We present load-balancing strategies to improve performances of parallel MPI applications running in a Grid environment. We analyze the data distribution constraints found in two scientific codes and propose adapted code transformations to load-balance computations. We present the general framework for our load-balancing techniques. We then describe these techniques as well as their application to our examples. Experimental results confirm that adapted source code transformations can improve Grid application performances.

Abstract. We present a particle-mesh N-body integrator running on GPU using CUDA. Relying on a grid-based description of the gravitational potential, it can simulate the evolution of self-interacting 'stars' in order to model e.g. galaxies. All the steps of the application have been ported on the GPU , namely 1/ an histogramming algorithm with CUDPP, 2/ of the resolution of the Poisson equation by means of FFT with CUFFT and multi-grid relaxation, 3/ of an optimized finitedifference scheme to compute the accelerations of stars and 4/ of an update procedure for positions and velocities. We present several tests at different resolution, and reach a speedup from 2 to 50 depending on the resolution and on the test case.

A general overview is given of the use of massively parallel computers in the determination of electromagnetic fields. The emphasis is on parallel machines with a single-instruction multiple-data ) architecture, in which all processing elements (PE's) execute the same instruction but on different data elements stored in their local memory. Various measures of program performance are critically discussed as is the issue of scalability of the Computations. An analysis of the parallelism inherent in the method of moments (MOM), the finite-difference time-domain (FDTD) method, and the finite element method (FEM) is presented. Since communication is an important component in a parallel algorithm, the interconnection network between processors becomes an essential consideration in program analysis. Most of the discussion centers around two-dimensional meshes and hypercubes, complemented by a brief overview of embedding theory, which allows other networks to be emulated.These theoretical concepts are illustrated on a specific example involving the modeling, by the FDTD method, of the scattering of a plane wave off a dielectric sphere. Calculations were performed on the MasPar MP-1 family of SIMD computers. Specific models used contain between 1,024 and 8,192 processors arranged in a two-dimensional mesh with nearest and next-nearest neighbor connections between PE's. Code development, starting from a sequential program, is discussed, as are the details of the data mapping. Timing results are presented for a range of problem sizes and show considerable speed-up compared to sequential programming. These results are compared and contrasted with those obtained by other authors.

In direct and large eddy simulations, turbulence in flows is often sustained using a random excitation. In this paper, the problem of receptivity of a linearized stable dynamical system to stochastic perturbations is reformulated in terms of the Lyapunov equation. The latter provides directly the statistical characterization of the random solution. It is shown how to describe the excitation term to obtain a time-step invariant response. The solution of the Lyapunov equation is equivalent to the spatial correlation matrix of the proper orthogonal decomposition ͑POD͒. It can thus be further post-treated to yield POD modes. The method is tested in the case of a weakly turbulent slightly heated jet by comparing the results obtained by statistical accumulation of data provided by a fully nonlinear unsteady Navier-Stokes simulation to the solution of the Lyapunov equation. The traces and POD modes are found in a very good agreement. The obtained results not only validate the method but also show that some flows may respond in an essentially linear way to random excitation and that, in this case, the direct statistical approach is more efficient and provides more reliable results than the classical Monte Carlo approach.

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