PAPER:

Furtivity and masking problems in time dependent acoustic obstacle scattering

 

L. FATONE

Dipartimento di Matematica e Fisica, Università di Camerino, Via Madonna delle Carceri,
62032 Camerino (MC) Italy,
E-mail: fatone@campus.unicam.it

M.C. RECCHIONI

Istituto di Teoria delle Decisioni e Finanza Innovativa (DE.F.IN.), Università di Ancona, Piazza Martelli 8,
60121 Ancona, Italy,
E-mail: recchioni@posta.econ.unian.it

F. ZIRILLI

Dipartimento di Matematica ``G. Castelnuovo'', Università di Roma ``La Sapienza'', Piazzale Aldo Moro 2,
00185 Roma, Italy
E-mail: f.zirilli@caspur.it

 

Abstract

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.

References

[1]
D. M. Milder, ``An improved formalism for wave scattering from rough surface", Journal of the Acoustical Society of America 89, 529-541 (1991).

[2]
E. Mecocci, L. Misici, M. C. Recchioni and F. Zirilli, ``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]
S. Piccolo, M. C. Recchioni and F. Zirilli, ``The time harmonic electromagnetic field in a disturbed half-space: an existence theorem and a computational method", Journal of Mathematical Physics 37, 2762-2786 (1996).

[5]
L. Misici, G. Pacelli and F. Zirilli, ``A new formalism for wave scattering from a bounded obstacle", Journal of the Acoustical Society of America 103, 106-113 (1998).

[6]
L. Fatone, C. Pignotti, M. C. Recchioni and F. Zirilli, ``Time harmonic 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 ui = e-(z+t)2

 

 

 

 

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