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Innovative compatible discretization techniques for Partial Differential Equations

Innovative compatible discretization techniques for Partial Differential Equations

Objective

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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Principal Investigator

Annalisa Buffa (Dr.)

Host institution

CONSIGLIO NAZIONALE DELLE RICERCHE

Address

Piazzale Aldo Moro 7
00185 Roma

Italy

Activity type

Higher or Secondary Education Establishments

EU Contribution

€ 750 000

Principal Investigator

Annalisa Buffa (Dr.)

Administrative Contact

Giovanni Sacchi (Dr.)

Beneficiaries (1)

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CONSIGLIO NAZIONALE DELLE RICERCHE

Italy

EU Contribution

€ 750 000

Project information

Grant agreement ID: 205004

Status

Closed project

  • Start date

    1 July 2008

  • End date

    30 June 2013

Funded under:

FP7-IDEAS-ERC

  • Overall budget:

    € 750 000

  • EU contribution

    € 750 000

Hosted by:

CONSIGLIO NAZIONALE DELLE RICERCHE

Italy

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