Premium
Numerical investigation of the acoustic scattering problem from penetrable prolate spheroidal structures using the Vekua transformation and arbitrary precision arithmetic
Author(s) -
Gergidis Leonidas N.,
Kourounis Drosos,
Mavratzas Stylianos,
Charalambopoulos Antonios
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5058
Subject(s) - helmholtz equation , mathematics , mathematical analysis , scattering , transformation (genetics) , prolate spheroid , field (mathematics) , kernel (algebra) , convergence (economics) , geometry , boundary value problem , optics , physics , pure mathematics , biochemistry , chemistry , economics , gene , economic growth
A complete set of radiating “outwards” eigensolutions of the Helmholtz equation, obtained by transforming appropriately through the Vekua mapping the kernel of Laplace equation, is applied to the investigation of the acoustic scattering by penetrable prolate spheroidal scatterers. The scattered field is expanded in terms of the aforementioned set, detouring so the standard spheroidal wave functions along with their inherent numerical deficiencies. The coefficients of the expansion are provided by the solution of linear systems, the conditioning of which calls for arbitrary precision arithmetic. Its integration enables the polyparametric investigation of the convergence of the current approach to the solution of the direct scattering problem. Finally, far‐field pattern visualization in the 3D space clarifies the preferred scattering directions for several frequencies of the incident wave, ranging from the “low” to the “resonance” region.