B-spline FEM for time-harmonic acoustic scattering and propagation

Tahsin Khajah (1) , Xavier Antoine (2, 3) , Stéphane P.A. Bordas (4, 5, 6)

1 Departement of Mechanical Engineering, University of Tyler, USA
2 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization
3 IECL - Institut Élie Cartan de Lorraine
4 Uni.lu - Université du Luxembourg
5 Cardiff University
6 University of Western Australia, Intelligent Systems for Biomedecine Laboratory

We study the application of a B-splines Finite Element Method 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 makes B-Spline Finite Element Method a very promising platform to solve high-frequency acoustic problems.

Mots clés: Helmholtz problem; pollution error; time-harmonic acoustics; Scattering; high frequency; Isogeometric Analysis

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Tahsin Khajah, Xavier Antoine, Stéphane P.A. Bordas. B-spline FEM for time-harmonic acoustic scattering and propagation. Journal of Theoretical and Computational Acoustics, 2019, 27 (3), pp.1850059. ⟨10.1142/S2591728518500597⟩. ⟨hal-01377485⟩