IMDISCO · Isogeometric multipatch discretizations of smooth de Rham complexes

Линиите свързват координатора с партньорите.

Накратко на български

Цел на проекта

In the mathematical modeling and analysis of real-life processes, from physics to biology, curved, non-trivial geometry, efficiency requirements, and stability issues often come together. Through the development of Finite Element Exterior Calculus (FEEC) for the design of stable schemes, and Isogeometric Analysis (IGA) to integrate computer-aided design into the computational process, novel and powerful approximation methods have emerged over the past 20 years. Even an elegant linking of IGA and FEEC via isogeometric discrete differential forms is possible; however, important questions remain open in this context, such as their generalization to higher-order Hilbert complexes.Recent progress in multipatch coupling over the last few years provides an ideal starting point for addressing a central topic in this proposal: smooth multipatch isogeometric differential forms, specifically the structure-preserving discretization of the smooth de Rham complex on a multipatch domain. This will allow me to go beyond the classical de Rham spaces and extend the connections between FEEC and IGA. Exploiting patch-wise tensor product B-splines would facilitate efficient and clearer analysis of crucial coupling conditions that arise between patches, opening up promising new features such as the fast and combined regulation of smoothness and polynomial degree, or the exact incorporation of complex curved geometries.Furthermore, within the FEEC framework, the development of conforming subcomplexes lays the foundation for new, accurate, point-wise divergence-free finite element spaces, particularly suitable in the context of fluid mechanics and the Stokes equations. My goal is therefore not only the theoretical construction of these methods but also their integration with practical implementations in the open-source software package GeoPDEs, along with the performance of numerical tests.

Оригинален текст от CORDIS (на английски).

Участници

• CONSORCIO CENTRO DE INVESTIGACIÓN E TECNOLOXÍA MATEMÁTICA DE GALICIA · Santiago De CompostelaКоординаторИспания

Връзки

• Виж в CORDIS
• DOI: 10.3030/101270046