Project description DEENESFRITPL How integrators could enhance computation of dispersive equations A geometric integrator is a numerical method that preserves the geometric properties of the exact flow of a differential equation. Some of nature’s most fascinating phenomena, such as shock waves and the breaking of ocean waves at the shore, are mathematically best described using discontinuities (low regularity). However, there are few methods that can perform well in low-regularity regimes and at the same time preserve the geometric structure of the underlying differential equation. Funded by the Marie Skłodowska-Curie Actions programme, the GLIMPSE project will address this need for structure-preserving, low-regularity integrators for dispersive partial differential equations. If successful, numerical methods developed in GLIMPSE could be used to improve simulations used in weather forecasting and disaster prevention from extreme ocean events. Show the project objective Hide the project objective Objective If mathematics is the language of physical sciences, differential equations are their grammar. Yet, to understand them, we need computational algorithms. Some of the most intriguing phenomena in nature arise when the underlying physical laws can be described using nonlinear dispersive partial differential equations. This means that waves of different frequencies travel at different speeds -- a mechanism that is, for instance, responsible for the breaking of ocean waves near the shore. When a computer is asked to approximate solutions that exhibit discontinuities (low-regularity), as is the case for instance in shock waves, these nonlinear frequency interactions pose a significant challenge which has recently been addressed by the development of so-called resonance-based numerical schemes. In many applications, it is desirable to apply geometric numerical integrators -- algorithms that preserve geometric structure of the underlying equation such as conservation of energy or time reversibility. However, there is only a very limited set of methods available that can address both challenges in unison, i.e. perform well in low-regularity regimes and preserve geometric structure of the underlying differential equation. Such algorithms, if more widely developed, would provide a valuable tool for a range of applications, including extreme events in ocean waves and atmospheric models. The goal of this proposed research is to address this need for structure-preserving low-regularity integrators for dispersive partial differential equations. The proposed project lies at the interface of computational mathematics, analysis and physical applications and, if successful, the results of this proposal have the potential to enhance both our current understanding of numerics for dispersive equations and, in the medium term, improve practical simulations which are used in weather forecasting and efficient disaster prevention from extreme ocean events. Fields of science natural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equationssocial scienceslawnatural sciencesphysical sciences Programme(s) HORIZON.1.2 - Marie Skłodowska-Curie Actions (MSCA) Main Programme Topic(s) HORIZON-MSCA-2021-PF-01-01 - MSCA Postdoctoral Fellowships 2021 Call for proposal HORIZON-MSCA-2021-PF-01 See other projects for this call Funding Scheme HORIZON-AG-UN - HORIZON Unit Grant Coordinator SORBONNE UNIVERSITE Net EU contribution € 146 936,16 Address 21 rue de l'ecole de medecine 75006 Paris France See on map Region Ile-de-France Ile-de-France Paris Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Other funding € 0,00
