High order methods for acoustic scattering: Coupling farfield expansions ABC with deferred-correction methods

• Published in: Wave Motion
• Main Authors: Villamizar, Vianey, Grundvig, Dane, Rojas, Otilio, Acosta, Sebastian
• Other Authors: Barcelona Supercomputing Center
• Format: Article in Journal/Newspaper
• Language: English
• Published: Elsevier 2020
• Subjects: Àrees temàtiques de la UPC::Informàtica::Aplicacions de la informàtica::Aplicacions informàtiques a la física i l‘enginyeria; High performance computing; Acoustic scattering; High order absorbing boundary conditions; Helmholtz equation; High order numerical methods; Deferred-correction methods; Càlcul intensiu (Informàtica); Helmholtz; Equació de; Brigham; Acosta; Rojas; Orca
• Online Access: http://hdl.handle.net/2117/345928; https://doi.org/10.1016/j.wavemoti.2020.102529

Arbitrary high order numerical methods for time-harmonic acoustic scattering problems originally defined on unbounded domains are constructed. This is done by coupling recently developed high order local absorbing boundary conditions (ABCs) with finite difference methods for the Helmholtz equation. These ABCs are based on exact representations of the outgoing waves by means of farfield expansions. The finite difference methods, which are constructed from a deferred-correction (DC) technique, approximate the Helmholtz equation and the ABCs, with the appropriate number of terms, to any desired order. As a result, high order numerical methods with an overall order of convergence equal to the order of the DC schemes are obtained. A detailed construction of these DC finite difference schemes is presented. Additionally, a rigorous proof of the consistency of the DC schemes with the Helmholtz equation and the ABCs in polar coordinates is also given. The results of several numerical experiments corroborate the high order convergence of the novel method. The first and third authors acknowledge the support provided by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant No 777778 (MATHROCKS), and by the Office of Research and Creative Activities (ORCA) of Brigham Young University, United States of America. The work of S. Acosta was partially supported by National Science Foundation, United States of America [grant number DMS-1712725]. O. Rojas was also partially supported by the European Union’s Horizon 2020 research and innovation programme under the ChEESE project, grant agreement No. 823844. Peer Reviewed Postprint (author's final draft)