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Third Workshop of the strategic action DIP

Troisième Workshop de l’action stratégique INRIA TOTAL “DIP : Depth Imaging Partnership”

Pau, les 22 et 23 juin 2015

Salle de Réunion de l’IPRA, RdC

Université de Pau et des Pays de l’Adour

Organisatrice: Hélène Barucq

Programme

  • Monday, June 22nd 2015
    •   9h30–10h00 : Welcome coffee
    • 10h00–11h00 : Frédéric Alauzet, Senior research scientist, Inria Rocquencourt, Gamma3, « A unified framework for advanced mesh generation and mesh modification », abstract
    • 11h00–11h30 : Florian Faucher, PhD Student, Inria Magique3D – DIP, « Elastic isotropic full waveform inversion via quantitative stability estimates », abstract
    • 11h30–12h00 : Marie Bonnasse-Gahot, PhD Student, Inria Magique3D/Nachos – DIP, « Modelling of elastic Helmholtz equations by hybridizable Discontinuous Galerkin method (HDGm) for geophysical applications », abstract
    • 12h00–14h00 : Déjeuner (restaurant de l’UPPA)
    • 14h00–15h00 : Régis Duvigneau, Junior Research Scientist, Inria Sophia-Antipolis, Acumes, « Isogeometry: a unified approach for geometry and analysis ? », abstract
    • 15h00–16h00 : Léo Nouveau, PhD student, Inria Bordeaux Sud-Ouest, Cardamom, « Mesh adaptation by local remeshing and application to immersed boundary methods in fluid mechanics », abstract
    • 16h00–16h30 : Pause café
    • 16h30–17h30 :  Cédric Lachat, Research Engineer, Inria Bordeaux Sud-Ouest, Tadaam), « Parallel remeshing on unstructured meshes », abstract
    • 17h30 : Discussions
    • 20h00 : Dinner at the restaurant “Le bistro d’à côté” in Pau down town (http://lebistrotdacotepau.free.fr/)
  • Tuesday, June 23th 2015
    •   9h30–10h30 : Adrianna Gillman, Assistant Professor, Rice University, Texas, « An efficient high accuracy direct solution technique for variable coefficient elliptic PDEs », abstract
    • 10h30–11h00 : Pause café
    • 11h00–12h00 : Maarten De Hoop, Professor, Purdue University, « Direct nonlinear inverse problems », abstract
    • 12h00–14h00 : Déjeuner (restaurant de l’UPPA)
    • 14h00–14h30 : Corentin Rossignon, PhD student, Total – Réservoirs, « A solution to solve some granularity problems », abstract
    • 14h30–15h00 : Stojce Nakov, PhD student, Inria Hiepacs – DIP, « Hierarchical hybrid sparse linear solver for multicore platforms », abstract
    • 15h00–15h30 : Lionel Boillot, Engineer-PhD, Inria Magique3D – DIP, « Stable TTI Acousto-Elastic simulations », abstract
    • 15h30–16h00 : Théophile Chaumont-Frelet, PhD student, Inria Magique3D – DIP, « Multiscale Medium Approximation for the Helmholtz equation. Application to geophysical benchmarks. », abstract
    • 16h00 : Conclusions

Abstracts (conf. order)

  • Frédéric Alauzet, Senior research scientist, Inria Rocquencourt, Gamma3, « A unified framework for advanced mesh generation and mesh modification »
This presentation gives a unified framework to address many issues in mesh generation/modification. This framework utilizes at best the notion of metric and all meshing operations are based on a unique cavity operator. We demonstrate that this methodology addresses efficiently surface (re)meshing, non-manifold geometry, adaptive anisotropic (re)meshing, structured boundary layer (re)meshing, moving mesh, … We also discuss the parallelization of the process. Finally, a few perspectives are provided. In particular, we show how this framework can be extended naturally to hybrid element meshes.
  • Florian Faucher, PhD Student, Inria Magique3D – DIP, « Elastic isotropic full waveform inversion via quantitative stability estimates »

We study the seismic inverse problem in the complex frequency-domain. We consider an elastic isotropic medium and the recovery of the Lamé parameters and density. The problem follows a Lipschitz type stability, we compute successive stability estimates to provide a control of the convergence of our algorithm. Hence we develop a multi-level approach with a hierarchical compressed reconstruction. It allows us to accurately reconstruct the sub-surface parameters while starting with minimal prior information. We carry out numerical experiments for elastic reconstruction in two and three dimensions.

  • Marie Bonnasse-Gahot, PhD Student, Inria Magique3D/Nachos – DIP, « Modelling of elastic Helmholtz equations by hybridizable Discontinuous Galerkin method (HDGm) for geophysical applications »

The advantage of performing seismic imaging in frequency domain is that it is not necessary to store the solution at each time step of the forward simulation. But the main drawback of the elastic Helmholtz equations, when considering 3D realistic elastic case, lies in solving large linear systems, which represents today a challenging tasks even with the use of high performance computing (HPC).
To reduce the size of the global linear system, we develop a hybridizable discontinuous Galerkin method (HDGm). It consists in expressing the unknowns of the initial problem in function of the trace of the numerical solution on each face of the mesh cells. In this way the size of the matrix to be inverted only depends on the number of degrees of freedom on each face and on the number of the faces of the mesh. The solution to the initial problem is then recovered thanks to independent elementwise calculation.

  • Régis Duvigneau, Junior Research Scientist, Inria Sophia-Antipolis, Acumes, « Isogeometry: a unified approach for geometry and analysis ? »
The isogeometric paradigm has been proposed recently to overcome the limitations arising from the use of different geometrical representations in engineering design (CAD, mesh, ad-hoc design parameters, etc).
It relies on a unique geometrical description for the computational domain and physical solution, based on NURBS basis functions, yielding “exact” geometry simulations and hierarchical high-order discretization schemes.
Main features of the method, advantages and drawbacks, will be presented  and illustrated for elliptic and hyperbolic PDE systems, as well as inverse problems.
  • Léo Nouveau, PhD student, Inria Bordeaux Sud-Ouest, Cardamom, « Mesh adaptation by local remeshing and application to immersed boundary methods in fluid mechanics. »

In this talk, the MMG open source platform will be presented. This platform is composed with 3 softwares : MMGS: a surface remesher, MMG2D : a 2D remesher, and MMG3D : a 3D remesher. After a brief overview of the platform, some examples of surface remeshing and mesh adaptation illustrations will be given. Finally, one of the possible applications of MMG use will be described : improve the precision of the solutions obtained in computational fluid dynamics by adapting the mesh to the solution (and in the case of immersed boundary method, around the definition of the object). Exemples in 2D and 3D will be given.

  • Cédric Lachat, Research Engineer, Inria Bordeaux Sud-Ouest, Tadaam), « Parallel remeshing on unstructured meshes »

This talk presents new features of PaMPA, a library dedicated to the management of distributed meshes, including  parallel repartitioning and
parallel remeshing features. PaMPA performs parallel remeshing by selecting independent  subsets of elements that need remeshing and running concurrently a user-provided sequential remesher (e.g. MMG3D)  on each of these subsets. This process is repeated on yet un-remeshed areas until all of the mesh is  remeshed. The new mesh is then repartitioned to restore load balance. We present experimental results where we  generate high quality, anisotropic tetrahedral meshes comprising several hundred million elements from initial meshes of several million elements.

  •   Adrianna Gillman, Assistant Professor, Rice University, Texas, « An efficient high accuracy direct solution technique for variable coefficient elliptic PDEs »

In this talk, we present a high-order accurate discretization technique designed for variable coefficient problems with smooth solutions.   The resulting linear system is solved via a fast direct solver with $O(N)$ complexity where $N$ is the number of discretization points.  Each additional solve is also $O(N)$ but with a much smaller constant.  Unlike direct solvers designed for the finite element discretization of PDEs, the constants for the solver do not grow dramatically when the order of the discretization is increased.  Numerical results will illustrate the performance of the proposed method.
Additionally, we will present a solution technique for free-space scattering problems with locally varying media which utilizes the proposed method.
This technique can solve problems 100 wavelengths in size to 9 digits of accuracy in a few minutes on a workstation.  For each new incident wave the solution can be found in 3 seconds.

  • Maarten De Hoop, Professor, Purdue University, « Direct nonlinear inverse problems »

TO BE UPDATED

  • Corentin Rossignon, PhD student, Total – Réservoirs, « A solution to solve some granularity problems »

We present some solutions to handle a problem commonly encountered when dealing with fine grain parallelization on multi-core architecture: Expressing algorithms using a task grain size suitable for the hardware.
To evaluate the benefit of our work we present some experiments on the fine grain parallelization of an iterative solver for sparse linear systems with some comparisons with the Intel TBB approach.

  • Stojce Nakov, PhD student, Inria Hiepacs – DIP, « Hierarchical hybrid sparse linear solver for multicore platforms »

The solution of large sparse linear systems is a critical operation for many numerical simulations. To cope with the hierarchical design of modern supercomputers, hybrid solvers based on Domain Decomposition Methods (DDM) have been been proposed. Among them, approaches consisting of solving the problem on the interior of the domains with a sparse direct method and the problem on their interface with a preconditioned iterative method applied to the related Schur Complement have shown an attractive potential as they can combine the robustness of direct methods and the low memory footprint of iterative methods. In this talk, we consider an Additive Schwarz preconditioner for the Schur Complement, which represents a scalable candidate but whose numerical robustness may decrease when the number of domains becomes too large. We thus propose a two-level MPI/thread parallel approach to control the number of domains and hence the numerical behavior. We show that the resulting method can process matrices such as tdr455k for which we previously either ran out of memory on few nodes or failed to converge on a larger number of nodes. Matrices such as Nachos\_4M that could be correctly processed in the past can now be efficiently processed up to a very large number of CPU cores ($24,576$ cores). In the context of the DIP project, we have shown that this method can be efficiently applied on matrices arising from the discretization of the elastodynamic system on 3D meshes for exploiting modern multicore clusters. The corresponding code has been incorporated into the Maphys package.

  • Lionel Boillot, Engineer-PhD, Inria Magique3D – DIP, « Stable TTI Acousto-Elastic simulations »

Anisotropy of the subsurface is assumed to be Tilted Transverse Isotropic (TTI). In such media, common boundary conditions like Perfectly Matched Layers (PML) are unstable. We proposed a way to construct stable Absorbing Boundary Conditions (ABC) last year, for TTI elastic media.
In this talk we will illustrate the behavior of our ABC in TTI Acousto-Elastic media, both in time-domain and frequential-domain.

  • Théophile Chaumont-Frelet, PhD student, Inria Magique3D – DIP, « Multiscale Medium Approximation for the Helmholtz equation. Application to geophysical benchmarks. »

In the first part of this talk, the Multiscale Medium Approximation method (MMAM) is described. This technique permits to take into account small scale heterogeneities on a coarse finite element mesh. In the second part, we approximate Helmholtz problems on geophysical benchmark models using the MMAM. We discuss the best choice of mesh step h and polynomial degree p depending on the frequency. Our main result is that the number of degrees of freedom required to obtain a given accuracy is greatly reduced if high order polynomials and the MAMM are used instead of standard linear elements.

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