The scheme also employs COMSOL Script for solver scripting as well as for hands-on postprocessing with the Fourier decomposition of the Helmholtz- Kirchhoff far-field integral (see Figure 4). The modeling method significantly reduced problem size, and the team was able to model echoes from objects in the mid-frequency regime.

Figure 4: The Frequency Domain Response can be post-processed with the inverse Fourier transform to convert the result into a time-domain echo, whichis what would be measured physically at a receiver. The time-domain echo can in turn be transformed into a time-frequency spectrogram by applying a short time-window Fourier transform. The time-frequency spectrogram exhibits various “ringing” features, which are closely related to the material propertiesand the geometry of the scuba tank.

The team's studies don't fall into conventional areas, so there are no specialized tools for this type of project. With the multiphysics software, the team was able to tailor virtually everything to its particular needs. For instance, the team used weak-form modeling heavily for the azimuthal Fourier decomposition of the structural-acoustics equations.

This work was done by Dr. Mario Zampolli, Dr. Alessandra Tesei, Dr. Gaetano Canepa, and Dr. Finn Jensen of the NATO Undersea Research Centre, using software from COMSOL, Inc. For more information, visit