Abstract
New representations for compact source regions are developed. The wave field satisfies the homogeneous Helmholtz equation outside of some finite region, and is assumed known on some value of r = constant, possibly infinite. Given this data, we represent the radiated field by an equivalent distribution of sources in complex space. The point sources are located on the complex “sphere” r = ia, with a weighting uniquely defined by the far-field. Each complex point source acts like a Gaussian beam with a well defined directionality. This type of representation offers an alternative to the usual multipole expansion, and may be preferable if the source is highly directional. In the high frequency limit the far-field pattern function is proportional to the associated weighting function for the complex sources. The theory is developed for both 2D and 3D, and numerical examples are presented for a 3D end-fire array.
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© 1997 Springer-Verlag New York, Inc.
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Norris, A.N., Hansen, T.B. (1997). Wavefield Representation Using Compact and Directionally Localized Sources. In: Engquist, B., Kriegsmann, G.A. (eds) Computational Wave Propagation. The IMA Volumes in Mathematics and its Applications, vol 86. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2422-8_9
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DOI: https://doi.org/10.1007/978-1-4612-2422-8_9
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