A masking problem in time dependent acoustic obstacle scattering

Fatone, Lorella; Recchioni, Maria Cristina; Zirilli, Francesco

doi:10.1121/1.1638811

Cited by 9 publications

(20 citation statements)

References 3 publications

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“…Indeed, the dependence of the boundary conditions (18), (22) on the values ofũ s for x / ∈ ∂ is also contained in the normal derivative ∂· /∂n that appears in (18) and (22). That "non-locality" of the boundary conditions (18) and (22) is not a specific characteristic of the definite-band ghost-obstacle problem, and it was already present through the term involving the normal derivative in the furtivity and masking problems considered in [1,4] while the "non-locality" of the functional F λ,µ, given in (9) is a specific characteristic of the definite-band ghost problem and also the dependence of (22) at time t on the valuesũ s (x, τ ) with τ ∈ IR seems to be a specific non-local characteristic of definite-band problems. That is, the "non-locality" appears in the definite-band problems in a new form.…”

Section: Mathematical Formulation Of the Definite-band Ghost-obstaclementioning

confidence: 92%

“…Consequently, the first-order optimality conditions of these new optimal-control problems change substantially and cannot be deduced from those derived in [1,4,5] for the optimal-control problems (1)- (3). That is, the first-order optimality conditions are not expressed by two wave equations coupled by local boundary conditions as in [1,4,5], but the coupling between the two wave equations is given by non-local (in time) boundary conditions (see Eq. (22)).…”

Section: Introductionmentioning

confidence: 91%

“…Note that the functional F λ,µ, given in (9) is "non-local" with respect to the state variables since it depends on the values of u s (x, t), (x, t) ∈ ∂ × IR and that the functionals considered previously in the furtivity and in the masking problems in [1], [4] seem to be "local" in the previous sense. Hence, one of the difficulties of the model (10), (1), (4)-(6) is the "non-local" character of the functional given in (9).…”

Section: Mathematical Formulation Of the Definite-band Ghost-obstaclementioning

confidence: 97%

“…(22). The furtivity problem and the ghost-obstacle problem studied in [1][2][3][4][5] can be considered as particular cases of the corresponding definite-band problems. The furtivity problem, studied in [1] can be interpreted as an "infinite" band furtivity problem; in fact, the furtivity problem of [1] amounts to making the wave scattered by the obstacle as small as possible in the entire frequency space (i.e., corresponds to the choice K = IR).…”

Section: Mathematical Formulation Of the Definite-band Ghost-obstaclementioning

confidence: 99%

“…(2) To appear with a shape and a boundary impedance different from the actual ones (i.e., masking problem) [2][3][4]. (3) To appear in a location in space different from its actual one, eventually with a shape and boundary impedance different from its actual ones (i.e., ghost obstacle problem) [5].…”

Section: Introductionmentioning

confidence: 99%

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Optimal-control methods for two new classes of smart obstacles in time-dependent acoustic scattering

et al. 2006

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Time-dependent acoustic scattering problems involving "smart" obstacles are considered. When hit by an incident acoustic field, smart obstacles react in an attempt to pursue a preassigned goal. Let IR 3 be the three-dimensional real Euclidean space, and let ⊂ IR 3 be a bounded simply connected open set with a Lipschitz boundary characterized by a constant acoustic boundary impedance χ , immersed in an isotropic and homogeneous medium that fills IR 3 \ . The closure of will be denoted as . When hit by an incident field, the obstacle pursues the preassigned goal through the action of a control input acting on its boundary (i.e., a quantity with dimensions of a pressure divided by a time). The obstacles considered in this paper monitor the control input acting on their boundaries in order to achieve one of the following goals: (i) be furtive in a given set of the frequency space, and (ii) appear in a given set of the frequency space and outside a given set of IR 3 containing and G as similar as possible to a "ghost" obstacle G having boundary acoustic impedance χ G . It is assumed that ∩ G = ∅ and G = ∅. The problem corresponding to the first goal will be called the definite-band furtivity problem, and the problem corresponding to the second goal will be called the definite-band ghost-obstacle problem. These two L. Fatone 386 J Eng Math (2006) 56:385-413 goals define two classes of smart obstacles. In this paper, these problems are modeled as optimal-control problems for the wave equation introducing a control input acting on the boundary of for time t ∈ IR. The cost functionals proposed depend on the value of the control input on the boundary of the obstacle and on the value of the scattered acoustic field generated by the obstacle on the boundary in the "furtivity case", and on the boundary of a suitable set containing and G in the "ghost-obstacle case". Under some assumptions, the use of the Pontryagin maximum principle allows us to formulate the first-order optimality conditions for the definite-band furtivity problem and for the definite-band ghost-obstacle problem as exterior problems outside the obstacle for a system of two coupled wave equations. Numerical methods to solve these exterior problems are developed by extending previous work. These methods belong to the class of the operator-expansion methods that are highly parallelizable. Numerical experiments proving the validity of the control problems proposed as mathematical models of the definite-band furtivity problem and definite-band ghost obstacle problem are presented. The numerical results obtained with a parallel implementation of the numerical methods developed are discussed and their properties are established. The speed-up factors obtained using parallel computing are really impressive. The website: http://www.econ.univpm.it/recchioni/w11 contains animations and virtual reality applications relative to the numerical experiments.

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Section: Mathematical Formulation Of the Definite-band Ghost-obstaclementioning

confidence: 92%

Section: Introductionmentioning

confidence: 91%

Section: Mathematical Formulation Of the Definite-band Ghost-obstaclementioning

confidence: 97%

Section: Mathematical Formulation Of the Definite-band Ghost-obstaclementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimal-control methods for two new classes of smart obstacles in time-dependent acoustic scattering

et al. 2006

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A numerical method for time dependent acoustic scattering problems involving smart obstacles and incoming waves of small wavelengths

Fatone¹,

Recchioni²,

Zirilli³

2006

AIP Conference Proceedings

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In this paper we propose a highly parallelizable numerical method for time dependent acoustic scattering problems involving realistic smart obstacles hit by incoming waves having wavelengths small compared with the characteristic dimension of the obstacles. A smart obstacle is an obstacle that when hit by an incoming wave tries to pursue a goal circulating on its boundary a pressure current. In particular we consider obstacles whose goal is to be undetectable and we refer to them as furtive obstacles. These scattering problems are modelled as optimal control problems for the wave equation. We validate the method proposed to solve the optimal control problem considered on some test problems where a "smart" simplified version of the NASA space shuttle is hit by incoming waves with small wavelengths compared to its characteristic dimension. That is we consider test problems with ratio between the characteristic dimension of the obstacle and wavelength of the time harmonic component of the incoming wave up to approximately one hundred. The website: http://www.econ.univpm.it/recchioni/w14 contains animations and virtual reality applications showing some numerical experiments relative to the problems studied in this paper.

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A method to solve an acoustic inverse scattering problem involving smart obstacles

Fatone¹,

Recchioni²,

Zirilli³

2006

Waves in Random and Complex Media

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A time-harmonic acoustic inverse scattering problem involving smart obstacles is formulated and a method to solve it is proposed. A smart obstacle is an obstacle that, when hit by an incoming acoustic wave, tries to pursue a given goal circulating a suitable pressure current on its boundary. A pressure current is a quantity whose physical dimension is pressure divided by time. The goals pursued by the smart obstacles that we have considered are the following ones: to be undetectable or to appear with a shape and/or acoustic boundary impedance different from its actual ones eventually in a location in space different from the actual location. The following time-harmonic inverse scattering problem is considered: from the knowledge of several far fields generated by the smart obstacle when hit by known time-harmonic waves, the knowledge of the goal pursued by the smart obstacle and of its acoustic boundary impedance reconstruct the boundary of the obstacle. A method to solve this inverse problem that generalizes the so-called Herglotz function method is proposed. Some numerical experiments that validate the method proposed are presented. The website http://www.econ.univpm.it/recchioni/w13 contains some auxiliary material that helps the understanding of the current paper

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A masking problem in time dependent acoustic obstacle scattering

Cited by 9 publications

References 3 publications

Optimal-control methods for two new classes of smart obstacles in time-dependent acoustic scattering

Optimal-control methods for two new classes of smart obstacles in time-dependent acoustic scattering

A numerical method for time dependent acoustic scattering problems involving smart obstacles and incoming waves of small wavelengths

A method to solve an acoustic inverse scattering problem involving smart obstacles

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