Furtivity and masking problems in time dependent acoustic obstacle scattering

62032 Camerino (MC) Italy,

E-mail: fatone@campus.unicam.it

60121 Ancona, Italy,

E-mail: recchioni@posta.econ.unian.it

00185 Roma, Italy

E-mail: f.zirilli@caspur.it

We consider ``furtivity" and ``masking" problems in time dependent acoustic obstacle scattering. Roughly speaking a ``furtivity" (``masking") problem consists in making ``undetectable" (``unrecognizable") an object immersed in a medium where an acoustic wave that scatters on the object is propagating. The detection (recognition) of the obstacle must be made through the knowledge of the acoustic field scattered by the object when hit by the propagating wave. These problems are interesting in several application fields. We formulate a mathematical model for the ``furtivity" and ``masking" problems considered consisting in optimal control problems for the wave equation. Using the Pontryagin maximum principle we show that the solution of these control problems can be characterized as the solution of a suitable exterior problem for a system of two coupled wave equations. The numerical solution of these systems involving partial differential equations in four (space, time) independent variables is a critical issue when reliable and efficient procedures to solve the furtivity or masking problem are required. High performance parallel algorithms are desirable to solve these systems. We suggest a computational method well suited for parallel computing and based on the operator expansion method introduced in [1] and developed by the authors and some co-authors in [2]-[9]. Finally we make some comments on the possible extension of this work to electromagnetic obstacle scattering and fluid mechanics.

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``A new formalism for time dependent wave scattering from a bounded
obstacle",
*Journal of the Acoustical Society of America***107**, 1825-1840 (2000). - [3]
- F. Mariani, M.C. Recchioni and F. Zirilli,
``The use of the Pontryagin
maximum principle in a furtivity problem in time-dependent acoustic
obstacle scattering",
*Waves in Random Media***11**, 1-27 (2001). - [4]
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a disturbed half-space: an existence theorem and a computational method",
*Journal of Mathematical Physics***37**, 2762-2786 (1996). - [5]
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from a bounded obstacle",
*Journal of the Acoustical Society of America***103**, 106-113 (1998). - [6]
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electromagnetic scattering from a bounded obstacle: an existence theorem
and a computational method",
*Journal of Mathematical Physics***40**, 4859-4887 (1999). - [7]
- M. C. Recchioni and F. Zirilli,
``High performance algorithms for time dependent wave scattering from a
bounded obstacle", in the website: http://www.cineca.it/mpp-workshop/fullpapers/zirilli/zirilli.html, in
*Proceedings Fifth European SGI/CRAY MPP - Massive Parallel Processing Workshop, Bologna (Italy), September 9-10, 1999*, in the website: http://www.cineca.it/mpp-workshop/proceedings.htm (1999). - [8]
- M. C. Recchioni and F. Zirilli, ``The use of wavelets
in the operator expansion method for time dependent acoustic obstacle
scattering", submitted to
*SIAM Journal on Scientific Computing*. - [9]
- M. C. Recchioni and F. Zirilli, ``A new formalism for
time dependent electromagnetic scattering from a bounded obstacle",
in print on
*Journal of Engineering Mathematics*.### ANIMATION: Truncated octahedron u

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