From bf69930aa62f1d4d9f0fd920ed73f89187e28d6c Mon Sep 17 00:00:00 2001 From: Martin Kronbichler Date: Tue, 2 Jun 2020 07:58:36 +0200 Subject: [PATCH] Add reference --- 9.2/paper.bib | 29 ++++++++++++++++++++++++++++- 9.2/paper.tex | 27 +++++++++++++-------------- 2 files changed, 41 insertions(+), 15 deletions(-) diff --git a/9.2/paper.bib b/9.2/paper.bib index 1a4dd04..6a113c3 100644 --- a/9.2/paper.bib +++ b/9.2/paper.bib @@ -13,6 +13,18 @@ doi = {10.1145/1268776.1268779} } +@Article{dealII2020design, + title = {The {deal.II} finite element library: design, features, and + insights}, + author = {Daniel Arndt and Wolfgang Bangerth and Denis Davydov and Timo + Heister and Luca Heltai and Martin Kronbichler and Matthias Maier + and Jean-Paul Pelteret and Bruno Turcksin and David Wells}, + journal = {Computers \& Mathematics with Applications}, + volume = {in press}, + year = {2020}, + DOI = {10.1016/j.camwa.2020.02.022}, +} + @Misc{changes84, Title = {List of Changes}, Note = {\url{https://www.dealii.org/developer/doxygen/deal.II/changes_between_8_3_and_8_4.html}}, @@ -317,6 +329,22 @@ doi = "10.1515/jnma-2018-0054" pages = {2/1--32}, year = 2019} +@inproceedings{Arndt2020sppexa, +author = {Daniel Arndt and Niklas Fehn and Guido Kanschat and Katharina Kormann and Martin Kronbichler and Peter Munch and Wolfgang A. Wall and Julius Witte}, +title = {{ExaDG} -- High-Order Discontinuous {G}alerkin for the Exa-Scale}, +booktitle="Software for Exascale Computing -- SPPEXA 2016--2019", +series={Lecture Notes in Computational Science and Engineering 136}, +year="2020", +publisher="Springer International Publishing", +address="Cham", +editor="Bungartz, Hans-Joachim +and Nagel, Wolfgang E. +and Reiz, Severin +and Uekermann, Benjamin +and Neumann, Philipp", +doi = {10.1007/978-3-030-47956-5_8} +} + @techreport{DeSimoneHeltaiManigrasso2009, Author = {A. DeSimone and L. Heltai and C. Manigrasso}, @@ -1050,4 +1078,3 @@ doi = {10.1016/0096-3003(82)90191-6} Year = {2019}, Url = {https://arxiv.org/abs/1907.06696} } - diff --git a/9.2/paper.tex b/9.2/paper.tex index 3cb9424..c533745 100644 --- a/9.2/paper.tex +++ b/9.2/paper.tex @@ -406,20 +406,17 @@ processes and pack/unpack routines either by implementing the interface \texttt{CA::\allowbreak Process} or by providing \texttt{std::function} objects to \texttt{CA::AnonymousProcess}. -\todo[inline]{Aren't the target processes the result of the operation, and the - input global numbers of indices that we request?} - By replacing the collective communications during set up and removing the arrays that contain information for each process (enabled by the application of consensus algorithms and other modifications---a full list of modifications leading to this improvement can be found online), we were able to significantly improve the set up time for large-scale simulations and to solve a Poisson problem with multigrid -with \num{2.1e12} unknowns. -\todo[inline]{the figure only shows 2e11 unknowns. Is this a typo? If not, do we have a reference?} +with \num{2.1e12} unknowns on the SuperMUC-NG supercomputer with 304,152 +cores~\cite{dealII2020design,Arndt2020sppexa}. Figure~\ref{fig:init_costs} compares timings of simulations of various problem sizes (including set up) on 49,152 MPI ranks using a matrix-free -solver~\cite{KronbichlerKormann2019,KronbichlerWall2018}; this solver uses discontinuous elements of +solver~\cite{Arndt2020sppexa,KronbichlerKormann2019,KronbichlerWall2018}; this solver uses discontinuous elements of degree $5$ in a geometric multigrid (GMG) scheme. The comparison between the previous release 9.1 and the current release 9.2 shows that while the scaling for the V-cycle had been very good before, many initialization routines have been considerably @@ -547,6 +544,8 @@ For more details, see \cite{clevenger_stokes19}. \todo[inline]{Timo added the paragraph above. Thoughts on how much we should mention (none of this worked with 9.1)?} +\todo[inline]{Martin: I think (ii) worked in 9.1/9.0/8.5, and (iv) definitely worked in the uniform case for 8.5, see Fig 1 in that paper, data line `8B cells'. We just happened to break things in between. But ``fixes'' is a good wording here because it doesn't exclude that some problems with those configurations have been solved before. So I like the text.} + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \subsection{Better support for parallel $hp$-adaptive algorithms} \label{subsec:hp} @@ -653,28 +652,28 @@ In the previous release we added support for symbolic expressions, leveraging th SymEngine library \cite{symengine-web-page}. Although effective, evaluating lengthy expressions could be a bottleneck as this was performed using dictionary-based substitution. -We have improved on this by implementing a \texttt{BatchOptimizer} class in the +We have improved on this by implementing a \texttt{BatchOptimizer} class in the namespace \texttt{Differentiation::SD} that collects several \texttt{Expression}s and transforms them in such a way that the equivalent result is returned through a quicker code path. This may be done by simply using common subexpression elimination (CSE) for the -dictionary-based expressions, by transformation to a set of nested +dictionary-based expressions, by transformation to a set of nested \texttt{std::function} objects (the equivalent to \texttt{SymPy}'s ``lambdify'', with or without using CSE), or by offloading these expressions to the \texttt{LLVM} just-in-time (JIT) compiler. Although each of these features is implemented and tested in the SymEngine library itself, the \texttt{BatchOptimizer} class provides both a uniform interface to their classes and a convenient interface for scalar expressions, -as well as tensorial expressions formed using the \texttt{deal.II} tensor and +as well as tensorial expressions formed using the \texttt{deal.II} tensor and symmetric tensor classes. It, like the \texttt{Expression} class, is also serializable. The way the batch optimizer may be employed within a user's code is shown in the pseudo-code below. -As per usual, one would first define some independent variables, and -subsequently compute some symbolic expressions that are dependent on these -independent variables. -These expression could be, for example, scalar expressions or tensors of +As per usual, one would first define some independent variables, and +subsequently compute some symbolic expressions that are dependent on these +independent variables. +These expression could be, for example, scalar expressions or tensors of expressions. Instead of evaluating these expressions directly, the user would now create an optimizer to evaluate the dependent functions. @@ -689,7 +688,7 @@ all of the dependent functions at once. However, in many cases each evaluation has significantly less computational cost than evaluating the symbolic expressions directly. Evaluation is performed when the user constructs a substitution map, giving each -independent variable a numerical representation, and passes those to the +independent variable a numerical representation, and passes those to the optimizer. After this step, the numerical equivalent of the individual dependent expressions may finally be retreived from the optimizer. -- 2.39.5