Frédéric Magoulès

Two-level domain decomposition methods with Lagrange multipliers for the fast iterative solution of acoustic scattering problems

We present two different but related Lagrange multiplier based domain decomposition (DD) methods for solving iteratively large-scale systems of equations arising from the finite element discretization of high-frequency exterior Helmholtz problems. The proposed methods are essentially two distinct extensions of the regularized finite element tearing and interconnecting (FETI) method to indefinite or complex problems. The first method employs a single Lagrange multiplier field to glue the local solutions at the subdomain interface boundaries. The second method employs two Lagrange multiplier fields for that purpose. The key ingredients of both of these FETI methods are the regularization of each subdomain matrix by a complex lumped mass matrix defined on the subdomain interface boundary, and the preconditioning of the global interface problem by a coarse second-level problem constructed with planar waves. We show numerically that both methods are scalable with respect to the mesh size, the subdomain size, and the wavenumber, but that the FETI method with a single Lagrange multiplier field – labeled FETI-H (H for Helmholtz) in this paper – delivers superior computational performances. We apply the FETI-H method to the parallel solution on a 24-processor Origin 2000 of an acoustic scattering problem with a submarine shaped obstacle, and report performance results that highlight the unique efficiency of this DD method for the solution of high frequency acoustic scattering problems.

Parallel Support Vector Machines Applied to the Prediction of Multiple Buildings Energy Consumption

Analyzing the energy performance in a building is an important task in energy conservation. To accurately predict the energy consumption is difficult in practice since the building is a complex system with many parameters involved. To obtain enough historical data of energy uses and to find out an approach to analyze them become mandatory. In this paper, we propose a simulation method with the aim of obtaining energy data for multiple buildings. Support vector machines method with Gaussian kernel is applied to obtain the prediction model. For the first time, a parallel implementation of support vector machines is used to accelerate the model training process. Our experimental results show very good performance of this approach, paving the way for further applications of support vector machines method on large energy consumption datasets.

Vapnik's learning theory applied to energy consumption forecasts in residential buildings

For the purpose of energy conservation, we present in this paper an introduction to the use of support vector (SV) learning machines used as a data mining tool applied to buildings energy consumption data from a measurement campaign. Experiments using a SVM-based software tool for the prediction of the electrical consumption of a residential building is performed. The data included 1 year and 3 months of daily recordings of electrical consumption and climate data such as temperatures and humidities. The learning stage was done for a first part of the data and the predictions were done for the last month. Performances of the model and contributions of significant factors were also derived. The results show good performances for the model. The second experiment consists of model re-estimations on a 1-year daily recording dataset lagged at 1-day time intervals in such a way that we derive temporal series of influencing factors weights along with model performance criteria. Finally, we introduce a perturbation in one of the influencing variables to detect a model change. Comparing contributing weights with and without the perturbation, the sudden contributing weight change could have diagnosed the perturbation. The important point is the ease of the production of many models. This method announces future research work in the exploitation of possibilities of this ‘model factory’.

Feature Selection for Predicting Building Energy Consumption Based on Statistical Learning Method

Machine learning methods are widely studied and applied to predict building energy consumption. Since the factors associated with building energy behaviors are quite abundant and complex, this paper investigates for the first time how the selection of subsets of features influence the model performance when statistical learning method is adopted to derive the model. In this paper the optimal features are selected based on the feasibility of obtaining them and on the scores they provide under the evaluation of some filter methods. The selected subset is then evaluated on three data sets by support vector regression involving two kernel functions: radial basis function and polynomial function. Experimental results confirm the validity of the selected subset and show that the proposed feature selection method can guarantee the prediction accuracy and reduces the computational time for data analyzing.

SimMapReduce: A Simulator for Modeling MapReduce Framework

As a parallel programming framework, MapReduce has attracted more and more attention from both IT enterprises and research institutes that work for large dataset processing. SimMapReduce, a MapReduce simulator based on Grid Sim, is introduced to facilitate research on resource management and performance evaluation. With SimMapReduce simulator, researchers are free to implement scheduling algorithms and resource allocation policies by inheriting the provided java classes without concerns of implementation details. A File Manager is integrated to manage files transfers, so that the file transmission time is recorded and taken into account as a part of job completion time. Different simulation scenarios are modeled by predefining parameters in a configuration file. Experiment results illustrate that SimMapReduce can be easily executed in a personal computer and can provide qualitative analysis for MapReduce systems.

A Hadoop MapReduce Performance Prediction Method

More and more Internet companies rely on large scale data analysis as part of their core services for tasks such as log analysis, feature extraction or data filtering. Map-Reduce, through its Hadoop implementation, has proved to be an efficient model for dealing with such data. One important challenge when performing such analysis is to predict the performance of individual jobs. In this paper, we propose a simple framework to predict the performance of Hadoop jobs. It is composed of a dynamic light-weight Hadoop job analyzer, and a prediction module using locally weighted regression methods. Our framework makes some theoretical cost models more practical, and also well fits for the diversification of the jobs and clusters. It can also help those users who want to predict the cost when applying for an on-demand cloud service. At the end, we do some experiments to verify our framework.

Iterative Methods for Sparse Linear Systems on Graphics Processing Unit

Many engineering and science problems require a computational effort to solve large sparse linear systems. Krylov subspace based iterative solvers have been widely used in that direction. Iterative Krylov methods involve linear algebra operations such as summation of vectors, dot product, norm, and matrix-vector multiplication. Since these operations could be very costly in computation time on Central Processing Unit (CPU), we propose in this paper to focus on the design of iterative solvers to take advantage of massive parallelism of Graphics Processing Unit (GPU). We consider Stabilized BiConjugate Gradient (BiCGStab), Stabilized BiConjugate Gradient (L) (BiCGStabl), Generalized Conjugate Residual (P-GCR), Bi-Conjugate Gradient Conjugate Residual (P-BiCGCR), transpose-free Quasi Minimal Residual (P-tfQMR) for the solution of sparse linear systems with non symmetric matrices and Conjugate Gradient (CG) for symmetric positive definite matrices. We discuss data format and data structure for sparse matrices, and how to efficiently implement these solvers on the Nvidias CUDA platform. The scalability and performance of the methods are tested on several engineering problems, together with numerous numerical experiments which clearly illustrate the robustness, competitiveness and efficiency of our own proper implementation compared to the existing libraries.

Algebraic approach to absorbing boundary conditions for the Helmholtz equation

Recent work has shown that designing absorbing boundary conditions through algebraic approaches may be a nice alternative to the continuous approaches based on a Fourier analysis. In this paper, an original algebraic technique based on the computation of small patches is presented for the Helmholtz equation. This new technique is not directly linked to the continuous equations of the problem, nor to the numerical scheme. These properties make this technique very convenient to implement in a domain decomposition context. The proposed algebraic absorbing boundary conditions are used in a non-overlapping domain decomposition method and are defined on the interface between the subdomains. An additional coarse grid correction is then applied to ensure full scalability of the domain decomposition method upon the number of subdomains. This coarse grid correction involves trigonometric functions defined on the interface between the subdomains. Numerical experiments are presented and illustrate the robustness and parallel efficiency of the proposed method for acoustics applications.

Fast sparse matrix-vector multiplication on graphics processing unit for finite element analysis

Finite element analysis involves the solution of linear systems described by large size sparse matrices. Iterative Krylov methods are well suited for such type of problems. These methods require linear algebra operations, including sparse matrix-vector multiplication which can be computationally expensive for large size matrices. In this paper, we present the best way to perform these operations, in double precision, on Graphics Processing Unit (GPU). Several linear algebra libraries are considered and compared to our proper implementation. These libraries and our proper implementation are then integrated within an iterative Krylov method on the GPU. Numerical experiments done on a set of finite element matrices are presented and illustrate the performance, robustness and accuracy of our proper implementation compared to the existing libraries and its suitability for finite element analysis. Dynamic tuning of the gridification, upon the GPU architecture and the finite element matrix characteristics, is finally applied to faster the sparse matrix-vector multiplication operation.

Analysis of Patch Substructuring Methods

Analysis of Patch Substructuring Methods Patch substructuring methods are non-overlapping domain decomposition methods like classical substructuring methods, but they use information from geometric patches reaching into neighboring subdomains, condensated on the interfaces, to enhance the performance of the method, while keeping it non-overlapping. These methods are very convenient to use in practice, but their convergence properties have not been studied yet. We analyze geometric patch substructuring methods for the special case of one patch per interface. We show that this method is equivalent to an overlapping Schwarz method using Neumann transmission conditions. This equivalence is obtained by first studying a new, algebraic patch method, which is equivalent to the classical Schwarz method with Dirichlet transmission conditions and an overlap corresponding to the size of the patches. Our results motivate a new method, the Robin patch method, which is a linear combination of the algebraic and the geometric one, and can be interpreted as an optimized Schwarz method with Robin transmission conditions. This new method has a significantly faster convergence rate than both the algebraic and the geometric one. We complement our results by numerical experiments.