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Innovative compatible discretization techniques for Partial Differential Equatio...

Innovative compatible discretization techniques for Partial Differential Equations Partial Differential Equations (PDEs) are one of the most powerful mathematical modeling tool and their use spans from life science to engineering and physics. In abstract terms, PDEs describe the distribution of a field on a phys... ver más

30/06/2013

CNR

750K€

Presupuesto del proyecto: 750K€

Líder del proyecto

CONSIGLIO NAZIONALE DELLE RICERCHE No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Fecha límite participación Sin fecha límite de participación.

Financiación concedida El organismo FP7 notifico la concesión del proyecto el día 2013-06-30 No tenemos la información de la convocatoria

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Líder del proyecto

CONSIGLIO NAZIONALE DELLE RICERCHE No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Presupuesto del proyecto 750K€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto Partial Differential Equations (PDEs) are one of the most powerful mathematical modeling tool and their use spans from life science to engineering and physics. In abstract terms, PDEs describe the distribution of a field on a physical domain. The Finite Element Method (FEM) is by large the most popular technique for the computer-based simulation of PDEs and hinges on the assumption that the discretized domain and field are represented both by means of piecewise polynomials. Such an isoparametric feature is at the very core of FEM. However, CAD software, used in industry for geometric modeling, typically describes physical domains by means of Non-Uniform Rational B-Splines (NURBS) and the interface of CAD output with FEM calls for expensive re-meshing methods that result in approximate representation of domains. This project aims at developing isoparametric techniques based on NURBS for simulating PDEs arising in electromagnetics, fluid dynamics and elasticity. We will consider discretization schemes that are compatible in the sense that the discretized models embody conservation principles of the underlying physical phenomenon (e.g. charge in electromagnetism, mass and momentum in fluid motion and elasticity). The key benefits of NURBS-based methods are: exact representation of the physical domain, direct use of the CAD output, a substantial increase of the accuracy-to-computational-effort ratio. NURBS schemes start appearing in the Engineering literature and preliminary results show that they hold great promises. However, their understanding is still in infancy and sound mathematical groundings are crucial to quantitatively assess the performance of NURBS techniques and to design new effective computational schemes. Our research will combine competencies in different fields of mathematics besides numerical analysis, such as functional analysis and differential geometry, and will embrace theoretical issues as well as computational testing.

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