Use of A Network Enabled Server System for a Sparse Linear Algebra Grid Application

Solving systems of linear equations is one of the key operations in linear algebra. Many different algorithms are available in that purpose. These algorithms require a very accurate tuning to minimise runtime and memory consumption. The TLSE project provides, on one hand, a scenario-driven expert site to help users choose the right algorithm according to their problem and tune accurately this algorithm, and, on the other hand, a test-bed for experts in order to compare algorithms and define scenarios for the expert site. Both features require to run the available solvers a large number of times with many different values for the control parameters (and maybe with many different architectures). Currently, only the grid can provide enough computing power for this kind of application. The DIET middleware is the GRID backbone for TLSE. It manages the solver services and their scheduling in a scalable way.La résolution de systèmes linéaires creux est une opération clé en algèbre linéaire. Beaucoup d’algorithmes sont utilisés pour cela, qui dépendent de nombreux paramètres, afin d’offrir une robustesse, une performance et une consommation mémoire optimales. Le projet GRID-TLSE fournit d’une part, un site d’expertise basé sur l’utilisation de scénarios pour aider les utilisateurs à choisir l’algorithme qui convient le mieux à leur problème ainsi que les paramètres associés; et d’autre part, un environnement pour les experts du domaine leur permettant de comparer efficacement des algorithmes et de définir dynamiquement de nouveaux scénarios d’utilisation. Ces fonctionnalités nécessitent de pouvoir exécuter les logiciels de résolution disponibles un grand nombre de fois,avec beaucoup de valeurs différentes des paramètres de contrôle (et éventuellement sur plusieurs architectures de machines). Actuellement, seule la grille peut fournir la puissance de calcul pour ce type d’applications. L’intergiciel DIETest utilisé pour gérer la grille, les différents services, et leur ordonnancement efficace

An unsymmetrized multifrontal LU factorization

A well-known approach to compute the LU factorization of a general unsymmetric matrix A is to build the elimination tree associated with the pattern of the symmetric matrix A + A rm T and use it as a computational graph to drive the numerical factorization. This approach, although very efficient on a large range of unsymmetric matrices, does not capture the unsymmetric structure of the matrices. We introduce a new algorithm which detects and exploits the structural unsymmetry of the submatrices involved during the process of the elimination tree. We show that with the new algorithm significant gains both in memory and in time to perform the factorization can be obtained

An Unsymmetrized Multifrontal LU Factorization

A well known approach to compute the LU factorization of a general unsymmetric matrix A is to build the elimination tree associated with the pattern of the symmetric matrix A+A T and use it as a computational graph to drive the numerical factorization. This approach, although very efficient on a large range of unsymmetric matrices, does not capture the unsymmetric structure of the matrices. We introduce a new algorithm which detects and exploits the structural asymmetry of the submatrices involved during the processing of the elimination tree. We show that, with the new algorithm, significant gains both in memory and in time to perform the factorization can be obtained

Management of Services Based on a Semantic Description Within the GRID-TLSE Project

International audienceThe goal of the GRID-TLSE Project is to design an expert site that provides an easy access to a number of tools allowing comparative analysis of sparse matrix packages on a user-submitted problem, as well as on particular matrices from the matrix collection also available on the site. When making available a large amount of software over a computational Grid, facilitating its deployment and its exploitation become crucial. Within the GRID-TLSE Project, we use a software component approach based on a high level semantic description of the scientific computing services. In this paper, we focus on one aspect of this description of the computational services: the use of meta-data called abstract parameters. Our approach allows the automatic discovery and the exploitation of new services throught the concept of scenario

GRID-TLSE: A Web Site for Experimenting with Sparse Direct Solvers on a Computational Grid

International audienceno abstrac

Parallel Algorithms for Structured Systems of Linear Equations

International audienceno abstrac

An Overview of the GRID-TLSE Project

International audienc

An Overview of the GRID-TLSE Project

International audienc

Does 3D frequency-domain FWI of full-azimuth/long-offset OBN data feasible? The Gorgon case study

Frequency-domain Full Waveform Inversion (FWI) is potentially amenable to efficient processing of full-azimuth long-offset stationary-recording seabed acquisition carried out with sparse layout of ocean bottom nodes (OBNs) and broadband sources because the inversion can be performed with a few discrete frequencies. However, computing efficiently the solution of the forward (boundary-value) problem in the frequency domain with linear algebra solvers remains a challenge for large computational domains involving tens to hundreds of millions of parameters. We illustrate the feasibility of 3D frequency-domain FWI with the 2015/16 Gorgon OBN case study in the NorthWestern shelf, Australia. We solve the forward problem with the massively-parallel multifrontal direct solver MUMPS, which includes four key features to reach high computational efficiency: An efficient parallelism combining message-passing interface and multithreading, block low-rank compression, mixed precision arithmetic and efficient processing of sparse sources. The Gorgon subdataset involves 650 OBNs that are processed as reciprocal sources and 400,000 sources. Mono-parameter FWI for vertical wavespeed is performed in the visco-acoustic VTI approximation with a classical frequency continuation approach proceeding from a starting frequency of 1.7 Hz to a final frequency of 13 Hz. The target covers an area ranging from 260 km2 (frequency > 8.5 Hz) to 705 km2 (frequency < 8.5 Hz) for a maximum depth of 8 km. Compared to the starting model, FWI dramatically improves the reconstruction of the bounding faults of the Gorgon horst at reservoir depths as well as several intra-horst faults and several horizons of the Mungaroo formation down to a depth of 7 km