Sylvain Contassot-Vivier

Parallel iterative algorithms : from sequential to grid computing

Focusing on grid computing and asynchronism, Parallel Iterative Algorithms explores the theoretical and practical aspects of parallel numerical algorithms. Each chapter contains a theoretical discussion of the topic, an algorithmic section that fully details implementation examples and specific algorithms, and an evaluation of the advantages and drawbacks of the algorithms. Several exercises also appear at the end of most chapters. The first two chapters introduce the general features of sequential iterative algorithms and their applications to numerical problems. The book then describes different kinds of parallel systems and parallel iterative algorithms. It goes on to address both linear and nonlinear parallel synchronous and asynchronous iterative algorithms for numerical computation, with an emphasis on the multisplitting approach. The final chapter discusses the features required for efficient implementation of asynchronous iterative algorithms. Providing the theoretical and practical knowledge needed to design and implement efficient parallel iterative algorithms, this book illustrates how to apply these algorithms to solve linear and nonlinear numerical problems in parallel environments, including local, distant, homogeneous, and heterogeneous clusters.

SCILAB to SCILAB // : the Ouragan project

In this paper, we present the developments realized in the Ouragan project around the parallelization of a Matlab-like tool called Scilab. These developments use high-performance numerical libraries and different approaches based either on the duplication of Scilab processes or on computational servers. This tool, Scilab//, allows users to perform high-level operations on distributed matrices in a metacomputing environment. We also present performance results on different architectures.

Radiative transfer equation for predicting light propagation in biological media: comparison of a modified finite volume method, the Monte Carlo technique, and an exact analytical solution

Abstract. We examine the accuracy of a modified finite volume method compared to analytical and Monte Carlo solutions for solving the radiative transfer equation. The model is used for predicting light propagation within a two-dimensional absorbing and highly forward-scattering medium such as biological tissue subjected to a collimated light beam. Numerical simulations for the spatially resolved reflectance and transmittance are presented considering refractive index mismatch with Fresnel reflection at the interface, homogeneous and two-layered media. Time-dependent as well as steady-state cases are considered. In the steady state, it is found that the modified finite volume method is in good agreement with the other two methods. The relative differences between the solutions are found to decrease with spatial mesh refinement applied for the modified finite volume method obtaining <2.4%. In the time domain, the fourth-order Runge-Kutta method is used for the time semi-discretization of the radiative transfer equation. An agreement among the modified finite volume method, Runge-Kutta method, and Monte Carlo solutions are shown, but with relative differences higher than in the steady state.

Impact of asynchronism on GPU accelerated parallel iterative computations

We study the impact of asynchronism on parallel iterative algorithms in the particular context of local clusters of workstations including GPUs. The application test is a classical PDE problem of advection-diffusion-reaction in 3D. We propose an asynchronous version of a previously developed PDE solver using GPUs for the inner computations. The algorithm is tested with two kinds of clusters, a homogeneous one and a heterogeneous one (with different CPUs and GPUs).

An efficient multi-algorithms sparse linear solver for GPUs

We present a new sparse linear solver for GPUs. It is designed to work with structured sparse matrices where all the non-zeros are on a few diagonals. Several iterative algorithms are implemented, both on CPU and GPU. The GPU code is designed to be fast yet simple to read and understand. It aims to be as accurate as possible, even on chips that do not support double-precision floating-point arithmetic. Several benchmarks show that GPU algorithms are much faster than their CPU counterpart while their accuracy is satisfying.

Random Walk in a N-Cube Without Hamiltonian Cycle to Chaotic Pseudorandom Number Generation: Theoretical and Practical Considerations

Designing a pseudorandom number generator (PRNG) is a difficult and complex task. Many recent works have considered chaotic functions as the basis of built PRNGs: the quality of the output would indeed be an obvious consequence of some chaos properties. However, there is no direct reasoning that goes from chaotic functions to uniform distribution of the output. Moreover, embedding such kind of functions into a PRNG does not necessarily allow to get a chaotic output, which could be required for simulating some chaotic behaviors. In a previous work, some of the authors have proposed the idea of walking into a N-cube where a balanced Hamiltonian cycle has been removed as the basis of a chaotic PRNG. In this article, all the difficult issues observed in the previous work have been tackled. The chaotic behavior of the whole PRNG is proven. The construction of the balanced Hamiltonian cycle is theoretically and practically solved. An upper bound of the expected length of the walk to obtain a uniform distributio...

Canonical Form of Gray Codes in N-cubes

In previous works, the idea of walking into a \(\mathsf {N}\)-cube where a balanced Hamiltonian cycle have been removed has been proposed as the basis of a chaotic PRNG whose chaotic behavior has been proven. However, the construction and selection of the most suited balanced Hamiltonian cycles implies practical and theoretical issues. We propose in this paper a canonical form for representing isomorphic Gray codes. It provides a drastic complexity reduction of the exploration of all the Hamiltonian cycles and we discuss some criteria for the selection of the most suited cycles for use in our chaotic PRNG.

Generic Algorithmic Scheme for 2D Stencil Applications on Hybrid Machines

Hardware accelerators are classic scientific coprocessors in HPC machines. However, the number of CPU cores on the mother board is increasing and constitutes a non negligible part of the total computing power of the machine. So, running an application both on an accelerator like a GPU or a Xeon-Phi device and on the CPU cores can provide the highest performance. Moreover, it is now possible to include different accelerators in a machine, in order to support and to speedup a larger set of applications. Then, running an application part on the most suitable device allows to reach high performance, but using all unused devices in the machine should permit to improve even more the performance of that part. However, the overlapping of computations with inter-device data transfers is mandatory to limit the overhead of this approach, leading to complex asynchronous algorithms and multi-paradigm optimized codes. This article introduces our research and experiments on cooperation between several CPU and both a GPU and a Xeon-Phi accelerators, all included in a same machine.

Simulation of light propagation in biological tissue using a modified finite volume method applied to three-dimensional radiative transport equation

An important issue in tissue optics and Optical Tomography is to have an efficient forward solver. In this work, a new numerical algorithm was developed for solving light propagation with the radiative transport equation within a three-dimensional absorbing and a highly forward-scattering medium such as a biological tissue subjected to an incident beam. Both elastically scattered light and fluorescence light were studied. Two steady state problems used to assess the performance and accuracy of the proposed algorithm are presented. We show that it is possible to obtain a good level of accuracy with a deterministic numerical method: relative differences less than 1.7% and 4.5% were obtained when compared against Monte Carlo solutions for problems of elastically scattered light and fluorescence light, respectively.

A Near Linear Algorithm for Testing Linear Separability in Two Dimensions

We present a near linear algorithm for determining the linear separability of two sets of points in a two-dimensional space. That algorithm does not only detects the linear separability but also computes separation information. When the sets are linearly separable, the algorithm provides a description of a separation hyperplane. For non linearly separable cases, the algorithm indicates a negative answer and provides a hyperplane of partial separation that could be useful in the building of some classification systems.