Extension of the Helmholtz integral equation method to shorter wavelengths

• Published in: The Journal of the Acoustical Society of America Vol. 80; no. 6; pp. 1828 - 1837
• Main Author: TOBOCMAN, W
• Format: Journal Article
• Language: English
• Published: Woodbury, NY Acoustical Society of America 01-12-1986; American Institute of Physics
• Subjects: Acoustics; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Linear acoustics; Physics; Target; Wave propagation; Wave scattering; Helmholtz equation; Acustical wave; Integral equation; Padé approximant; Calculating method
• ISSN: 0001-4966; 1520-8524
• DOI: 10.1121/1.394298

The Helmholtz integral equation method (HIEM) has been shown to be an efficient method for calculating the scattering of waves by arbitrarily shaped targets in the intermediate wavelength regime. The problems involved in treating the scattering of shorter wavelength waves by this method are investigated. The use of the Padé approximant method in place of matrix inversion by Gauss–Jordan elimination mitigates to a significant extent the need for large amounts of random access memory and computing time in shorter wavelength cases. Both the method of Schenck [J. Acoust. Soc. Am. 44, 41 (1968)] and the method of Burton and Miller [Proc. R. Soc. London Ser. A 323, 201 (1971)] are found to be effective in remedying the failure of the HIEM at the characteristic frequencies. However, it is found that when shorter wavelengths are used, the reduction in accuracy of the HIEM at characteristic frequencies tends to become less important. It was observed that at very short wavelengths low-order iteration of the HIE with the Kirchhoff approximation as zeroth iterate is probably the most practical method.