by V.A. Dougalis, N.A. Kampanis
Models based on parabolic approximations to describe acoustic propagation in a multi-layered, range-dependent ocean environment in the absence of significant backscatter, are very widespread in computational underwater acoustics. Novel and efficient finite difference and finite element methods for the numerical solution of such "standard" and "wide-angle" approximations, in environments with cylindrical symmetry, have been successfully developed and analyzed. Currently, the focus of research is concentrated on extending these methods to fully 3-dimensional environments.
Computational underwater acoustics is concerned with the numerical prediction of the acoustic field due to a point harmonic source, in a realistic range-dependent ocean environment, with multi-layered bottom structure and variable topography of the water-bottom interface. The use of parabolic approximations is one of the most popular methods to model underwater acoustic propagation in the absence of significant backscatter. These are evolution equations in the direction of the range (distance from the source), of Schrodinger type, occurring as paraxial approximations to the far-field Helmholtz equation.
The numerical solution of the "standard" and the "wide-angle" parabolic approximations in problems with cylindrical symmetry is of main practical interest. Innovative methods for the solution of these equations are being developed and analysed, based on finite difference and finite element techniques. Attention has been given to devising novel methods that handle accurately interface conditions between adjacent layers of the medium, even in the case of variable interface topography. Much care has also been given to the realistic treatment of the seabed and the sea surface, by introducing in the models boundary conditions that more closely approximate reality, like the nonlocal (impedance) boundary conditions of J. S. Papadakis.
Theoretical research has been further accompanied by the implementation of the resulting methods in efficient, fast and accurate computer codes, organized in a user-friendly environment at IACM-FORTH. Novel computer architectures, such as a two-processor CONVEX C3420 system with shared memory are hosted by FORTH and are used to study parallelization at coarse-grain of these methods. This work is partially funded by several National projects, as well as by the European Commission, within the framework of the MAST programme. Results were also presented at the ERCIM Workshop on Numerical Methods for Linear and Nonlinear Problems in Wave Propagation held in Heraklion, Greece, October 29-30, 1992.
Current research activities are concentrated on 3-dimensional parabolic approximation models. Well-known methods in the literature for the numerical solution of such models have been extended, e.g. by coupling them with appropriate impedance type boundary conditions. This work is also concerned with the development of new finite difference and finite element methods and their efficient computer implementation.
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