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. Fields of science natural sciencesphysical scienceselectromagnetism and electronicselectromagnetismnatural sciencesmathematicspure mathematicsmathematical analysisfunctional analysisnatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equationsnatural sciencesmathematicsapplied mathematicsnumerical analysisnatural sciencesmathematicsapplied mathematicsmathematical model Keywords Compatible discretizations Isogeometric analysis Numerical methods for PDEs Variational techniques Programme(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Topic(s) ERC-SG-PE1 - ERC Starting Grant - Mathematical foundations 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 EU contribution € 750 000,00 Address PIAZZALE ALDO MORO 7 00185 Roma Italy See on map Region Centro (IT) Lazio Roma Activity type Research Organisations Principal investigator Annalisa Buffa (Dr.) Administrative Contact Giovanni Sacchi (Dr.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data Beneficiaries (1) Sort alphabetically Sort by EU Contribution Expand all Collapse all CONSIGLIO NAZIONALE DELLE RICERCHE Italy EU contribution € 750 000,00 Address PIAZZALE ALDO MORO 7 00185 Roma See on map Region Centro (IT) Lazio Roma Activity type Research Organisations Principal investigator Annalisa Buffa (Dr.) Administrative Contact Giovanni Sacchi (Dr.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data
