\section{Introduction}
-The lattice Boltzmann (LB) method \index{Lattice Boltzmann method} (for an overview see, e.g.,
+The lattice Boltzmann (LB) method \index{lattice Boltzmann method} (for an overview see, e.g.,
\cite{succi-book}) has become a popular approach to a variety of fluid
dynamics problems. It provides a way to solve the incompressible
isothermal Navier-Stokes equations and has the attractive features of
being both explicit in time and local in space. This makes the LB
-method wellsuited to parallel computation. Many efficient parallel
+method well suited to parallel computation. Many efficient parallel
implementations of the LB method have been undertaken, typically using
a combination of distributed domain decomposition and the Message
Passing Interface (MPI). However, the potential
performance benefits offered by GPUs has motivated a new ``mixed-mode''
approach to address very large problems. Here, fine-grained
parallelism is implemented on the GPU, while MPI is reserved for
-largerscale parallelism. This mixed mode is of increasing interest
+larger scale parallelism. This mixed mode is of increasing interest
to application programmers at a time when many supercomputing services
are moving
toward clusters of GPU accelerated nodes. The design questions which
matrix related to the choice of
$\mathbf{c}_i$. The nonconserved hydrodynamic quantities are then
relaxed toward their (known) equilibrium values and are transformed
-back to new postcollision distributions via the inverse transformation
+back to new post-collision distributions via the inverse transformation
${\cal M}^{-1}_{ij}$. This gives rise to the need for a minimum of $2\times 19^2$
floating point multiplications per lattice site. (Additional operations are
required to implement, for example, the force $\mathbf{f}(\mathbf{r})$.)
consecutive memory addresses allows the prefetcher to engage fully.
(The temporary scalar \texttt{a\_tmp} allows caching of the
intermediate accumulated value in the innermost loop.) A variety of
-standard sequential optimisations are relevant for the collision stage
+standard sequential optimizations are relevant for the collision stage
(loop unrolling, inclusion of SIMD operations, and so on
\cite{wellein2006}). For example, the collision stage in
\textit{Ludwig} includes explicit SIMD code, which is useful if the
-compiler on a given platform cannot identify it. The propagation
-stage is separate and is organised as a ``pull'' (again, various
+compiler on a given platform cannot identify the appropriate vectorization.
+The propagation
+stage is separate and is organized as a ``pull'' (again, various
optimizations have been considered, e.g.,
\cite{pohl2003,mattila2007,wittmann2012}). No further optimization is
done here beyond ensuring that the ordering of the discrete velocities
optimizations are important, it should be remembered that for some
complex fluid problems, the hydrodynamics embodied in the LB
calculation is a relatively small part of the total computational cost
-(at the 10\%level in some cases). This means optimization effort may
+(at the 10\% level in some cases). This means optimization effort may
be better concentrated elsewhere.
For the D3Q19 model, this reduces the volume of data traffic from 19 to
5 of the $f_i(\mathbf{r};t)$ per lattice site at each edge. In the CPU
version, the necessary transfers are implemented in place using
-a vector of appropriately strided MPI datatypes for each direction.
-
+a vector of MPI datatypes with appropriate stride for each direction.
+\clearpage
\section{Single GPU implementation}\label{ch14:sec:singlegpu}
assigned to the fast {\it constant} on-chip device memory.
For the propagation stage, the GPU implementation adds a second time
-level of distribution values. The datadependencies inherent in the
+level of distribution values. The data dependencies inherent in the
propagation mean that the in-place propagation of the CPU version
cannot be parallelized effectively without the additional time level.
As both time levels may remain resident on the GPU, this is not a
through the host (in the future, direct GPU-to-GPU data transfers via
MPI may be possible, obviating the need for these steps). This
means host MPI sends must be preceded by appropriate device-to-host
-transfers and host MPI receives must be followed by corresponding host-to-device transfers.
+transfers and host MPI receives must be followed by corresponding
+host-to-device transfers.
%To execute on multiple GPUs in parallel we decompose the problem using
%the existing high-level parallelisaton framework: each MPI task acts
hosts at the same time as kernels for packing and retrieving of
data for the second coordinate direction are
executed. This
-overlapping must respect the synchronisation required to ensure
+overlapping must respect the synchronization required to ensure
that data values at the corners of the subdomain are transferred
correctly.
We use a separate CUDA stream for each coordinate direction:
\begin{figure}[t]
\centering
%\includegraphics[width=10cm]{Chapters/chapter14/figures/bbl}
-\includegraphics[width=10cm]{Chapters/chapter14/figures/colloid_new}
+\includegraphics[width=10cm]{Chapters/chapter14/figures/colloid_new_gray}
\caption[A two-dimensional schematic picture of spherical particles on the lattice.]{
A two-dimensional schematic picture of spherical particles on the lattice.
Left: a particle is allowed
to move continuously across the lattice, and the position of the
-surface defines fluid lattice sites (light blue) and solid lattice
-sites (dark red). The discrete surface is defined by links
+surface defines fluid lattice sites (gray) and solid lattice
+sites (black). The discrete surface is defined by links
where propagation would intersect the surface (arrows). Note the
discrete shape of the two particles is different. Right: post-collision
distributions are reversed at the surface by the process of bounce-back
In this section, we give a brief overview of the essential features
of the CPU implementation, and how the considerations raised in the
previous sections---maximizing parallelism and minimising both
-host-to-device and GPU to GPU data movement---shape the design decisions
+host-to-device and GPU-to-GPU data movement---shape the design decisions
for a GPU implementation. We restrict our discussion to a simple fluid
in this section; additional solid-fluid boundary conditions (e.g.,
wetting at a fluid-fluid-solid contact line) usually arise elsewhere
-in the calculation broadly independent of the hydrodynamic boundary
+in the calculation and are broadly independent of the hydrodynamic boundary
conditions which are described in what follows.
Moving solid particles (here, spheres) are defined by a center position
intercept or cut the spherical shell (see Fig.~\ref{ch14:fig:bbl}).
Hydrodynamic boundary conditions are then implemented via the standard
approach of bounce-back on links \cite{ladd1994, nguyen2002}, where the
-relevant postcollision distribution values are reversed at the
+relevant post-collision distribution values are reversed at the
propagation stage with an appropriate correction to allow for the
solid body motion. The exchange of momentum at each link must then be
accumulated around the entire particle surface to provide the net
molecular dynamics-like step.
For the CPU implementation, a number of additional MPI communications
-are required: (1) to exchange the center position, radius, etc of each
-particle as it moves and (2), to allow the accumulation of the force
+are required: (1) to exchange the center position, radius, etc.\ of each
+particle as it moves and (2) to allow the accumulation of the force
and torque for each particle (the links of which may be distributed
between up to 8 MPI tasks in three dimensions). Appropriate marshaling
of these data can provide an effective parallelization for relatively
concerns which are relevant to a GPU implementation:
\begin{enumerate}
\item
-Minimisation of host-device data transfer would argue for moving the
+Minimization of host-device data transfer would argue for moving the
entire particle code to the GPU. However, the code in question involves
largely conditional logic (e.g., identifying cut surface links) and
irregular memory accesses (e.g., access to distribution elements around
We have implemented the second option as follows. For each subdomain,
-a list of boundary-cutting links is assembled on the CPU which includes
-the identity of the relevant element of the distribution. This list,
+a list of boundary-cutting links is assembled on the CPU; the list includes
+the identity of the relevant element of the distribution in each case.
+This list,
together with the particle information required to compute the correct
-bounce-back term, are transferred to the GPU. The updates to the relevant
+bounce-back term, is transferred to the GPU. The updates to the relevant
elements of the distribution can then take place on the GPU. The
corresponding information to compute the update of the particle dynamics
is returned
-
+\clearpage
\section{Summary}
\label{ch14:sec:summary}
% use section* for acknowledgement
-\section*{Acknowledgments}
+\section{Acknowledgments}
AG was supported by the CRESTA project, which has received
funding from the European Community's Seventh Framework Programme
(ICT-2011.9.13) under Grant Agreement no. 287703. KS was supported
% set second argument of \begin to the number of references
% (used to reserve space for the reference number labels box)
+\clearpage
\putbib[Chapters/chapter14/biblio14]
%\begin{thebibliography}{1}
