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Reduced MHD models in Tokamak geometry are convenient simplifications of full MHD and are fundamental for the numerical simulation of MHD stability in Tokamaks. This presentation will address the mathematical well-posedness and the justification of the such models.
The first result is a systematic design of hierachies of well-posed reduced MHD models. Here well-posed means that the system is endowed with a physically sound energy identity and that existence of a weak solution can be proved. Some of these models will be detailed.
The second result is perhaps more important for applications. It provides understanding on the fact the the growth rate of linear instabilities of the initial (non reduced) model is lower bounded by the growth rate of linear instabilities of the reduced model.
This work has been done with Rémy Sart.
Reduced MHD models in Tokamak geometry are convenient simplifications of full MHD and are fundamental for the numerical simulation of MHD stability in Tokamaks. This presentation will address the mathematical well-posedness and the justification of the such models.
The first result is a systematic design of hierachies of well-posed reduced MHD models. Here well-posed means that the system is endowed with a physically sound energy ...

76W05 ; 35L65 ; 65M60 ; 35Q30

KEEN - Vlasov plasmas - acoustic waves - semi-Lagrangian scheme - Vlasov-Poisson equation; - BGK mode

76X05 ; 82D10 ; 65M60

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

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

I will review several relaxations of the classical Monge Optimal Transport problem using a dynamic time2 extension and discuss the corresponding available numerical methods. They also apply to some instances of variational mean field games.

49Q20 ; 49M25 ; 35J70 ; 65M60 ; 35J96

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