Reference : Geometry-Independent Field approximaTion: CAD-Analysis Integration, geometrical exact... |

Scientific journals : Article | |||

Engineering, computing & technology : Multidisciplinary, general & others | |||

Computational Sciences | |||

http://hdl.handle.net/10993/15781 | |||

Geometry-Independent Field approximaTion: CAD-Analysis Integration, geometrical exactness and adaptivity | |

English | |

[fr] Approximation de champ indépendante de la géométrie: Intégration CAD-analyse, précision géométrique et adaptation | |

[de] Geometrie-Unabhängige Feld-Approximation: CAD-Analyse Integration, geometrische Genauigkeit und Adaptivität | |

Xu, Gang [> >] | |

Atroshchenko, Elena [> >] | |

Ma, Weiyin [> >] | |

Bordas, Stéphane [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >] | |

1-Sep-2014 | |

Computer Methods in Applied Mechanics and Engineering | |

Elsevier Science | |

Isogeometric Analysis | |

Yes (verified by ORBi^{lu}) | |

International | |

0045-7825 | |

Lausanne | |

Switzerland | |

[en] generalised isogeometric analysis ; splines ; geometry-independent approximation | |

[en] In isogeometric analysis (IGA), the same spline representation is employed for both the geometry
of the domain and approximation of the unknown fields over this domain. This identity of the geometry and field approximation spaces was put forward in the now classic 2005 paper [20] as a key advantage on the way to the integration of Computer Aided Design (CAD) and subsequent analysis in Computer Aided Engineering (CAE). [20] claims indeed that any change to the geometry of the domain is automatically inherited by the approximation of the field variables, without requiring the regeneration of the mesh at each change of the domain geometry. Yet, in Finite Element versions of IGA, a parameterization of the interior of the domain must still be constructed, since CAD only provides information about the boundary. The identity of the boundary and field representation decreases the flexibility in which this parameterization can be generated and somewhat constrains the modeling and simulation process, because an approximation able to represent the domain geometry accurately need not be adequate to also approximate the field variables accurately, in particular when the solution is not smooth. We propose here a new paradigm called Geometry-Independent Field approximaTion (GIFT) where the spline spaces used for the geometry and the field variables can be chosen and adapted independently while preserving geometric exactness and tight CAD integration. GIFT has the following features: (1) It is possible to flexibly choose between different spline spaces with different properties to better represent the solution of the problem, e.g. the continuity of the solution field, boundary layers, singularities, whilst retaining geometrical exactness of the domain boundary. (2) For multi-patch analysis, where the domain is composed of several spline patches, the continuity condition between neighboring patches on the solution field can be automatically guaranteed without additional constraints in the variational form. (3) Refinement operations by knot insertion and degree elevation are performed directly on the spline space of the solution field, independently of the spline space of the geometry of the domain, which makes the method versatile. GIFT with PHT-spline solution spaces and NURBS geometries is used to show the effectiveness of the proposed approach. Keywords : Super-parametric methods, Isogeometric analysis (IGA), Geometry-independent Spline Space, PHT-splines, local refinement, adaptivity | |

Researchers ; Professionals ; Students ; Others | |

http://hdl.handle.net/10993/15781 | |

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