Geometry Independent Field approximaTion (GIFT); Isogeometric analysis; Partition of unity; PHT-splines; Recovery-based & residual-based adaptive refinement; Time-harmonic acoustics; Adaptive refinement; Field approximations; Geometry independent field approximation; Non-uniform rational B-splines; PHT-spline; Time-harmonic; Time-harmonic acoustic; Civil and Structural Engineering; Modeling and Simulation; Materials Science (all); Mechanical Engineering; Computer Science Applications; (GIFT); Recovery-based & residual-based adaptive; refinement; General Materials Science
Abstract :
[en] Isogeometric Analysis (IGA) provides an alternative to Lagrange based finite element methods by representing the geometry and field with the same Non-Uniform Rational B-Splines (NURBS) shape functions within a weak Galerkin formulation. IGA has proven to be highly efficient in solving the Helmholtz equation, due to the ease with which the order and continuity of the approximation space can be increased, as well as the geometrical exactness enabled by the use of NURBS. In Atroshchenko et al. (2018), we generalize IGA, by allowing an independent representation of the geometry and fields (Geometry Independent Field approximaTion, GIFT or Generalized IGA Marussig et al., 2015). GIFT with NURBS and PHT-splines (for the geometry and the field, respectively) allows to keep original coarse parameterization of CAD geometry and enables adaptive local refinement of the solution. In the present work, we investigate the possibility to further improve the approach by enriching the PHT-splines field approximation with a set of plane-waves propagating in different directions. Plane wave enrichment is commonly used to capture oscillatory behaviour of the solution and achieve smaller error on coarser meshes. The performance of PUPHT-splines for varying frequencies, degree of PHT-splines, number of plane waves, different refinement strategies is demonstrated on three benchmark problems.
Disciplines :
Mechanical engineering
Author, co-author :
JANSARI, Chintankumar Vipulbhai ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Engineering (DoE)
Videla, Javier; School of Civil and Environmental Engineering, University of New South Wales, Sydney, Australia
Natarajan, Sundararajan; Mechanics Application to Responsive Systems Lab, Department of Mechanical Engineering, Indian Institute of Technology Madras, India
BORDAS, Stéphane ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Engineering (DoE) ; The University of Utah > Department of Mechanical Engineering > Clyde Visiting Fellow ; China Medical University Hospital, China Medical University, Taichung, Taiwan > Department of Medical Research
ATROSHCHENKO, Elena ; University of Luxembourg ; School of Civil and Environmental Engineering, University of New South Wales, Sydney, Australia
External co-authors :
yes
Language :
English
Title :
Adaptive enriched geometry independent field approximation for 2D time-harmonic acoustics
Horizon 2020 Framework Programme Horizon 2020 Université du Luxembourg
Funding text :
Stéphane P.A. Bordas acknowledges the funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 811099 TWINNING Project DRIVEN for the University of Luxembourg.St?phane P.A. Bordas acknowledges the funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 811099 TWINNING Project DRIVEN for the University of Luxembourg.
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