Efficient Grid Resource Selection for a CEM Application

Eddy CARON, Cristian KLEIN, Christian P EREZLIP, Ecole Normale Superieur de Lyon,46 Allee d'Italie69364 Lyon, FrancefEddy.Caron,Cristian.Klein g@ens-lyon.fr, Christian.Perez@inria.frResum eComputational Electromagnetics (CEM) is a domain which provides numerical solutions to compute an-tenna performance, electromagnetic compatibility, radar cross section and electromagnetic wave propaga-tion. The ever-increasing need for more precision and larger meshes raises the natural question whetherit is worth porting CEM algorithms to computer grids. Due to the nature of the computations, CEM al-gorithms are not trivially parallelisable, as data dependency inside the mesh implies communication. Thegoal of this paper is to answer the question: given a set of resources, what is the subset of resources oneshould chose among, to minimise the time it takes to solve a CEM problem. After presenting a model ofthe application execution time, several algorithms for selecting resources are described. The limits of thetheoretical model is then compared against experimental results, obtained from the Grid'5000 platform.Mots-cles : CEM, Grid, Mapping, Grid'50001. IntroductionPartial Di erential Equations (PDE) are involved in the solution to many problems, like car crash testsimulation or dynamics uid. However, solving the PDEs by variables elimination is dicult for all butthe simple cases. For solving real-world problems, one may use the Finite Element Method (FEM), whichconsists in representing the space as a mesh. The resulting algorithms are non-trivially parallelisable,having irregular computations. As the size of the meshes increases, the question whether such applicationscould be speed up by deploying them in grid environments is naturally raised. The DiscoGrid project [1]aims to eciently use hierarchical platforms, by proposing a message-passing API [3] with hierarchy-speci c functions, which would allow an application to take better data-placement decisions. For example,the project focuses on Computational ElectroMagnetics (CEM) applications, which uses the FEM to solveelectromagnetic problems.The MAXDG1 software is used for the numerical resolution of the three-dimensional Maxwell equationsin the time domain, for heterogeneous media and using tetrahedral unstructured meshes. Initially paral-lelized using MPI, it has already been ported to use the DiscoGrid API. Running the application consistsin two steps. First, the mesh is being partitioned based on a resource description le, having the abilityto assign bigger meshes to resources with more computation power. This is achieved using the partIttool [4]. Second, the created submeshes are used to launch the application on the chosen resources.Given a hierarchical topology, partIt is able to eciently partition the mesh to minimise communicationbetween resources, however, partitioning is always done for all resources, without taking into accountthat communication time might actually slow down the application. This article studies how to improveon this, and, given a set of resources and a mesh, how to choose the subset of resources which wouldminimise the execution time of the application.The remaining of the paper is organised as follows: Section2introduces the application and resourcemodel used to estimate the execution time; Section3presents and compares several algorithms to select