that the $Q_1^d\times Q_0$ combination is not inf-sup stable (requiring a
larger velocity space), and that the $Q_2^d\times Q_0$ combination is
stable but converges with only first-order at the cost of the large
- number of velocity unknowns. The BR space is thus intermediate to the
+ number of velocity unknowns. The BR space is thus intermediate between the
$Q_1^d$ and $Q_2^d$ spaces.
The element is currently only implemented for parallelogram meshes due to
can be found
\href{https://dealii.org/developer/doxygen/deal.II/changes_between_9_0_1_and_9_1_0.html}{
in the file that lists all changes for this release}, see \cite{changes91}.
-(The file is also linked to from the web site of each release as well as
-the release announcement.)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Improved support for automatic differentiation}
The second context aims directly at constitutive model formulations, and serves to
compute the directional derivatives of components of (multi-field) constitutive laws
-with respect to the scalar, vector, tensor and symmetric tensor fields in terms
+with respect to the scalar, vector, tensor, and symmetric tensor fields in terms
of which they are parameterized. The \texttt{ScalarFunction} class may be used to
define a scalar function (such as strain energy function) that may be twice
differentiated, while the \texttt{VectorFunction} may be used to define a vector
and \texttt{SymmetricTensor} classes and associated functions. We have
also implemented a set of utility functions with the following features:
\begin{itemize}
-\item \texttt{differentiate} scalar expressions, tensor and symmetric tensors of expressions
-with respect to other scalar expressions, tensor and symmetric tensors of expressions;
+\item \texttt{differentiate} scalar, tensor, and symmetric tensor expressions
+with respect to other scalar, tensor, or symmetric tensor expressions;
\item create symbolic substitution maps;
\item resolve explicit dependencies between expressions; and
\item perform scalar and tensor valued substitution (including conversion from symbolic to
\end{itemize}
In the next release we expect to implement classes to assist in performing assembly operations
-in the same spirit as that which has been done in the \texttt{Differentiation::AD} namespace,
+in the same spirit as it is already possible using automatic differentation using the \texttt{Differentiation::AD} namespace,
although in a fully symbolic manner.
We will also address performance issues of the \texttt{Expression} class by leveraging
the optimization capabilities of SymEngine, including common subexpression elimination (CSE),
Attributes are commonly used to store simulation parameters.
\end{itemize}
As we have shown in \texttt{step-62}, the \dealii{}'s \texttt{HDF5} interface can be easily used
-to exchange data with python and jupyter notebooks.
+to exchange data with Python and Jupyter notebooks.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{GPU support via CUDA}
\texttt{Host} and the behavior is unchanged compared to previous versions.
When using CUDA, the ghost exchange can be performed either by first copying
the relevant data to the host, performing MPI communication, and finally
- move the data to the device or, if CUDA-aware MPI is available, by
+ moving the data to the device or, if CUDA-aware MPI is available, by
performing MPI communication directly between GPUs.
\item Constrained degrees of freedom: the matrix-free framework now
supports constrained degrees of freedom. The implementation is based on
LINPACK performance of the machine of 19.5 PFlop/s (the machine is listed on
position 8 of the top-500 list of November 2018), this can be considered an
extremely good value for a PDE solver which have classically only reached a
-few percent of the LINPACK performance, and given the optimization steps
-contained in the matrix-free module of \dealii that aim to minimize the time
-to solution rather than maximize the number of floating point operations. The
+few percent of the LINPACK performance.
+More importantly, this is achieved within a flexible framework supporting
+arbitrary polynomial order on adaptively refined, unstructured meshes and
+with algorithms in the matrix-free module of \dealii designed to minimize time
+to solution and scalability, rather than maximizing the number of floating point operations. The
largest Poisson problem that has been solved on 304k cores contained 2.15
trillion unknowns (or 7.1 million unknowns per MPI rank) and was solved in 3.5
seconds. Also, CFD production runs with up to $10^{11}$ unknowns and $10^5$
further improvements in setup times for the next release.
Furthermore, the implementation of the Chebyshev iteration, \dealii's most
-popular smoother in the matrix-free context, has been revised to reduce the
+popular smoother in the matrix-free context, has been revised to reduce the number of
vector accesses. The vector operations have become an increasing bottleneck
due to the level of optimization available for the operator evaluation with
our matrix-free framework \cite{KronbichlerKormann2019}, especially on newer
use of absorbing boundary conditions through the Perfectly Matched
Layer technique.
-\item \texttt{step-63} implements a multigrid preconditioner
+\item \texttt{step-63} implements a geometric multigrid preconditioner
and solver for the advection-diffusion equation, yielding optimal
- complexity.
+ complexity. The tutorial compares
+ point-based smoothers to cell-based smoothers and
+ demonstrates the effect of downstream ordering on smoother performance.
\item \texttt{step-64} demonstrates the usage of matrix-free methods on Nvidia GPUs.
-GPUs are advantageous for these kind of operations because of their superior
+GPUs are shown to be advantageous for these kind of operations because of their superior
hardware characteristics, in particular a higher memory bandwidth than server
CPUs within a given power envelope.
\item The \texttt{MCMC-Laplace} code gallery program is a code useful
- for the forward solution that is used as a building block in
+ for the forward solution used as a building block in
Bayesian inverse problems, and for sampling the parameter space
through a Metropolis-Hastings sampler (a kind of Monte Carlo
Markov Chain method).
\texttt{SmartPointer} class, now requires a pointer to a
\texttt{std::atomic<bool>} that tracks whether or not the pointer to the
subscribed-to object is still valid.
-\item The \texttt{ConstraintMatrix} class gained a template parameter for scalar
+\item The \texttt{ConstraintMatrix} class gained a template parameter for the scalar
type and was been renamed \texttt{AffineConstraints}. Several methods that
take vectors or matrices as arguments,
such as \texttt{AffineConstraints::distribute\_local\_to\_global()},
Galerkin for the exa-scale'' (\mbox{ExaDG}) within the priority program ``Software
for Exascale Computing'' (SPPEXA).
-W.~Bangerth and T.~Heister were partially
+W.~Bangerth, T.~C.~Clevenger, and T.~Heister were partially
supported by the National Science Foundation under award OAC-1835673
as part of the Cyberinfrastructure for Sustained Scientific Innovation (CSSI)
-program; by award DMS-1821210; and by the Computational Infrastructure
+program and by the Computational Infrastructure
in Geodynamics initiative (CIG), through the National Science
Foundation under Award No.~EAR-1550901 and The
University of California -- Davis.
+W.~Bangerth and T.~Heister were also partially supported by award DMS-1821210.
+
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
projects / release-papers.git / commitdiff