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Documents  65Y05 | enregistrements trouvés : 14

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

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

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

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

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

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

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

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

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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