new

[book_gpu.git] / BookGPU / Chapters / chapter13 / ch13.tex

diff --git a/BookGPU/Chapters/chapter13/ch13.tex b/BookGPU/Chapters/chapter13/ch13.tex
index 89e2ce73adfc7e59d93c63cc4cf6bb510e632826..90dd94649b135a21f31083cd392c7674b442114e 100755 (executable)
--- a/BookGPU/Chapters/chapter13/ch13.tex
+++ b/BookGPU/Chapters/chapter13/ch13.tex
@@ -299,12 +299,12 @@ and $\forall j\in\{1,\ldots,\alpha\}$,
 \label{ch13:eq:15}
 \end{equation}
 
 \label{ch13:eq:15}
 \end{equation}
 

-The previous asynchronous scheme\index{asynchronous} of the projected Richardson
+The previous asynchronous scheme\index{asynchronous iterations} of the projected Richardson

 method models computations that are carried out in parallel without order or
 synchronization (according to the behavior of the parallel iterative method) and
 describes a subdomain method without overlapping. It is a general model that takes
 into account all possible situations of parallel computations and nonblocking message
 method models computations that are carried out in parallel without order or
 synchronization (according to the behavior of the parallel iterative method) and
 describes a subdomain method without overlapping. It is a general model that takes
 into account all possible situations of parallel computations and nonblocking message

-passing. So, the synchronous iterative scheme\index{synchronous} is defined by
+passing. So, the synchronous iterative scheme\index{synchronous iterations} is defined by

 \begin{equation}
 \forall j\in\{1,\ldots,\alpha\} \mbox{,~} \forall p\in\mathbb{N} \mbox{,~} \rho_j(p)=p.
 \label{ch13:eq:16}
 \begin{equation}
 \forall j\in\{1,\ldots,\alpha\} \mbox{,~} \forall p\in\mathbb{N} \mbox{,~} \rho_j(p)=p.
 \label{ch13:eq:16}


@@ -477,7 +477,7 @@ The first operation of this function is implemented as kernels to be performed b
 \end{itemize}
 As mentioned previously, we develop the \emph{synchronous} and \emph{asynchronous}
 algorithms of the projected Richardson method. Obviously, in this scope, the
 \end{itemize}
 As mentioned previously, we develop the \emph{synchronous} and \emph{asynchronous}
 algorithms of the projected Richardson method. Obviously, in this scope, the

-synchronous\index{synchronous} or asynchronous\index{asynchronous} communications
+synchronous\index{synchronous iterations} or asynchronous\index{asynchronous iterations} communications

 refer to the communications between the CPU cores (MPI processes) on the GPU cluster,
 in order to exchange the vector elements associated to subdomain boundaries. For
 the memory copies between a CPU core and its GPU, we use the synchronous communication
 refer to the communications between the CPU cores (MPI processes) on the GPU cluster,
 in order to exchange the vector elements associated to subdomain boundaries. For
 the memory copies between a CPU core and its GPU, we use the synchronous communication


@@ -587,7 +587,7 @@ of relaxations is possible in both synchronous and asynchronous cases. On the
 other hand, an iteration is the update of at least all vector components with
 $F_i$.
 
 other hand, an iteration is the update of at least all vector components with
 $F_i$.
 

-In the synchronous\index{synchronous} algorithm, the global convergence is detected
+In the synchronous\index{synchronous iterations} algorithm, the global convergence is detected

 when the maximal value of the absolute error, $error$, is sufficiently small and/or
 the maximum number of relaxations, $MaxRelax$, is reached, as follows:
 $$
 when the maximal value of the absolute error, $error$, is sufficiently small and/or
 the maximum number of relaxations, $MaxRelax$, is reached, as follows:
 $$


@@ -602,7 +602,7 @@ where the function $AllReduce()$ uses the MPI global reduction subroutine\index{
 \verb+MPI_Allreduce()+ to compute the maximal value, $maxerror$, among the local
 absolute errors, $error$, of all computing nodes, and $p$ (in Algorithm~\ref{ch13:alg:02})
 is used as a counter of the local relaxations carried out by a computing node. In
 \verb+MPI_Allreduce()+ to compute the maximal value, $maxerror$, among the local
 absolute errors, $error$, of all computing nodes, and $p$ (in Algorithm~\ref{ch13:alg:02})
 is used as a counter of the local relaxations carried out by a computing node. In

-the asynchronous\index{asynchronous} algorithms, the global convergence is detected
+the asynchronous\index{asynchronous iterations} algorithms, the global convergence is detected

 when all computing nodes locally converge. For this, we use a token ring architecture
 around which a boolean token travels, in one direction, from a computing node to another.
 Starting from node $0$, the boolean token is set to $true$ by node $i$ if the local
 when all computing nodes locally converge. For this, we use a token ring architecture
 around which a boolean token travels, in one direction, from a computing node to another.
 Starting from node $0$, the boolean token is set to $true$ by node $i$ if the local


@@ -860,9 +860,9 @@ number of computing nodes on the cluster. This is due to the fact that the ratio
 between the time of the computation over that of the communication is reduced when
 the computations are performed on GPUs. Indeed, GPUs compute faster than CPUs and
 communications are more time-consuming. In this context, asynchronous algorithms
 between the time of the computation over that of the communication is reduced when
 the computations are performed on GPUs. Indeed, GPUs compute faster than CPUs and
 communications are more time-consuming. In this context, asynchronous algorithms

-are more scalable than synchronous ones. So, with large scale GPU clusters, synchronous\index{synchronous}
+are more scalable than synchronous ones. So, with large scale GPU clusters, synchronous\index{synchronous iterations}

 algorithms might be more penalized by communications, as can be deduced from Figure~\ref{ch13:fig:07}.
 algorithms might be more penalized by communications, as can be deduced from Figure~\ref{ch13:fig:07}.

-That is why we think that asynchronous\index{asynchronous} iterative algorithms
+That is why we think that asynchronous\index{asynchronous iterations} iterative algorithms

 are all the more interesting in this case.
 
 
 are all the more interesting in this case.