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Documents  Moireau, Philippe | enregistrements trouvés : 28

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Post-edited  Interview au CIRM : Yvon Maday
Maday, Yvon (Personne interviewée) | CIRM (Editeur )

Le CIRM : écrin estival du CEMRACS depuis 20 ans !

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Multi angle  Tutorial with Freefem++
Hecht, Frédéric (Auteur de la Conférence) | CIRM (Editeur )

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Multi angle  Time parallel time integration
Gander, Martin (Auteur de la Conférence) | CIRM (Editeur )

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When solving wave scattering problems with the Boundary Element Method (BEM), one usually faces the problem of storing a dense matrix of huge size which size is proportional to the (square of) the number N of unknowns on the boundary of the scattering object. Several methods, among which the Fast Multipole Method (FMM) or the H-matrices are celebrated, were developed to circumvent this obstruction. In both cases an approximation of the matrix is obtained with a O(N log(N)) storage and the matrix-vector product has the same complexity. This permits to solve the problem, replacing the direct solver with an iterative method.
The aim of the talk is to present an alternative method which is based on an accurate version of the Fourier based convolution. Based on the non-uniform FFT, the method, called the sparse cardinal sine decomposition (SCSD) ends up to have the same complexity than the FMM for much less complexity in the implementation. We show in practice how the method works, and give applications in as different domains as Laplace, Helmholtz, Maxwell or Stokes equations.
This is a joint work with Matthieu Aussal.
When solving wave scattering problems with the Boundary Element Method (BEM), one usually faces the problem of storing a dense matrix of huge size which size is proportional to the (square of) the number N of unknowns on the boundary of the scattering object. Several methods, among which the Fast Multipole Method (FMM) or the H-matrices are celebrated, were developed to circumvent this obstruction. In both cases an approximation of the matrix is ...

65T50 ; 65R10 ; 65T40

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Parametrized PDE (Partial Differential Equation) Apps are PDE solvers which satisfy stringent per-query performance requirements: less-than or approximate 5-second problem specification time; less-than or approximate 5-second problem solution time, field and outputs; less-than or approximate 5% solution error, specified metrics; less-than or approximate 5-second solution visualization time. Parametrized PDE apps are relevant in many-query, real-time, and interactive contexts such as design, parameter estimation, monitoring, and education.
In this talk we describe and demonstrate a PDE App computational methodology. The numerical approach comprises three ingredients: component => system synthesis, formulated as a static-condensation procedure; model order reduction, informed by evanescence arguments at component interfaces (port reduction) and low-dimensional parametric manifolds in component interiors (reduced basis techniques); and parallel computation, implemented in a cloud environment. We provide examples in acoustics and also linear elasticity.
Parametrized PDE (Partial Differential Equation) Apps are PDE solvers which satisfy stringent per-query performance requirements: less-than or approximate 5-second problem specification time; less-than or approximate 5-second problem solution time, field and outputs; less-than or approximate 5% solution error, specified metrics; less-than or approximate 5-second solution visualization time. Parametrized PDE apps are relevant in many-query, ...

65N30 ; 65N15 ; 65M60 ; 65M15 ; 93B50

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We review Optimized Schwarz waveform relaxation methods which are space-time domain decomposition methods. The main ideas are explained on the heat equation, and extension to advection-diffusion equations are illustrated by numerical results. We present the Schwarz for TrioCFD project, which aims at using this kind of methods for the Stokes equations.

65M55 ; 65M60 ; 65M12 ; 65Y20

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Multi angle  OpenCL introduction
Desprez, Frédéric (Auteur de la Conférence) | CIRM (Editeur )

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Facing energy future is one of the large challenges of the world, with numerous implications for R&D strategy of energy companies. One of the Total R&D missions is the development of competences on advanced technologies, such as Advanced Computing (HPC), Material sciences, Biotechnologies, Nanotechnologies, New analytical techniques, IT Technologies. HPC allows also tackling the challenge in code coupling: both a horizontal direction -multi-physics-, (chemistry and transport, or structural mechanics, acoustics, fluid dynamics, and thermal heat transfer, ...) and in the vertical direction -multi-scale models- (i.e. from continuum to mesoscale to molecular dynamics to quantum chemistry) which requires bridging space and time scales that span many orders of magnitude. This leads to improve at the same time more accurate physical model and numerical methods and algorithms and these improvements of numerical simulations will be illustrated by their application, use and impact in Total strategic activities such as: seismic, depth imaging by solving waves equation; oil reservoir modeling by solving transport, thermal and chemical equations; multi scale process modeling and control, such as slurry loop process; mechanical structures and geomecanics.
Facing energy future is one of the large challenges of the world, with numerous implications for R&D strategy of energy companies. One of the Total R&D missions is the development of competences on advanced technologies, such as Advanced Computing (HPC), Material sciences, Biotechnologies, Nanotechnologies, New analytical techniques, IT Technologies. HPC allows also tackling the challenge in code coupling: both a horizontal direction -m...

68Uxx ; 65Y05

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In this talk we overview some of the challenges of cardiac modeling and simulation of the electrical depolarization of the heart. In particular, we will present a strategy allowing to avoid the 3D simulation of the thin atria depolarization but only solve an asymptotic consistent model on the mid-surface. In a second part, we present a strategy for estimating a cardiac electrophysiology model from front data measurements using sequential parallel data assimilation strategy.
In this talk we overview some of the challenges of cardiac modeling and simulation of the electrical depolarization of the heart. In particular, we will present a strategy allowing to avoid the 3D simulation of the thin atria depolarization but only solve an asymptotic consistent model on the mid-surface. In a second part, we present a strategy for estimating a cardiac electrophysiology model from front data measurements using sequential ...

92C30 ; 35Q92 ; 65C20

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Multi angle  Linear solvers for reservoir simulation
Hénon, Pascal (Auteur de la Conférence) | CIRM (Editeur )

In this presentation, we will first present the main goals and principles of reservoir simulation. Then we will focus on linear systems that arise in such simulation. The main HPC challenge is to solve those systems efficiently on massively parallel computers. The specificity of those systems is that their convergence is mostly governed by the elliptic part of the equations and the linear solver needs to take advantage of it to be efficient. The reference method in reservoir simulation is CPR-AMG which usually relies on AMG to solve the quasi elliptic part of the system. We will present some works on improving AMG scalability for the reservoir linear systems (work done in collaboration with CERFACS). We will then introduce an on-going work with INRIA to take advantage of their enlarged Krylov method (EGMRES) in the CPR method.
In this presentation, we will first present the main goals and principles of reservoir simulation. Then we will focus on linear systems that arise in such simulation. The main HPC challenge is to solve those systems efficiently on massively parallel computers. The specificity of those systems is that their convergence is mostly governed by the elliptic part of the equations and the linear solver needs to take advantage of it to be efficient. The ...

65F10 ; 65N22 ; 65Y05

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Multi angle  Krylov subspace solvers and preconditioners
Vuik, Kees (Auteur de la Conférence) | CIRM (Editeur )

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I will review (some of) the HPC solution strategies developed in Feel++. We present our advances in developing a language specific to partial differential equations embedded in C++. We have been developing the Feel++ framework (Finite Element method Embedded Language in C++) to the point where it allows to use a very wide range of Galerkin methods and advanced numerical methods such as domain decomposition methods including mortar and three fields methods, fictitious domain methods or certified reduced basis. We shall present an overview of the various ingredients as well as some illustrations. The ingredients include a very expressive embedded language, seamless interpolation, mesh adaption, seamless parallelisation. As to the illustrations, they exercise the versatility of the framework either by allowing the development and/or numerical verification of (new) mathematical methods or the development of large multi-physics applications - e.g. fluid-structure interaction using either an Arbitrary Lagrangian Eulerian formulation or a levelset based one; high field magnets modeling which involves electro-thermal, magnetostatics, mechanical and thermo-hydraulics model; ... - The range of users span from mechanical engineers in industry, physicists in complex fluids, computer scientists in biomedical applications to applied mathematicians thanks to the shared common mathematical embedded language hiding linear algebra and computer science complexities.
I will review (some of) the HPC solution strategies developed in Feel++. We present our advances in developing a language specific to partial differential equations embedded in C++. We have been developing the Feel++ framework (Finite Element method Embedded Language in C++) to the point where it allows to use a very wide range of Galerkin methods and advanced numerical methods such as domain decomposition methods including mortar and three ...

65N30 ; 65N55 ; 65Y05 ; 65Y15

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Climate models simulate atmospheric flows interacting with many physical processes. Because they address long time scales, from centuries to millennia, they need to be efficient, but not at the expense of certain desirable properties, especially conservation of total mass and energy. Most of my talk will explain the design principles behind DYNAMICO, a highly scalable unstructured-mesh energy-conserving finite volume/mimetic finite difference atmospheric flow solver and potential successor of LMD-Z, a structured-mesh (longitude-latitude) solver currently operational as part of IPSL-CM, the Earth System Model developed by Institut Pierre Simon Laplace (IPSL). Specifically, the design exploits the variational structure of the equations of motion and their Hamiltonian formulation, so that the conservation of energy requires only that the discrete grad and div operators be compatible, i.e. that a discrete integration by parts formula holds.
I will finish my talk by sketching how the desirable properties of DYNAMICO may be obtained with a different approach based on mixed finite elements (FEM). Indeed while DYNAMICO is very fast and scalable, it is low-order and higher-order accuracy may be desirable. While FEM methods can provide higher-order accuracy, they are computationally more expensive. They offer a viable path only if the performance gap compared to finite differences is not too large. The aim of the CEMRACS project A-HA is to evaluate how wide this gap may be, and whether it can be narrowed by using a recently proposed duality-based approach to assemble the various matrices involved in a FEM method.
Climate models simulate atmospheric flows interacting with many physical processes. Because they address long time scales, from centuries to millennia, they need to be efficient, but not at the expense of certain desirable properties, especially conservation of total mass and energy. Most of my talk will explain the design principles behind DYNAMICO, a highly scalable unstructured-mesh energy-conserving finite volume/mimetic finite difference ...

76M25 ; 86A10

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In domain decomposition methods, most of the computational cost lies in the successive solutions of the local problems in subdomains via forward-backward substitutions and in the orthogonalization of interface search directions. All these operations are performed, in the best case, via BLAS-1 or BLAS-2 routines which are inefficient on multicore systems with hierarchical memory. A way to improve the parallel efficiency of the method consists in working with several search directions, since multiple forward-backward substitutions and reorthogonalizations involve BLAS-3 routines. In the case of a problem with several right-hand-sides, using a block Krylov method is a straightforward way to work with multiple search directions. This will be illustrated with an application in electromagnetism using FETI-2LM method. For problems with a single right-hand-side, deriving several search directions that make sense from the optimal one constructed by the Krylov method is not so easy. The recently developed S-FETI method gives a very good approach that does not only improve parallel efficiency but can also reduce the global computational cost in the case of very heterogeneous problems.
In domain decomposition methods, most of the computational cost lies in the successive solutions of the local problems in subdomains via forward-backward substitutions and in the orthogonalization of interface search directions. All these operations are performed, in the best case, via BLAS-1 or BLAS-2 routines which are inefficient on multicore systems with hierarchical memory. A way to improve the parallel efficiency of the method consists in ...

65N22 ; 65N30 ; 65N55 ; 65Y05 ; 65F10

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The heart undergoes some highly complex multi-scale multi-physics phenomena that must be accounted for in order to adequately model the biomechanical behavior of the complete organ. In this respect, a major focus of our work has been on formulating modeling ingredients that satisfy the most crucial thermomechanical requirements - in particular as regards energy balances - throughout the various forms of physical and scale-related couplings. This has led to a "beating heart" model for which some experimental and clinical validations have already been obtained. Concurrently, with the objective of building "patient-specific" heart models, we have investigated some original approaches inspired from data assimilation concepts to benefit from the available clinical data, with a particular concern for medical imaging. By combining the two fundamental sources of information represented by the model and the data, we are able to extract some most valuable quantitative knowledge on a given heart, e.g. as regards some uncertain constitutive parameter values characterizing a possible pathology, with important perspectives in diagnosis assistance. In addition, once the overall uncertainty has been adequately controlled via this adjustment process, the model can be expected to become "predictive", hence should provide clinically-relevant quantitative information, both in the current state of the patient and under various scenarii of future evolutions, such as for therapy planning.
The heart undergoes some highly complex multi-scale multi-physics phenomena that must be accounted for in order to adequately model the biomechanical behavior of the complete organ. In this respect, a major focus of our work has been on formulating modeling ingredients that satisfy the most crucial thermomechanical requirements - in particular as regards energy balances - throughout the various forms of physical and scale-related couplings. This ...

92C10 ; 92C55 ; 74H15

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