Formulation and accuracy of on-surface radiation conditions for acoustic multiple scattering problems

Hasan Alzubaidi (1) , Xavier Antoine (2, 3) , Chokri Chniti (4)

1 Umm Al-Qura University
2 SPHINX - Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization
3 IECL - Institut Élie Cartan de Lorraine
4 Faculty of Applied Sciences, Umm Al-Qura University

The aim of this paper is 1) to address an extension of the On-Surface Radiation Condition (OSRC) method to multiple scattering by a cluster of convex obstacles and 2) to analyze the numerical accuracy of the formulation for some model problems. First, the acoustic scattering problem is considered and materials about integral equations and OSRCs are recalled. Then, an OSRC integral equation formulation is developed for the Dirichlet multiple scattering problem. Finally, an extensive numerical study of the method is proposed in the special case of the scattering by circular cylinders. Even if this situation is not completely general, it provides an assessment of the accuracy of the approximation, with respect to various parameters, including thanks to the choice of the OSRC operators.

Mots clés: acoustics; on-surface radiation conditions; multiple scattering; Helmholtz equation; numerical method

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

Hasan Alzubaidi, Xavier Antoine, Chokri Chniti. Formulation and accuracy of on-surface radiation conditions for acoustic multiple scattering problems. Applied Mathematics and Computation, 2016, 277, pp.82-100. ⟨10.1016/j.amc.2015.12.023⟩. ⟨hal-01244517⟩