TY - GEN

T1 - A Fast Boundary Integral Solution for the Acoustic Response of Three-Dimensional Axi-Symmetric Scatterers

AU - Schuster, Gerard

PY - 1989/1/1

Y1 - 1989/1/1

N2 - A Boundary Integral Equation (BIE) method is presented which efficiently computes the harmonic acoustic response of axi-symmetric structures. The key idea is that the BIE's are Fourier transformed via FFT's in the azimuthal variable; this reduces the azimuthal periodic convolutions to simple multiplications. The original three-dimensional problem is transformed into a series of M decoupled two-dimensional problems, where M is the number of azimuthal Fourier components. If N is the number of nodal points along the semi-perimeter of a scatterer, then the harmonic response can be computed with just O(N3M) algebraic operations. This is far less expensive than solving the original problem which requires O(N6) algebraic operations per frequency. Moreover, the active memory requirement is reduced from O(N4) to O(N2) complex words, and the algorithm is ideally suited to a parallel computer. Examples are given where less than three minutes were required by a Gould computer (4 MIPs) to compute the harmonic response of a scatterer four wavelengths in dimension.

AB - A Boundary Integral Equation (BIE) method is presented which efficiently computes the harmonic acoustic response of axi-symmetric structures. The key idea is that the BIE's are Fourier transformed via FFT's in the azimuthal variable; this reduces the azimuthal periodic convolutions to simple multiplications. The original three-dimensional problem is transformed into a series of M decoupled two-dimensional problems, where M is the number of azimuthal Fourier components. If N is the number of nodal points along the semi-perimeter of a scatterer, then the harmonic response can be computed with just O(N3M) algebraic operations. This is far less expensive than solving the original problem which requires O(N6) algebraic operations per frequency. Moreover, the active memory requirement is reduced from O(N4) to O(N2) complex words, and the algorithm is ideally suited to a parallel computer. Examples are given where less than three minutes were required by a Gould computer (4 MIPs) to compute the harmonic response of a scatterer four wavelengths in dimension.

UR - http://www.scopus.com/inward/record.url?scp=85012605097&partnerID=8YFLogxK

U2 - 10.1016/B978-0-08-037018-7.50015-5

DO - 10.1016/B978-0-08-037018-7.50015-5

M3 - Conference contribution

AN - SCOPUS:85012605097

T3 - Handbook of Geophysical Exploration: Seismic Exploration

SP - 252

EP - 278

BT - Handbook of Geophysical Exploration

ER -