Distributed and parallel sparse convex optimization for radio interferometry with PURIFY

Next generation radio interferometric telescopes are entering an era of big data with extremely large data sets. While these telescopes can observe the sky in higher sensitivity and resolution than before, computational challenges in image reconstruction need to be overcome to realize the potential of forthcoming telescopes. New methods in sparse image reconstruction and convex optimization techniques (cf. compressive sensing) have shown to produce higher fidelity reconstructions of simulations and real observations than traditional methods. This article presents distributed and parallel algorithms and implementations to perform sparse image reconstruction, with significant practical considerations that are important for implementing these algorithms for Big Data. We benchmark the algorithms presented, showing that they are considerably faster than their serial equivalents. We then pre-sample gridding kernels to scale the distributed algorithms to larger data sizes, showing application times for 1 Gb to 2.4 Tb data sets over 25 to 100 nodes for up to 50 billion visibilities, and find that the run-times for the distributed algorithms range from 100 milliseconds to 3 minutes per iteration. This work presents an important step in working towards computationally scalable and efficient algorithms and implementations that are needed to image observations of both extended and compact sources from next generation radio interferometers such as the SKA. The algorithms are implemented in the latest versions of the SOPT (https://github.com/astro-informatics/sopt) and PURIFY (https://github.com/astro-informatics/purify) software packages {(Versions 3.1.0)}, which have been released alongside of this article.Comment: 25 pages, 5 figure

Vertex centred Discretization of Two-Phase Darcy flows on General Meshes

International audienceThis paper concerns the discretization of multiphase Darcy flows, in the case of heterogeneous anisotropic porous media and general 3D meshes used in practice to represent reservoir and basin geometries. An unconditionally coercive and symmetric vertex centred approach is introduced in this paper. This scheme extends the Vertex Approximate Gradient scheme (VAG), already introduced for single phase diffusive problems in \cite{Eymard.Herbin.ea:2010}, to multiphase Darcy flows. The convergence of the VAG scheme is proved for a simplified two-phase Darcy flow model, coupling an elliptic equation for the pressure and a linear hyperbolic equation for the saturation. The ability for the VAG scheme to efficiently deal with highly heterogeneous media and complex meshes is exhibited on immiscible and miscible two phase Darcy flow models

ComPASS: a tool for distributed parallel finite volume discretizations on general unstructured polyhedral meshes

International audienceThe objective of the ComPASS project is to develop a parallel multiphase Darcy flow simulator adapted to general unstructured polyhedral meshes (in a general sense with possibly non planar faces) and to the parallelization of advanced finite volume discretizations with various choices of the degrees of freedom such as cell centres, vertices, or face centres. The main targeted applications are the simulation of CO2 geological storage, nuclear waste repository and reservoir simulations. The CEMRACS 2012 summer school devoted to high performance computing has been an ideal framework to start this collaborative project. This paper describes what has been achieved during the four weeks of the CEMRACS project which has been focusing on the implementation of basic features of the code such as the distributed unstructured polyhedral mesh, the synchronization of the degrees of freedom, and the connection to scientific libraries including the partitioner METIS, the visualization tool PARAVIEW, and the parallel linear solver library PETSc. The parallel efficiency of this first version of the ComPASS code has been validated on a toy parabolic problem using the Vertex Approximate Gradient finite volume spacial discretization with both cell and vertex degrees of freedom, combined with an Euler implicit time integration

Grid Orientation Effect in coupled Finite Volume Schemes

International audienceThe numerical simulation of two-phase flow in a porous medium may lead, when using coupled finite volume schemes on structured grids, to the apparition of the so-called Grid Orientation Effect (GOE). We propose in this paper a procedure to eliminate this phenomenon, based on the use of new fluxes with a new stencil in the discrete version of the convection equation, without changing the discrete scheme for computing the pressure field. Numerical results show that the GOE does not significantly decrease with the size of the discretization using the initial scheme on the coupled problem, but that it is efficiently suppressed by the new procedure, even on coarse meshes. A mathematical study, based on a weak BV inequality using the new fluxes, confirms the convergence of the modified scheme in a particular case

Gradient Discretization of Hybrid Dimensional Darcy Flows in Fractured Porous Media

International audienceThis article deals with the discretization of hybrid dimensional model of Darcy flow in fractured porous media. These models couple the flow in the fractures represented as the surfaces of codimension one with the flow in the surrounding matrix. The convergence analysis is carried out in the framework of Gradient schemes which accounts for a large family of conforming and nonconforming dis-cretizations. The Vertex Approximate Gradient (VAG) scheme and the Hybrid Finite Volume (HFV) scheme are applied to such models and are shown to verify the Gradient scheme framework. Our theoretical results are confirmed by a few numerical experiments performed both on tetrahedral and hexahedral meshes in heterogeneous isotropic and anisotropic media