ANALYTICAL BACKGROUND OF COMPUTATIONAL METHODS FOR UNDERWATER SOUND PROPAGATION.
LITTLE (ARTHUR D) INC CAMBRIDGE MASS
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The main purpose of this report is to provide a survey of the accuracy and speed that can be expected from various computational methods. In general, acoustic wave equation, is dealt with. The computational survey is planned to consist of three parts, of which only the first is completed. This first part summarizes the mathematical properties of certain wave equa tion techniques, from the viewpoint of ultimate computational use. In particular, the funda mental relationships between characteristic surfaces and rays, bicharacteristics, wave fronts, surfaces of constant phase, the sequence of eikonal approximations, the various interpre tations of Huygens principle, the integral formulations of Poisson, Kirchhoff, and Helmholtz, and Hamilton-Jacobi theory are rather thoroughly considered, and are illustrated by a comparative discussion of certain problems in the reflection, refraction, and diffraction of acoustic waves. Author