Asymptotic Numerical meThods for Oscillatory partial Di fferential Equations with uncertainties


Keywords: multi-scale, kinetic, quantum, Vlasov equation for plasmas, semi-classical modelsfor graphene, high-oscillations, uncertainty quantification, space-time, asymptotic preserving, uniformly accurate.

Abstract: The main scienti fic objective of ANTipODE consists in marrying uniformly accurate
(UA) and uncertainty quanti cation (UQ) techniques for multi-scale PDEs with uncertain data, two domains which usually come within the competency of separate communities.

The ringing of an old alarm clock bell on an uneven table induces a fast swaying from one side to the other and a slow drift along the steepest slope. Though the clock’s vibrations are not interesting per se (the drift is what matters), their computation is an absolute prerequisite to the overall motion, while the tiny step-size required for that renders the simulation prohibitively costly, or even impossible. Such discrepant scales (slow -say 1- and fast -say 1/ε- for small values of ε) are characteristic of multi-scale models, amongst which prominent examples originate from the simulation of fusion as envisaged in ITER or from quantum models. Besides, many real-life problems are also rife with sources of uncertainties which are ampli ed by oscillations.


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