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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.

Field of science

  • /natural sciences/mathematics/applied mathematics/mathematical model
  • /humanities/languages and literature/literature - general
  • /natural sciences/mathematics/applied mathematics/numerical analysis
  • /natural sciences/computer and information sciences/software
  • /natural sciences/mathematics/pure mathematics/geometry
  • /natural sciences/physical sciences/electromagnetism and electronics/electromagnetism
  • /natural sciences/mathematics
  • /natural sciences/mathematics/pure mathematics/mathematical analysis/differential equations/partial differential equations
  • /natural sciences/physical sciences/classical mechanics/fluid mechanics/fluid dynamics

Call for proposal

ERC-2007-StG
See other projects for this call

Funding Scheme

ERC-SG - ERC Starting Grant

Host institution

CONSIGLIO NAZIONALE DELLE RICERCHE
Address
Piazzale Aldo Moro 7
00185 Roma
Italy
Activity type
Research Organisations
EU contribution
€ 750 000
Principal investigator
Annalisa Buffa (Dr.)
Administrative Contact
Giovanni Sacchi (Dr.)

Beneficiaries (1)

CONSIGLIO NAZIONALE DELLE RICERCHE
Italy
EU contribution
€ 750 000
Address
Piazzale Aldo Moro 7
00185 Roma
Activity type
Research Organisations
Principal investigator
Annalisa Buffa (Dr.)
Administrative Contact
Giovanni Sacchi (Dr.)