- In a grid environment, it is common to distinguish, on the one hand, the
- "intra-network" which refers to the links between nodes within a cluster and
- on the other hand, the "inter-network" which is the backbone link between
- clusters. In practice, these two networks have different speeds.
- The intra-network generally works like a high speed local network with a
- high bandwith and very low latency. In opposite, the inter-network connects
- clusters sometime via heterogeneous networks components throuth internet with
- a lower speed. The network between distant clusters might be a bottleneck
- for the global performance of the application.
-
-\subsection{Comparison of GMRES and Krylov Multisplitting algorithms in synchronous mode}
-
-In the scope of this paper, our first objective is to analyze when the Krylov
-Multisplitting method has better performance than the classical GMRES
-method. With a synchronous iterative method, better performance means a
-smaller number of iterations and execution time before reaching the convergence.
-For a systematic study, the experiments should figure out that, for various
-grid parameters values, the simulator will confirm the targeted outcomes,
-particularly for poor and slow networks, focusing on the impact on the
-communication performance on the chosen class of algorithm.
-
-The following paragraphs present the test conditions, the output results
-and our comments.\\
-
-
-\subsubsection{Execution of the algorithms on various computational grid
-architectures and scaling up the input matrix size}
-\ \\
-% environment
+ In a grid environment, it is common to distinguish, on one hand, the
+ \textit{intra-network} which refers to the links between nodes within a
+ cluster and on the other hand, the \textit{inter-network} which is the
+ backbone link between clusters. In practice, these two networks have
+ different speeds. The intra-network generally works like a high speed
+ local network with a high bandwidth and very low latency. In opposite, the
+ inter-network connects clusters sometime via heterogeneous networks components
+ through internet with a lower speed. The network between distant clusters
+ might be a bottleneck for the global performance of the application.
+
+
+\subsection{Comparison between GMRES and two-stage multisplitting algorithms in
+synchronous mode}
+In the scope of this paper, our first objective is to analyze
+when the synchronous Krylov two-stage method has better performance than the
+classical GMRES method. With a synchronous iterative method, better performance
+means a smaller number of iterations and execution time before reaching the
+convergence.
+
+Table~\ref{tab:01} summarizes the parameters used in the different simulations:
+the grid architectures (i.e. the number of clusters and the number of nodes per
+cluster), the network of inter-clusters backbone links and the matrix sizes of
+the 3D Poisson problem. However, for all simulations we fix the network
+parameters of the intra-clusters links: the bandwidth $bw$=10Gbs and the latency
+$lat=8\mu$s. In what follows, we will present the test conditions, the output
+results and our comments.
