Acceleration of the modal series in the Neumann scattering problem for a hemispherical shell

A mixed boundary value problem for the scalar acoustic field scattered by an axisymmetric plane wave incident upon a hard hemispherical shell is formulated. The resulting discontinuity in surface pressure is expressed in terms of a complete set of weighted Chebyshev polynomials that satisfy the corr...

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Bibliographic Details
Main Authors: Denison, D.R., Scharstein, R.W.
Format: Conference Proceeding
Language:English
Subjects:
Acceleration
Acoustic scattering
Acoustic waves
Boundary value problems
Chebyshev approximation
Diffraction
Electromagnetic scattering
Geometry
Polynomials
Radar scattering
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Summary:A mixed boundary value problem for the scalar acoustic field scattered by an axisymmetric plane wave incident upon a hard hemispherical shell is formulated. The resulting discontinuity in surface pressure is expressed in terms of a complete set of weighted Chebyshev polynomials that satisfy the correct asymptotic edge condition. In this way, the extremely slowly converging modal series of spherical wave functions is transformed to a convergent sum of physically motivated basis functions. Truncation to a finite number of unknown coefficients, together with Galerkin projection, yields a set of linear algebraic equations.
ISSN:0094-2898
2161-8135
DOI:10.1109/SSST.1993.522737