3D NURBS-Enhanced Finite Element Method (NEFEM)

Author (s): Sevilla, R;, Fernandez-Mendez, S. and Huerta A.
Journal: International Journal for Numerical Methods in Engineering

Volume: 88, Issue 2
Pages: 103 – 125
Date: 2011

This paper presents the extension of the recently proposed NURBS-Enhanced Finite Element Method (NEFEM) to 3D domains. NEFEM is able to exactly represent the geometry of the computational domain by means of its CAD boundary representation with Non-Uniform Rational B-Splines (NURBS) surfaces. Specific strategies for interpolation and numerical integration are presented for those elements affected by the NURBS boundary representation. For elements not intersecting the boundary, a standard finite element rationale is used, preserving the efficiency of classical FEM. In 3D NEFEM special attention must be paid to geometric issues that are easily treated in the 2D implementation. Several numerical examples show the performance and benefits of NEFEM compared to standard isoparametric or Cartesian finite elements. NEFEM is a powerful strategy to efficiently treat curved boundaries and it avoids excessive mesh refinement to capture small geometric features.



author = {Ruben Sevilla and Sonia Fernández‐Méndez and Antonio Huerta},
title = {3D NURBS‐enhanced finite element method (NEFEM)},
journal = {International Journal for Numerical Methods in Engineering},
volume = {88},
number = {2},
pages = {103-125},
keywords = {NURBS, accurate geometry representation, CAD, finite elements, discontinuous Galerkin, high‐order isoparametric approximations},
doi = {10.1002/nme.3164},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.3164},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.3164},