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LAHACODE

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Cerrado

Low regularity and high oscillations numerical analysis and computation of disp...

Low regularity and high oscillations numerical analysis and computation of dispersive evolution equations Partial differential equations (PDEs) play a central role in mathematics, allowing us to describe physical phenomena ranging from ultra-cold atoms (Bose–Einstein condensation) up to ultra-hot matter (nuclear fusion), from learning... ver más

30/11/2025

SORBONNE UNIVERSIT...

1M€

Presupuesto del proyecto: 1M€

Líder del proyecto

SORBONNE UNIVERSITE No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Fecha límite participación Sin fecha límite de participación.

Ver 3 Participantes

Financiación concedida El organismo H2020 notifico la concesión del proyecto el día 2019-10-15

ERC-2019-STG: ERC Starting Grant

I+D

Cerrada hace 6 años

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Información adicional privada

No hay información privada compartida para este proyecto. Habla con el coordinador.

3 Participantes

SORBONNE UNIVERSITE

1.50M€ | Lider

TSFUNDICIONES, S.A.

338.12K€ | Participante

LMU MUENCHEN

N.D. | Participante

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Duración del proyecto: 73 meses Fecha Inicio: 2019-10-15
Fecha Fin: 2025-11-30

Líder del proyecto

SORBONNE UNIVERSITE No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Presupuesto del proyecto 1M€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto Partial differential equations (PDEs) play a central role in mathematics, allowing us to describe physical phenomena ranging from ultra-cold atoms (Bose–Einstein condensation) up to ultra-hot matter (nuclear fusion), from learning algorithms to fluids in the human brain. To understand nature we have to understand their qualitative behavior: existence and long time behavior of solutions, their geometric and dynamical properties – as well as to compute reliably their numerical solution. While linear problems and smooth solutions are nowadays well understood, a reliable description of ‘non-smooth’ phenomena remains one of the most challenging open problems in computational mathematics since the underlying PDEs have very complicated solutions exhibiting high oscillations and loss of regularity. This leads to huge errors, massive computational costs and ultimately provokes the failure of classical schemes. Nevertheless, ‘non-smooth phenomena’ play a fundamental role in modern physical modeling (e.g., blow-up phenomena, turbulences, high frequencies, low dispersion limits, etc.) which makes it an essential task to develop suitable numerical schemes. The overall ambition of LAHACODE is to make a crucial step towards closing this gap – addressing the fundamental question: How and to what extent can we reproduce the qualitative behavior of differential equations in a finite (discretized) world? LAHACODE is situated at the challenging frontiers of analysis and numerics. The main objective is to develop a novel class of numerical schemes for nonlinear PDEs with strong geometric structure at low regularity and high oscillations. The key idea in the construction of the new schemes is to tackle and deeply embed the underlying structure of resonances in the numerical discretizations. As in the continuous case, these terms are central to structure preservation, and provide the new schemes with remarkable properties – allowing reliable approximations where classical schemes fail.

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