TY - EJOU
AU - Gergidis, L.N.
AU - Kourounis, D.
AU - Mavratzas, S.
AU - Charalambopoulos, A.
TI - Acoustic Scattering in Prolate Spheroidal Geometry via Vekua Tranformation -- Theory and Numerical Results
T2 - Computer Modeling in Engineering \& Sciences
PY - 2007
VL - 21
IS - 2
SN - 1526-1506
AB - A new complete set of scattering eigensolutions of Helmholtz equation in spheroidal geometry is constructed in this paper. It is based on the extension to exterior boundary value problems of the well known Vekua transformation pair, which connects the kernels of Laplace and Helmholtz operators. The derivation of this set is purely analytic. It avoids the implication of the spheroidal wave functions along with their accompanying numerical deficiencies. Using this novel set of eigensolutions, we solve the acoustic scattering problem from a soft acoustic spheroidal scatterer, by expanding the scattered field in terms of it. Two approaches concerning the determination of the expansion coefficients are extensively studied in terms of their numerical and convergence properties. The first one minimizes the *L*^{2}-norm of a suitably constructed error function and the second one relies on collocation techniques. The robustness of these approaches is established via the adoption of arbitrary precision arithmetic.
KW - Prolate Spheroid
KW - Acoustic Scattering
KW - Vekua Transformation
KW - Arbitrary Precision
KW - *L*^{2}-norm Minimization
KW - Collocation
KW - Mathematical Modeling
KW - Special Functions
KW - Scientific Computing
DO - 10.3970/cmes.2007.021.157