->as_dof_handler_iterator(dof_handler); +\end{c++} \end{itemize} % The changelog lists more than X other features and bugfixes. @@ -242,40 +255,293 @@ can be found %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{New Trilinos wrappers}\label{sec:trilinos} -\begin{itemize} -\item Belos -\item NOX -\end{itemize} +We have added a new wrapper to \texttt{Belos}. The package +\texttt{Belos} is the +successor of \texttt{AztecOO} and provides basic and advanced iterative solvers +that heavily rely on multivector operations. The interface of the +wrapper is similar to the one of the native iterative solvers +provided by \dealii: + +\begin{c++} +TrilinosWrappers::SolverBelos solver(/*...*/); +solver.solve(matrix, x, r, preconditioner); +\end{c++} + +Via additional data, the user can select the actual iterative +solver to be used and set its configurations. + +Furthermore, we have added a wrapper to \texttt{NOX}. This is a +nonlinear-solver library similar to \texttt{KINSOL} from \texttt{SUNDIALS} +and to \texttt{SNES} from \texttt{PETSc}. The basic interface +of the \texttt{NOX} wrapper is similar to the one of the other wrappers +mentioned before: + +\begin{c++} +TrilinosWrappers::NOXSolver solver(/*...*/); + +solver.residual = [ ](const auto &src, auto &dst) {/*...*/}; +solver.setup_jacobian = [&](const auto &src) {/*...*/}; +solver.apply_jacobian = [&](const auto &src, auto &dst) {/*...*/}; +solver.solve_with_jacobian = + [&](const auto &src, auto &dst, const auto tol) {/*...*/}; + +solver.solve(solution); +\end{c++} + +We refer interested readers to our documentation for other more advanced +functions of this wrapper which are related to the differences in features of these libraries. +In particular, we have added the possibility to reuse the preconditioner between +nonlinear steps (also known as \textit{preconditioner lagging}), which is +unfortunately natively only supported in the official \texttt{EPetra} implementations. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Advances in matrix-free infrastructure}\label{sec:mf} +In the matrix-free infrastructure, numerous advances have been made. Some of these +are: \begin{itemize} -\item element activation and deactivation, \texttt{FE\_Nothing}, categorization, DG, face integrals -\item pre/post for DG -\item \texttt{CellwiseInverseMassMatrix} operator for coupling (dyadic) coefficients +\item In release 9.3, we enabled parallel $hp$-operations in the matrix-free infrastructure. +The infrastructure did not work properly in the case that certain cells +did not get any degrees of freedom due to the usage of \texttt{FE\_Nothing}. This has been +fixed now. Furthermore, \texttt{FE\_Nothing} now also works together with DG (\texttt{FE\_DGQ}). Due to the popularity of \texttt{FE\_Nothing} as a mean to enable +or disable cells, we have introduced the new class +\texttt{ElementActivationAndDeactivationMatrixFree}, which wraps a \texttt{MatrixFree} object, only loops over all +active cells and optionally interprets faces between active and deactivated cells +as boundary face. A use case is shown in~\cite{proell2023highly} in the context of powder-bed-fusion additive +manufacturing. +\item The matrix-free infrastructure allows to interleave cell loops with vector updates +by providing \texttt{pre}/\texttt{post} functions that are run on index ranges. This +feature is used, e.g., in \dealii to improve the performance of (preconditioned) +conjugate gradient solvers~\cite{kronbichler2022cg} as well as of relaxation and Chebyshev iterations (see Subsection~\ref{sec:lac}). +Up to release~9.3, the \texttt{pre}/\texttt{post} infrastructure was only supported for +continuous elements (cell loop); now, it also works for discontinuous elements which require +face loops additionally. +\item The operator \texttt{CellwiseInverseMassMatrix} now also efficiently +evaluates the inverse for coupling (dyadic) coefficients in the case of multiple +components: +\begin{align*} +\left(v_j, D_{ji} u_i \right)_{\Omega^{(K)}} +\quad 1\le i,j \le c, +\end{align*} +with $c$ being the number of components and $D\in \mathbb{R}^{c\times c}$ the tensorial +coefficient. +This is possible due to the tensor-product structure of the resulting element matrix: +\begin{align*} +M = ( I_1 \otimes N^T) (D \otimes I_2 ) ( I_1 \otimes N), +\end{align*} +with $N$ being the tabulated shape functions and $I_1$/$I_2$ the appropriate identity matrices. +For square and invertible $N$, the inverse is explicitly given as: +\begin{align*} +M^{-1} = ( I_1 \otimes N^{-1}) (D^{-1} \otimes I_2 ) ( I_1 \otimes N^{-T}). +\end{align*} +Please note that $N^{-1} = N_{1D}^{-1} \otimes N_{1D}^{-1} \otimes N_{1D}^{-1}$ is given +for hypercube-shaped cells, allowing to use sum factorization. \end{itemize} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\subsection{Advance in non-matching support}\label{sec:nonmatching} - - +\subsection{Advances in non-matching support}\label{sec:nonmatching} + +The (matrix-free) non-matching support of \texttt{deal.II} heavily relies +on the classes \texttt{FE\-Point\-Eval\-u\-ation} and \texttt{RemotePointEvaluation}, +which have been introduced in release 9.3. While \texttt{FE\-Point\-Eval\-u\-a\-tion} +is responsible for efficient evaluation/integration at arbitrary (reference) +points within a cell, \texttt{RemotePointEvaluation} is responsible for +sorting the (real) points within cells and for the successive communication. + +In the current release, we considerably optimized \texttt{FEPointEvaluation}, e.g, +by caching the evaluated shape functions, templating loop bounds, and +exploiting the tensor-product structure of the shape functions if all points are +positioned on a face, a common use case in the context of fluid-structure +interaction. Furthermore, the extended class \texttt{NonMatching::MappingInfo} +allows to precompute and store metric terms, like the Jacobian, its determinant, +or the normals. This is useful in cases in which these metric terms do not change +and can be reused, e.g., in the context of iterative solvers. This development +is part of the efforts to make the interfaces of the +(matrix-free) non-matching support more similar to the ones of the +established matrix-free infrastructure of \dealii for structured (quadrature) points. + +In addition to these node-level performance optimizations, we added experimental +support 1) for generating intersections of distributed +non-matching grids and working on them +and 2) for multigrid with non-nested levels. In the following, we describe these +features in detail. + +\subsubsection*{Intersected meshes} +\begin{itemize} +\item uses \texttt{CGAL}~\cite{cgal-user-ref} +\item data can be used to fill \texttt{RemotePointEvaluation} (communication-free) +\item used successfully in \cite{heinz2023high} to perform Nitsche-type mortaring in the context +of the conservative formulation of acoustic equations discretized with +DG, in order to suppress artificial modes +\end{itemize} +\subsubsection*{Non-nested multigrid} + +The library \dealii provides traditionally strong support for multigrid methods. +We support, in the context of geometric multigrid, both local-smoothing~\cite{ClevengerHeisterKanschatKronbichler2019} +and global-coarsening algorithms~\cite{munch2022gc} for locally refined meshes. The global-coarsening +infrastructure, furthermore, allows to globally coarsen the polynomial degree ($p$-multigrid), +whose applicability to $hp$-adaptive problems has been demonstrated. Algebraic +multigrid is supported by interfacing to the external libraries \texttt{PETSc} +and \texttt{Trilinos}. In the current release, we have added support for the case +that multigrid levels are given by non-nested meshes~\cite{adams2002evaluation, bittencourt2001nonnested, bramble1991analysis}. An example for such meshes is +presented in Figure~\ref{fig:nonnested}. + +\begin{figure} + +\centering + +\fbox{\begin{minipage}{0.31\textwidth}\centering 0\vspace{5cm}\end{minipage}} +\fbox{\begin{minipage}{0.31\textwidth}\centering 1\vspace{5cm}\end{minipage}} +\fbox{\begin{minipage}{0.31\textwidth}\centering 2\vspace{5cm}\end{minipage}} + +\caption{Example of non-nested multigrid levels.}\label{fig:nonnested} + +\end{figure} + +The current implementation extends the existing global-coarsening infrastructure by +introducing, in addition to the (conformal) \texttt{MGTwoLevelTransfer}, + a new (non-conformal) two-level transfer operator + +\begin{c++} +MGTwoLevelTransferNonNested two_level_transfer(/*...*/); + +two_level_transfer.reinit(dof_handler_fine, dof_handler_coarse, + // the following parameters are optional + mapping_fine, mapping_coarse, + constraints_fine, constraints_coarse) +\end{c++} + +which can be passed to \texttt{MGTransferGlobalCoarsening} (and +\texttt{MGTransferBlockGlobalCoarsening}) in the usual way. Please note +the similarity between the interfaces of \texttt{MGTwoLevelTransfer} and +of \texttt{MGTwoLevel\-Transfer\-Non\-Nested}, with the difference that the latter also +takes \texttt{Mapping} instances. Furthermore, it is not limited to the case +that the \texttt{DoFHandler} instances need to share the same coarse triangulation +and the coarser mesh has to be able to be generated by a coarsening step from the fine +mesh. + +At the time of writing, the \texttt{MGTwoLevelTransferNonNested} operator performs +a pointwise interpolation (injection) from the coarse mesh to the support points +of the fine mesh. Adopting the notation of~\cite{munch2022gc}, we perform +for prolongation +\begin{align*} +x^{(f)} = \mathcal{W}^{(f)} \circ \sum_{e \in \{\text{coarse cells}\}} \mathcal{S}_e^{(f)} \circ \mathcal{P}_e^{(f, c)} +\circ \mathcal{C}_e^{(c)} \circ \mathcal{G}_e^{(c)} x^{(c)}, +\end{align*} +i.e., loop over all coarse cells and interpolate to all (fine support) points that fall +into the cell with \texttt{FEPointEvaluation}. The local result is scattered into a global +vector, which is finalized by a communication and a weighting step. + +The current implementation works for scalar and vectorial continuous (\texttt{FE\_Q}) +and discontinuous elements (\texttt{FE\_DGQ}) for hypercube-shaped cells. We plan to support +simplices and to add, in addition to the pointwise interpolation, also support +for projection. Furthermore, we envision to provide utility tools to generate coarser +meshes, based on a fine mesh. Currently, the users themselves +have to provide such meshes, +e.g., by generating meshes with different cell sizes in external mesh-generation tools. + +Note that the new class \texttt{MGTwoLevelTransferNonNested} is not limited to +multigrid but can be used to prolongate results and restrict residuals between any +two meshes. Indeed, the infrastructure has been successfully applied to perform +conservative interpolation between a fine (near) mesh and a coarse (far) mesh in the +context of aeroacoustic problems. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\subsection{New linear algebra features}\label{sec:lac} - +\subsection{New features regarding linear algebra}\label{sec:lac} +In addition to the new wrappers for linear-algebra functionalities of \texttt{PETSc} +and \texttt{Trilinos} (see Sections~\ref{sec:petsc} and \ref{sec:trilinos}) as well +as the new non-nested multigrid infrastructure, +we made multiple additions to our own linear-algebra infrastructure. \begin{itemize} - \item \texttt{SolverGMRES}: classical/modified Gram Schmidt process - \item James Lottes’s fourth-kind Chebyshev - \item \texttt{PreconditionChebyshev}, \texttt{PreconditionRelaxation} - \item restrict matrices - \item fast diagonalization method + \item Both \texttt{SolverGMRES} and \texttt{SolverFGMRES} now support the classical + Gram--Schmidt orthonormalization in addition to the existing modified one. This + allows to reduce the cost of vector operations in terms of + communication latency and memory transfer significantly. + \item Our Chebyshev preconditioner (\texttt{PreconditionChebyshev}) now also + supports James Lottes’s novel fourth-kind Chebyshev + polynomial~\cite{lottes2022optimal, phillips2022optimal}. + \item Our relaxation preconditioner (\texttt{PreconditionRelaxation}) now also + allows to interleave cell loops and vector updates related to relaxation. The + relaxation iteration reads as + \begin{align*} + x^{(i+1)} \gets x^{(i)} + \omega P^{-1}(b-Ax^{(i)}). + \end{align*} + E.g, in the case that the preconditioner $P$ is a diagonal matrix, the zeroing of + the destination vector $x_{i+1}$ can be performed during a \texttt{pre}-operation of $A$ + and the vector update $x^{(i+1)}_j \gets x^{(i)}_j + \omega P^{-1}_{j,j}(b_j-(Ax^{(i)})_j)$ + during a \texttt{post} operation, allowing to reduce the number of read and write + accesses from 8 and 4 to 1 and 3, respectively. The existing \texttt{pre}/\texttt{post} + support in our Chebyshev-preconditioner implementation (\texttt{PreconditionChebyshev}) + has been improved. In addition, both \texttt{PreconditionRelaxation} and + \texttt{PreconditionChebyshev} support \texttt{pre}/\texttt{post} optimizations + now not only for diagonal preconditioners but also for preconditioners that are + built around cell loops and, as a consequence, support interleaving. An example of + such a preconditioner are patch-based additive Schwarz preconditioners. + \item In the context of additive Schwarz methods, the preconditioner application + is defined as + \begin{align*} + v = P^{-1} u = \sum R_i^\top A_i^{-1} R_i u + \end{align*} + with $A_i = R_i A R_i^T$ being a block of the assembled system matrix restricted + to an index set (inverse of the assembly step). During the restriction step, + rows of the system matrix that are potentially owned by other + processes are needed. In \texttt{deal.II}, it is not possible to access remote entries + of sparse matrices. Two novel functions allow to query this information. The + function \texttt{restrict\_to\_serial\_sparse\_matrix()} creates, based + on a given index set, a serial + sparse matrix from a distributed one on each process: + +\begin{c++} +SparseMatrixTools::restrict_to_serial_sparse_matrix ( + sparse_matrix_in, sparsity_pattern, requested_is, + system_matrix_out, sparsity_pattern_out) +\end{c++} + +This function can be used, e.g., if the granularity of the additive Schwarz preconditioner +is a complete subdomain, potentially, with a fixed overlap. + +In contrast, \texttt{restrict\_to\_full\_matrices()} performs the restriction +for arbitrary number of patches/blocks: + +\begin{c++} +SparseMatrixTools::restrict_to_full_matrices ( + sparse_matrix_in, sparsity_pattern, indices_of_blocks, blocks) +\end{c++} + +The data is stored in full matrices, since the typical granularity is a (rather small) cell-centric or +vertex-star patch. + + \item For certain types of configurations, there are computationally more efficient + approaches than extracting submatrices from an assembled matrix. For example, the Laplace + operator on 2D Cartesian meshes, the (element/patch) matrix is given as + \begin{align*} + A_i^{\text{cart}} = K_1 \otimes M_0 + M_1 \otimes K_0, + \end{align*} + i.e., as the tensor product of 1D mass and stiffness matrices. The inverse is + explicitly given according to the fast diagnilization method~\cite{lynch1964direct}, as + \begin{align*} + \left(A_i^{\text{cart}}\right)^{-1} = (T_1 \otimes T_0) (\Lambda_1 \otimes I + I \otimes \Lambda_0)^{-1} (T_1^\top \otimes T_0^\top), + \end{align*} + with $T_i$ and $\Lambda_i$, being the (orthonormal) eigenvectors and the diagonal + matrix of eigenvalues, obtained from a generalized eigendecomposition + $K_iT_i = \Lambda_i M_i T_i$. Since $A_i \approx A_i^{\text{cart}}$ + might be a good approximation also in the case of non-Cartesian meshes and + $A_i^{\text{cart}}$ has an explicit inverse, it is considered in the + literature as patch preconditioners in the context of additive + Schwarz~\cite{witte2021fast, phillips2021auto, couzy1995spectral} and block-Jacobi methods~\cite{kronbichler2019hermite}. + In \dealii, the new function + \texttt{Tensor\-Product\-Matrix\-Creator::create\_\allowbreak laplace\_\allowbreak tensor\_\allowbreak product\_\allowbreak matrix()} computes $T_i$ and $\Lambda_i$ + for cell-centric patches with a specified overlap and given boundary conditions. + A set of $T_i$ and $\Lambda_i$ is applied to a cell via + \texttt{Tensor\-Product\-Matrix\-Symmetric\-Sum} or to a collection of cells + via the new class \texttt{Tensor\-Product\-Matrix\-Symmetric\-Sum\-Collection}, which + tries to reuse the eigenvalues and eigenvectors between cells. \end{itemize} @@ -286,25 +552,34 @@ Mention the C++20 work. Starting point: \dealii{} relies heavily on templates that are explicitly instantiated. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Build-system modernization}\label{sec:buildsystem} + +? + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{New and improved tutorials and code gallery programs} \label{subsec:steps} Many of the \dealii tutorial programs were revised in a variety of ways -as part of this release. In addition, there are a number of new tutorial -programs: -\begin{itemize} - \item -\end{itemize} - -There is also a new program in the code gallery (a collection of +as part of this release. +%In addition, there are a number of new tutorial +%programs: +%\begin{itemize} +% \item +%\end{itemize} + +There is also two new programs in the code gallery (a collection of user-contributed programs that often solve more complicated problems than tutorial programs, and that are intended as starting points for further research rather than as teaching tools): \begin{itemize} - \item + \item The program \texttt{A posteriori error estimator for first order hyperbolic problems} + was contributed by Marco Feder. + \item The program \texttt{Distributed moving laser heating} was contributed by + Hongfeng Ma and Tatiana E. Itina. \end{itemize} -Finally, @@ -461,9 +736,6 @@ T.~Heister was also partially supported by NSF Awards OAC-2015848, DMS-2028346, and EAR-1925575. -R.~Gassm{\"o}ller was also partially supported by the NSF Awards -EAR-1925677 and EAR-2054605. - L.~Heltai was partially supported by the Italian Ministry of Instruction, University and Research (MIUR), under the 2017 PRIN project NA-FROM-PDEs MIUR PE1, ``Numerical Analysis for Full and Reduced Order Methods for the efficient @@ -479,8 +751,6 @@ hybrid parallelization and improved data locality'' and ``Fast and scalable fini M.~Maier was partially supported by NSF Awards DMS-1912847 and DMS-2045636. -S.~Sticko was partially supported by eSSENCE of e-Science. - D.~Wells was supported by the NSF Award OAC-1931516. The Interdisciplinary Center for Scientific Computing (IWR) at Heidelberg -- 2.39.5