Commun. Comput. Phys., 10 (2011), pp. 672-694.

Acoustic Scattering Cross Sections of Smart Obstacles: A Case Study

Lorella Fatone 1, Maria Cristina Recchioni 2, Francesco Zirilli 3*

1 Dipartimento di Matematica e Informatica, Universitadi Camerino, Via Madonna delle Carceri 9, 62032 Camerino (MC), Italy.
2 Dipartimento di Scienze Sociali "D. Serrani", Universita Politecnica delle Marche, Piazza Martelli 8, 60121 Ancona, Italy.
3 CERI-Centro di Ricerca "Previsione Prevenzione e Controllo dei Rischi Geologici", Universita di Roma "La Sapienza", Piazza Umberto Pilozzi 9, 00038 Valmontone (RM), Italy.

Received 12 March 2010; Accepted (in revised version) 26 November 2010
Available online 1 June 2011


Acoustic scattering cross sections of smart furtive obstacles are studied and discussed. A smart furtive obstacle is an obstacle that, when hit by an incoming field, avoids detection through the use of a pressure current acting on its boundary. A highly parallelizable algorithm for computing the acoustic scattering cross section of smart obstacles is developed. As a case study, this algorithm is applied to the (acoustic) scattering cross section of a "smart" (furtive) simplified version of the NASA space shuttle when hit by incoming time-harmonic plane waves, the wavelengths of which are small compared to the characteristic dimensions of the shuttle. The solution to this numerically challenging scattering problem requires the solution of systems of linear equations with many unknowns and equations. Due to the sparsity of these systems of equations, they can be stored and solved using affordable computing resources. A cross section analysis of the simplified NASA space shuttle highlights three findings: i) the smart furtive obstacle reduces the magnitude of its cross section compared to the cross section of a corresponding "passive" obstacle; ii) several wave propagation directions fail to satisfactorily respond to the smart strategy of the obstacle; iii) satisfactory furtive effects along all directions may only be obtained by using a pressure current of considerable magnitude. Numerical experiments and virtual reality applications can be found at the website:

AMS subject classifications: 49j20, 49Mxx

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Key words: Acoustic obstacle scattering, smart obstacles, acoustic cross section, open loop control, operator expansion method, wavelet expansion.

*Corresponding author.
Email: (L. Fatone), (M. C. Recchioni), (F. Zirilli)

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