A performance study of NURBS-based isogeometric analysis for interior two-dimensional time-harmonic acoustics

This work evaluates the performance of a NURBS-based isogeometric finite element formulation for solving stationary acoustic problems in two dimensions. An initial assessment is made by studying eigenvalue problems for a square and a circular domain. The spectral approximation properties of NURBS fu...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2016-06, Vol.305, p.441-467
Main Authors: Coox, Laurens, Deckers, Elke, Vandepitte, Dirk, Desmet, Wim
Format: Article
Language:English
Subjects:
Acoustics
Computer simulation
Eigenvalues
Finite elements
Frequency ranges
Helmholtz problem
Isogeometric analysis
Mathematical analysis
Mathematical models
NURBS
Polynomials
Time-harmonic acoustics
Two dimensional
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Summary:This work evaluates the performance of a NURBS-based isogeometric finite element formulation for solving stationary acoustic problems in two dimensions. An initial assessment is made by studying eigenvalue problems for a square and a circular domain. The spectral approximation properties of NURBS functions of varying order are compared to those of conventional polynomials and are found to be superior, yielding more accurate representations of eigenvalues as well as eigenmodes. The higher smoothness of NURBS shape functions yields better approximations over an extended frequency range when compared to conventional polynomials. Two numerical case studies, including a geometrically complex domain, are used to benchmark the method versus the traditional finite element method. A convergence analysis confirms the higher efficiency of the isogeometric method on a per-degree-of-freedom basis. Simulations over a wider frequency range also illustrate that the method suffers less from the dispersion effects that deteriorate the acoustic response towards higher frequencies. The tensor product structure of NURBS, however, also imposes practical considerations when modelling a complex geometry consisting of multiple patches. •The performance of NURBS-based IGA for time-harmonic acoustics in 2D is studied.•NURBS functions exhibit better spectral approximation properties than polynomials.•IGA converges faster than conventional FEM on a per-DOF-basis.•IGA suffers less from the pollution effect than conventional FEM.•IGA also performs well for complex geometries and impedance boundary conditions.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2016.03.007