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See detailB-Spline FEM for Time-Harmonic Acoustic Scattering and Propagation
Khajah, Tahsin; Antoine, Xavier; Bordas, Stéphane UL

in Journal of Theoretical and Computational Acoustics (2019), 27

We study the application of a B-splines Finite Element Method (FEM) to time-harmonic scattering acoustic problems. The infinite space is truncated by a fictitious boundary and second-order Absorbing ... [more ▼]

We study the application of a B-splines Finite Element Method (FEM) to time-harmonic scattering acoustic problems. The infinite space is truncated by a fictitious boundary and second-order Absorbing Boundary Conditions (ABCs) are applied. The truncation error is included in the exact solution so that the reported error is an indicator of the performance of the numerical method, in particular of the size of the pollution error. Numerical results performed with high-order basis functions (third or fourth order) showed no visible pollution error even for very high frequencies. To prove the ability of the method to increase its accuracy in the high frequency regime, we show how to implement a high-order Padé-type ABC on the fictitious outer boundary. The above-mentioned properties combined with exact geometrical representation make B-Spline FEM a very promising platform to solve high-frequency acoustic problems. [less ▲]

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See detailh- and p-adaptivity driven by recovery and residual-based error estimators for PHT-splines applied to time-harmonic acoustics
Videla, Javier; Anitescu, Cosmin; Khajah, Tahsin et al

in Computers and Mathematics with Applications (2018), 77(9), 2369-2395

In this work, we demonstrate the application of PHT-splines for time-harmonic acoustic problems, modeled by the Helmholtz equation. Solutions of the Helmholtz equation have two features: global ... [more ▼]

In this work, we demonstrate the application of PHT-splines for time-harmonic acoustic problems, modeled by the Helmholtz equation. Solutions of the Helmholtz equation have two features: global oscillations associated with the wave number and local gradients caused by geometrical irregularities. We show that after a sufficient number of degrees of freedom is used to approximate global oscillations, adaptive refinement can capture local features of the solution. We compare residual-based and recovery-based error estimators and investigate the performance of -refinement. The simulations are done in the context of recently introduced Geometry Independent Field approximaTion (GIFT), where PHT-splines are only used to approximate the solution, while the computational domain is parameterized with NURBS. This approach builds on the natural adaptation ability of PHT-splines and avoids the re-parameterization of the NURBS geometry during the solution refinement process. [less ▲]

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See detailHigh Frequency Acoustic Scattering in Isogeometric Analysis
Khajah, Tahsin; Antoine, Xavier; Bordas, Stéphane UL

Scientific Conference (2017, May 15)

There is an emerging need to perform high frequency scattering analysis on high-fidelity models. Conventional Finite Element analysis suffers from irretrievable loss of the boundary accuracy as well as ... [more ▼]

There is an emerging need to perform high frequency scattering analysis on high-fidelity models. Conventional Finite Element analysis suffers from irretrievable loss of the boundary accuracy as well as pollution error. Man-made geometries can be represented exactly in Isogeometric Analysis (IGA) with no geometrical loss even with very coarse mesh. The aim of this paper is to analyze the accuracy of IGA for exterior acoustic scattering problems. The numerical results show extremely low pollution error even for very high frequencies. [less ▲]

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See detailIsogeometric finite element analysis of time-harmonic exterior acoustic scattering problems
Khajah, Tahsin; Antoine, Xavier; Bordas, Stéphane UL

E-print/Working paper (2016)

We present an isogeometric analysis of time-harmonic exterior acoustic problems. The infinite space is truncated by a fictitious boundary and (simple) absorbing boundary conditions are applied. The ... [more ▼]

We present an isogeometric analysis of time-harmonic exterior acoustic problems. The infinite space is truncated by a fictitious boundary and (simple) absorbing boundary conditions are applied. The truncation error is included in the exact solution so that the reported error is an indicator of the performance of the isogeometric analysis, in particular of the related pollution error. Numerical results performed with high-order basis functions (third or fourth orders) showed no visible pollution error even for very high frequencies. This property combined with exact geometrical representation makes isogeometric analysis a very promising platform to solve high-frequency acoustic problems. [less ▲]

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