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}},
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},
Year = {2019},
Url = {https://arxiv.org/abs/1907.06696}
}
-
\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
\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}
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.
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.
projects / release-papers.git / commitdiff