Comparison of numerical solvers for anisotropic diffusion equations arising in plasma physics

International audienceThis work is devoted to the comparison of numerical schemes to approximate anisotropic diffusion problems arising in tokamak plasma physics. We focus on the spatial approximation by using finite volume method and on the time discretization. This latter point is delicate since the use of explicit integrators leads to a severe restriction on the time step. Then, implicit and semi-implicit schemes are coupled to finite volumes space discretization and are compared for some classical problems relevant for magnetically confined plasmas. It appears that the semi-implicit approaches (using ARK methods or directional splitting) turn out to be the most efficient on the numerical results, especially when nonlinear problems are studied on refined meshes, using high order methods in space

Automatic Collapsing of Non-Rectangular Loops

International audienceLoop collapsing is a well-known loop transformation which combines some loops that are perfectly nested into one single loop. It allows to take advantage of the whole amount of parallelism exhibited by the collapsed loops, and provides a perfect load balancing of iterations among the parallel threads. However, in the current implementations of this loop optimization , as the ones of the OpenMP language, automatic loop collapsing is limited to loops with constant loop bounds that define rectangular iteration spaces, although load imbalance is a particularly crucial issue with non-rectangular loops. The OpenMP language addresses load balance mostly through dynamic runtime scheduling of the parallel threads. Nevertheless, this runtime schedule introduces some unavoidable execution-time overhead, while preventing to exploit the entire parallelism of all the parallel loops. In this paper, we propose a technique to automatically collapse any perfectly nested loops defining non-rectangular iteration spaces, whose bounds are linear functions of the loop iterators. Such spaces may be triangular, tetrahedral, trapezoidal, rhomboidal or parallelepiped. Our solution is based on original mathematical results addressing the inversion of a multi-variate polynomial that defines a ranking of the integer points contained in a convex polyhedron. We show on a set of non-rectangular loop nests that our technique allows to generate parallel OpenMP codes that outperform the original parallel loop nests, parallelized either by using options " static " or " dynamic " of the OpenMP-schedule clause

Multifor for Multicore

International audienceWe propose a new programming control structure called ''multifor'', allowing to take advantage of parallelization models that were not naturally attainable with the polytope model before. In a multifor-loop, several loops whose bodies are run simultaneously can be defined. Respective iteration domains are mapped onto each other according to a run frequency -- the grain -- and a relative position -- the offset --. Execution models like dataflow, stencil computations or MapReduce can be represented onto one referential iteration domain, while still exhibiting traditional polyhedral code analysis and transformation opportunities. Moreover, this construct provides ways to naturally exploit hybrid parallelization models, thus significantly improving parallelization opportunities in the multicore era. Traditional polyhedral software tools are used to generate the corresponding code. Additionally, a promising perspective related to non-linear mapping of iteration spaces is also presented, yielding to run a loop nest inside any other one by solving the problem of inverting "ranking Ehrhart polynomials"

Loop-based Modeling of Parallel Communication Traces

This paper describes an algorithm that takes a trace of a distributed program and builds a model of all communications of the program. The model is a set of nested loops representing repeated patterns. Loop bodies collect events representing communication actions performed by the various processes, like sending or receiving messages, and participating in collective operations. The model can be used for compact visualization of full executions, for program understanding and debugging, and also for building statistical analyzes of various quantitative aspects of the program's behavior. The construction of the communication model is performed in two phases. First, a local model is built for each process, capturing local regularities; this phase is incremental and fast, and can be done on-line, during the execution. The second phase is a reduction process that collects, aligns, and finally merges all local models into a global, system-wide model. This global model is a compact representation of all communications of the original program, capturing patterns across groups of processes. It can be visualized directly and, because it takes the form of a sequence of loop nests, can be used to replay the original program's communication actions. Because the model is based on communication events only, it completely ignores other quantitative aspects like timestamps or messages sizes. Including such data would in most case break regularities, reducing the usefulness of trace-based modeling. Instead, the paper shows how one can efficiently access quantitative data kept in the original trace(s), by annotating the model and compiling data scanners automatically.Ce rapport de recherche décrit un algorithme qui prend en entrée la trace d'un programme distribué, et construit un modèle de l'ensemble des communications du programme. Le modèle prend la forme d'un ensemble de boucles imbriquées représentant la répétition de motifs de communication. Le corps des boucles regroupe des événements représentant les actions de communication réalisées par les différents processus impliqués, tels que l'envoi et la réception de messages, ou encore la participation à des opérations collectives. Le modèle peut servir à la visualisation compact d'exécutions complètes, à la compréhension de programme et au debugging, mais également à la construction d'analyses statistiques de divers aspects quantitatifs du comportement du programme. La construction du modèle de communication s'effectue en deux phases. Premièrement, un modèle local est construit au sein de chaque processus, capturant les régularités locales~; cette phase est incrémentale et rapide, et peut être réalisée au cours de l'exécution. La seconde phase est un processus de réduction qui rassemble, aligne, et finalement fusionne tous les modèles locaux en un modèle global décrivant la totalité du système. Ce modèle global est une représentation compacte de toutes les communications du programme original, représentant des motifs de communication entre groupes de processus. Il peut être visualisé directement et, puisqu'il prend la forme d'un ensemble de nids de boucles, peut servir à rejouer les opérations de communication du programme initial. Puisque le modèle construit se base uniquement sur les opérations de communication, il ignore complètement d'autres données quantitatives, telles que les informations chronologiques, ou les tailles de messages. L'inclusion de telles données briserait dans la plupart des cas les régularités topologiques, réduisant l'efficacité de la modélisation par boucles. Nous préférons, dans ce rapport, montrer comment, grâce au modèle construit, il est possible d'accéder efficacement aux données quantitatives si celles-ci sont conservées dans les traces individuelles, en annotant le modèle et en l'utilisant pour compiler automatiquement des programmes d'accès aux données

Controls on variations in sedimentary deposits produced by a retreating ice stream grounding line

The majority of glaciers draining the Antarctic Peninsula Ice Sheet are thinning and retreating rapidly1. It is widely understood that these changes are driven by both a warming ocean and atmosphere. However, there are other mechanisms, including pinning points created by bathymetric highs and a reverse bed gradient, that are thought to have an important control on ice stream behaviour (Weertman, 1974; Jamieson et al., 2012). Our understanding of the interplay between these mechanisms and time-scales over which they are important is currently limited in time to the advent of satellite monitoring. By reconstructing the cause and style of ice stream retreat following the Last Glacial Maximum (LGM; 25-19 ka BP), it is possible to gain a greater insight into the mechanisms which drive glacier retreat (Ó Cofaigh et al., 2014). Sedimentary sequences deposited during the LGM and the subsequent deglaciation on polar continental shelves, provide an important archive of past changes (Ó Cofaigh et al., 2014). Previous studies have typically identified three sediment facies assemblages; sub-glacial, transitional and open marine (Ó Cofaigh et al., 2014; Domack et al., 1988; Smith et al., 2011). Transitional sediment facies are deposited at the grounding line and are often targeted for radiocarbon dating, as they represent the onset of glaciomarine sedimentation following the retreat of grounded ice (Domack et al., 1988; Smith et al., 2014; Heroy et al., 1996). Despite the development of depositional models to help explain the processes occurring at grounding lines (Powell et al., 1995 and 1996), there is still significant uncertainty about the temporal and spatial variations in grounding line sedimentation along and across a palaeo-ice stream trough. Here we use a multi-proxy approach (water content, shear strength, magnetic susceptibility, density, contents of biogenic opal, Total Organic Carbon and CaCO3, grain size distribution and X-radiographs) on marine sediment cores recovered from the Anvers-Hugo Palaeo-Ice Stream Trough (AHT), western Antarctic Peninsula shelf, to identify variability in transitional sediment facies deposited along and across the trough. We discuss possible controls on the variability in transitional sediment facies and how this is related to the rate and style of ice stream retreat. Our data reveal systematic variability in the types and volume of transitional sediments deposited during the last deglaciation of AHT. A detailed analysis of the transitional sediment facies shows that this variability reflects different phases of ice stream behaviour. Large volumes of ice proximal sediment facies recovered seawards of grounding zone wedges are indicative of episodes of grounding line still-stands. Re-advances of the grounding line, concurrent with a shallowing of the reverse bed gradient and a narrowing of the trough, appear to have occurred during the final stages of deglaciation. This is indicated by interlaminated ice-proximal and ice-distal sediment facies within inner shelf cores. Transitional sediment variability additionally captures the evolution of the ice stream during deglaciation, including the formation of a small ice shelf on the inner shelf. Keywords: Antarctic Peninsula, Last Glacial Maximum, ice stream, sediment cores References Cook, A. J., Holland, P. R., Meredith, M. P., Murray, T., Luckman, A. & Vaughan, D. G, 2016. Ocean forcing of glacier retreat in the western Antarctic Peninsula. Science, 353, 283-286. Weertman, J, 1974. Stability of the Junction of an Ice Sheet and an Ice Shelf. Journal of Glaciology, 13, 3-11. Jamieson, S. S. R., Vieli, A., Livingstone, S. J., Cofaigh, C. O., Stokes, C., Hillenbrand, C.-D. & Dowdeswell, J. A, 2012. Ice-stream stability on a reverse bed slope. Nature Geoscience, 5, 799-802. Ó Cofaigh, C., Davies, B. J., Livingstone, S. J., Smith, J. A., Johnson, J. S., Hocking, E. P., Hodgson, D. A., Anderson, J. B., Bentley, M. J., Canals, M., Domack, E., Dowdeswell, J. A., Evans, J., Glasser, N. F., Hillenbrand, C.-D., Larter, R. D., Roberts, S. J. & Simms, A. R, 2014. Reconstruction of ice-sheet changes in the Antarctic Peninsula since the Last Glacial Maximum. Quaternary Science Reviews, 100, 87-110. Domack, E. W. & Harris, P. T, 1998. A new depositional model for ice shelves, based upon sediment cores from the Ross Sea and the Mac. Robertson shelf, Antarctica. Annals of Glaciology, 27, 281-284. Smith, J. A., Hillenbrand, C.-D., Kuhn, G., Larter, R. D., Graham, A. G. C., Ehrmann, W., Moreton, S. G. & Forwick, M, 2011. Deglacial history of the West Antarctic Ice Sheet in the western Amundsen Sea Embayment. Quaternary Science Reviews, 30, 488-505. Smith, J. A., Hillenbrand, C.-D., Kuhn, G., Klages, J. P., Graham, A. G. C., Larter, R. D., Ehrmann, W., Moreton, S. G., Wiers, S. & Frederichs, T, 2014. New constraints on the timing of West Antarctic Ice Sheet retreat in the eastern Amundsen Sea since the Last Glacial Maximum. Global and Planetary Change, 122, 224-237. Heroy, D. C. & Anderson, J. B, 1996. Radiocarbon constraints on Antarctic Peninsula Ice Sheet retreat following the Last Glacial Maximum (LGM). Quaternary Science Reviews, 26, 3286-3297. Powell, R. D., Dawber, M., McInnes, J. N. & Pyne, A. R, 1996. Observations of the Grounding-line Area at a Floating Glacier Terminus. Annals of Glaciology, 22, 217-223. 1Powell, R. D. & Domack, E, 1995. Modern Glacimarine Environments. In: Glacial Environments, Volume 1 (ed. J Menzies). Butterworth-Heinemann, 445-486

History of Anvers-Hugo Trough, western Antarctic Peninsula shelf, since the Last Glacial Maximum. Part I: Deglacial history based on new sedimentological and chronological data

Reconstructing the advance and retreat of past ice sheets provides important long-term context for recent change(s) and enables us to better understand ice sheet responses to forcing mechanisms and external boundary conditions that regulate grounding line retreat. This study applies various radiocarbon dating techniques, guided by a detailed sedimentological analyses, to reconstruct the glacial history of Anvers-Hugo Trough (AHT), one of the largest bathymetric troughs on the western Antarctic Peninsula (WAP) shelf. Existing records from AHT indicate that the expanded Antarctic Peninsula Ice Sheet (APIS) advanced to, or close to, the continental shelf edge during the Last Glacial Maximum (LGM; 23-19 cal kyr BP [ = calibrated kiloyears before present]), with deglaciation of the outer shelf after ∼16.3 cal kyr BP. Our new chronological data show that the APIS had retreated to the middle shelf by ∼15.7 cal kyr BP. Over this 600-year interval, two large grounding-zone wedges (GZW) were deposited across the middle (GZW2) and inner shelf (GZW3), suggesting that their formation occurred on centennial rather than millennial timescales. Expanded sequences of sub-ice shelf sediments occur seaward of the inner GZW3, which suggests that the grounding line remained stationary for a prolonged period over the middle shelf. Grounding-line retreat rates indicate faster retreat across the outer to middle shelf compared to retreat across the middle to inner shelf. We suggest that variable retreat rates relate to the broad-scale morphology of the trough, which is characterised by a relatively smooth, retrograde seabed on the outer to middle shelf and rugged morphology with a locally landward shallowing bed and deep basin on the inner shelf. A slowdown in retreat rate could also have been promoted by convergent ice flow over the inner shelf and the availability of pinning points associated with bathymetric highs around Anvers Island and Hugo Island

Anvers-Hugo Trough palaeo-ice stream, Antarctic Peninsula: geomorphological evidence for the role of subglacial water in facilitating ice stream flow

We will present new multibeam bathymetry data that make the Anvers-Hugo Trough west of the Antarctic Peninsula one of the most completely surveyed palaeo-ice stream pathways in Antarctica. We interpret landforms revealed by these data as indicating that subglacial water availability played an important role in facilitating ice stream flow in the trough during late Quaternary glacial periods. Specifically, we observe a set of northward-shoaling valleys that are eroded into the upstream edge of a sedimentary basin, extend northwards from a zone containing landforms typical of erosion by subglacial water flow, and coincide spatially with the onset of mega-scale glacial lineations. Water was likely supplied to the ice stream bed episodically as a result of outbursts from a subglacial lake previously hypothesized to have been located in the Palmer Deep basin on the inner continental shelf. In a palaeo-ice stream confluence area, close juxtaposition of mega-scale glacial lineations with landforms that are characteristic of slow, dry-based ice flow, suggests that water availability was also an important control on the lateral extent of these palaeo-ice streams. These interpretations are consistent with the hypothesis that subglacial lakes or areas of elevated geothermal heat flux play a critical role in the onset of many large ice streams. The interpretations also have implications for the dynamic behaviour of the Anvers-Hugo Trough palaeo-ice stream and, potentially, of several other Antarctic palaeo-ice streams. Keywords: multibeam bathymetry, ice stream, subglacial water, landfor

Contribution of Maternal Antiretroviral Therapy and Breastfeeding to 24-Month Survival in Human Immunodeficiency Virus-Exposed Uninfected Children: An Individual Pooled Analysis of African and Asian Studies

Background: Increasing numbers of HIV-infected pregnant women receive antiretroviral therapy (ART) to prevent mother-to-child transmission (PMTCT). Studies suggested that HIV-exposed uninfected (HEU) children face higher mortality than HIV-unexposed children, but evidence mostly relates to the pre-ART era, breastfeeding of limited duration and considerable maternal mortality. Maternal ART and prolonged breastfeeding under cover of ART may improve survival, although this has not been reliably quantified. Methods: Individual data on 19,219 HEU children from 21 PMTCT trials/cohorts undertaken 1995-2015 in Africa and Asia were pooled and the association between 24-month mortality and maternal/infant factors quantified using random-effects Cox proportional hazards models accounting for between-study heterogeneity. Adjusted attributable fractions of risks computed using the predict function in the R package "frailtypack" estimate the relative contribution of risk factors to overall mortality in HEU children. Results: Cumulative incidence of death was 5.5% (95%CI: 5.1-5.9) by age 24 months. Low birth weight (LBW<2500g, adjusted Hazard Ratio (aHR: 2.9), no breastfeeding (aHR: 2.5) and maternal death (aHR: 11.1) were significantly associated with increased mortality. Maternal ART (aHR: 0.5) was significantly associated with lower mortality. At population level, LBW accounted for 16.2% of child deaths by 24 months, never breastfeeding for 10.8%, mother not receiving ART for 45.6%, and maternal death for 4.3%; these factors combined explained 63.6% of deaths by age 24 months. Conclusion: Survival of HEU children could be substantially improved if public health strategies provided all mothers living with HIV with ART and supported optimal infant feeding and care for LBW neonates