In recent years, the scalability of large-scale implementation in a
distributed environment of algorithms becoming more and more complex has
always been hampered by the limits of physical computing resources
In recent years, the scalability of large-scale implementation in a
distributed environment of algorithms becoming more and more complex has
always been hampered by the limits of physical computing resources
during the execution. Two important factors determine the success of the
experimentation: the convergence of the iterative algorithm on a large
scale and the execution time reduction in asynchronous mode. Once again,
during the execution. Two important factors determine the success of the
experimentation: the convergence of the iterative algorithm on a large
scale and the execution time reduction in asynchronous mode. Once again,
accurate results which are difficult or even impossible to obtain in a
physical platform by exploiting the flexibility of the simulator on the
computing units clusters and the network structure design. Our
accurate results which are difficult or even impossible to obtain in a
physical platform by exploiting the flexibility of the simulator on the
computing units clusters and the network structure design. Our
simulated large scale growing environment and with larger problem size.
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simulated large scale growing environment and with larger problem size.
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the field. Indeed, the increasing complexity of these requested
applications combined with a continuous increase of their sizes lead to
write distributed and parallel algorithms requiring significant hardware
the field. Indeed, the increasing complexity of these requested
applications combined with a continuous increase of their sizes lead to
write distributed and parallel algorithms requiring significant hardware
-resources (grid computing, clusters, broadband network, etc\dots{}) but
+resources (grid computing, clusters, broadband network, etc.) but
also a non-negligible CPU execution time. We consider in this paper a
class of highly efficient parallel algorithms called iterative executed
in a distributed environment. As their name suggests, these algorithm
also a non-negligible CPU execution time. We consider in this paper a
class of highly efficient parallel algorithms called iterative executed
in a distributed environment. As their name suggests, these algorithm
iterations ($X_{n +1} = f(X_{n})$) from an initial value $X_{0}$ to find
an approximate value $X^*$ of the solution with a very low
residual error. Several well-known methods demonstrate the convergence
iterations ($X_{n +1} = f(X_{n})$) from an initial value $X_{0}$ to find
an approximate value $X^*$ of the solution with a very low
residual error. Several well-known methods demonstrate the convergence
section will give a brief description of iterative asynchronous model.
Then, the simulation framework SimGrid will be presented with the
settings to create various distributed architectures. The algorithm of
section will give a brief description of iterative asynchronous model.
Then, the simulation framework SimGrid will be presented with the
settings to create various distributed architectures. The algorithm of
and its adaptation to SimGrid with SMPI (Simulated MPI) will be in the
next section. At last, the experiments results carried out will be
presented before the conclusion which we will announce the opening of
and its adaptation to SimGrid with SMPI (Simulated MPI) will be in the
next section. At last, the experiments results carried out will be
presented before the conclusion which we will announce the opening of
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\section{Simulation of the multisplitting method}
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\section{Simulation of the multisplitting method}
the expected results, varying the input parameters and the program arguments
allows us to compare outputs from the code execution. We have noticed from this
study that the results depend on the following parameters: (1) at the network
the expected results, varying the input parameters and the program arguments
allows us to compare outputs from the code execution. We have noticed from this
study that the results depend on the following parameters: (1) at the network
network latency (lat). (2) Hosts power (GFlops) can also influence on the
results. And finally, (3) when submitting job batches for execution, the
arguments values passed to the program like the maximum number of iterations or
network latency (lat). (2) Hosts power (GFlops) can also influence on the
results. And finally, (3) when submitting job batches for execution, the
arguments values passed to the program like the maximum number of iterations or
algorithm but also to get the main objective of the experimentation of the
simulation in having an execution time in asynchronous less than in synchronous
algorithm but also to get the main objective of the experimentation of the
simulation in having an execution time in asynchronous less than in synchronous
-mode, in others words, in having a ``speedup'' less than 1 (Speedup = Execution
-time in synchronous mode / Execution time in asynchronous mode).
+mode, in others words, in having a \emph{speedup} less than 1
+({speedup}${}={}${execution time in synchronous mode}${}/{}${execution time in
+asynchronous mode}).
A priori, obtaining a speedup less than 1 would be difficult in a local area
network configuration where the synchronous mode will take advantage on the rapid
A priori, obtaining a speedup less than 1 would be difficult in a local area
network configuration where the synchronous mode will take advantage on the rapid
As a first step, the algorithm was run on a network consisting of two clusters
containing fifty hosts each, totaling one hundred hosts. Various combinations of
the above factors have providing the results shown in Table~\ref{tab.cluster.2x50} with a matrix size
As a first step, the algorithm was run on a network consisting of two clusters
containing fifty hosts each, totaling one hundred hosts. Various combinations of
the above factors have providing the results shown in Table~\ref{tab.cluster.2x50} with a matrix size
$171^{3} = \np{5211000}$ entries.
Then we have changed the network configuration using three clusters containing
$171^{3} = \np{5211000}$ entries.
Then we have changed the network configuration using three clusters containing
\item Description of the cluster architecture;
\item Maximum number of internal and external iterations;
\item Internal and external precisions;
\item Description of the cluster architecture;
\item Maximum number of internal and external iterations;
\item Internal and external precisions;
- \item Matrix size NX, NY and NZ;
- \item Matrix diagonal value = 6.0;
+ \item Matrix size $N_x$, $N_y$ and $N_z$;
+ \item Matrix diagonal value: \np{6.0};
The experimental results on executing a parallel iterative algorithm in
asynchronous mode on an environment simulating a large scale of virtual
computers organized with interconnected clusters have been presented.
The experimental results on executing a parallel iterative algorithm in
asynchronous mode on an environment simulating a large scale of virtual
computers organized with interconnected clusters have been presented.
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