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Documents  Moireau, Philippe | enregistrements trouvés : 28

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Outreach;Mathematics Education and Popularization of Mathematics

Le CIRM : écrin estival du CEMRACS depuis 20 ans !

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Research schools;Control Theory and Optimization;Partial Differential Equations

The question of using the available measurements to retrieve mathematical models characteristics (parameters, boundary conditions, initial conditions) is a key aspect of the modeling objective in biology or medicine. In a stochastic/statistical framework this question is seen as an estimation problems. From a deterministic point of view, we classical talk about inverse problems as we recover classical model inputs from outputs. When considering evolution problems,this question falls in the realm of data assimilation that can be seen from a deterministic of statistical point of view. Our objective in this course is to introduce the mathematical principles and numerical aspects behind data assimilation strategies with an emphasis on the deterministic formalism allowing to understand why data assimilation is a specific inverse problem. Our presentation will include considerations on finite dimensional problems but also on infinite dimensional problems such as the ones arising from PDE models. And we will illustrate the course with numerous examples coming from cardiovascular applications and biology. The question of using the available measurements to retrieve mathematical models characteristics (parameters, boundary conditions, initial conditions) is a key aspect of the modeling objective in biology or medicine. In a stochastic/statistical framework this question is seen as an estimation problems. From a deterministic point of view, we classical talk about inverse problems as we recover classical model inputs from outputs. When considering ...

93E11 ; 93B30 ; 93E10 ; 35R30 ; 35L05 ; 93B07

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Research schools;Control Theory and Optimization;Partial Differential Equations

The question of using the available measurements to retrieve mathematical models characteristics (parameters, boundary conditions, initial conditions) is a key aspect of the modeling objective in biology or medicine. In a stochastic/statistical framework this question is seen as an estimation problems. From a deterministic point of view, we classical talk about inverse problems as we recover classical model inputs from outputs. When considering evolution problems,this question falls in the realm of data assimilation that can be seen from a deterministic of statistical point of view. Our objective in this course is to introduce the mathematical principles and numerical aspects behind data assimilation strategies with an emphasis on the deterministic formalism allowing to understand why data assimilation is a specific inverse problem. Our presentation will include considerations on finite dimensional problems but also on infinite dimensional problems such as the ones arising from PDE models. And we will illustrate the course with numerous examples coming from cardiovascular applications and biology. The question of using the available measurements to retrieve mathematical models characteristics (parameters, boundary conditions, initial conditions) is a key aspect of the modeling objective in biology or medicine. In a stochastic/statistical framework this question is seen as an estimation problems. From a deterministic point of view, we classical talk about inverse problems as we recover classical model inputs from outputs. When considering ...

93E11 ; 93B30 ; 93E10 ; 35R30 ; 35L05 ; 93B07

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Research schools;Computer Science;Numerical Analysis and Scientific Computing

65F08 ; 65F10 ; 65Y05 ; 68W10

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Research schools;Computer Science;Numerical Analysis and Scientific Computing

68U20 ; 68W10 ; 65Y15 ; 65Y05

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Research schools;Numerical Analysis and Scientific Computing

65M55 ; 65N55 ; 65Y05

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Research schools;Computer Science;Numerical Analysis and Scientific Computing

68Uxx ; 65Y20 ; 65Y04 ; 65Y05

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Research schools;Numerical Analysis and Scientific Computing

65M55 ; 65N55 ; 65N30 ; 65F10 ; 65Y05

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Research schools;Computer Science;Numerical Analysis and Scientific Computing

68N15 ; 68M10 ; 68Q10 ; 65Y05

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Research schools;Numerical Analysis and Scientific Computing

65Y05 ; 65Y10

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Research schools;Computer Science;Numerical Analysis and Scientific Computing

68N19 ; 68Uxx ; 65Y05 ; 65Y10

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Research schools;Partial Differential Equations;Numerical Analysis and Scientific Computing

65N12 ; 65N30 ; 35J25 ; 65D05

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Research schools;Computer Science;Numerical Analysis and Scientific Computing

35J25 ; 65N30 ; 65Y05 ; 68N19

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Research schools;Mathematics in Science and Technology;Numerical Analysis and Scientific Computing

68Pxx ; 86A22 ; 65M15 ; 65Z05

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Research schools;Mathematics in Science and Technology;Probability and Statistics;Numerical Analysis and Scientific Computing

62P12 ; 62M20 ; 86A05 ; 86A32 ; 93E10

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Research talks;Numerical Analysis and Scientific Computing

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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Research talks;Numerical Analysis and Scientific Computing

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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Research talks;Mathematics in Science and Technology;Numerical Analysis and Scientific Computing

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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Research talks;Numerical Analysis and Scientific Computing

We review how to bound the error between the unknown weak solution of a PDE and its numerical approximation via a fully computable a posteriori estimate. We focus on approximations obtained at an arbitrary step of a linearization (Newton-Raphson, fixed point, ...) and algebraic solver (conjugate gradients, multigrid, domain decomposition, ...). Identifying the discretization, linearization, and algebraic error components, we design local stopping criteria which keep them in balance. This gives rise to a fully adaptive inexact Newton method. Numerical experiments are presented in confirmation of the theory. We review how to bound the error between the unknown weak solution of a PDE and its numerical approximation via a fully computable a posteriori estimate. We focus on approximations obtained at an arbitrary step of a linearization (Newton-Raphson, fixed point, ...) and algebraic solver (conjugate gradients, multigrid, domain decomposition, ...). Identifying the discretization, linearization, and algebraic error components, we design local ...

65N15 ; 65N22 ; 65Y05

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Research talks;Numerical Analysis and Scientific Computing

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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