1998
DOI: 10.1121/1.421082
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A new formalism for wave scattering from a bounded obstacle

Abstract: Let ⍀ʚR 3 be an obstacle that is a simply connected bounded domain. The exterior Dirichlet problem for the Helmholtz equation in R 3 ‫گ‬⍀ with the Sommerfeld radiation condition at infinity is considered. Based on an integral representation formula, a new method to compute the solution of the exterior boundary value problem mentioned above is proposed. This method generalizes the formalism introduced for an unbounded obstacle by Milder ͓J. Acoust. Soc. Am. 89, 529-541 ͑1991͔͒ and consists in computing a pertur… Show more

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Cited by 11 publications
(4 citation statements)
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“…(15)-(24), replacing u s G with zero in Eq. (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.…”
Section: Mathematical Formulation Of the Definite-band Ghost-obstaclementioning
confidence: 98%
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“…(15)-(24), replacing u s G with zero in Eq. (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.…”
Section: Mathematical Formulation Of the Definite-band Ghost-obstaclementioning
confidence: 98%
“…Finally, we emphasize that using the terminology introduced before, the boundary condition (22) given on ∂ has a "non-local" character since it depends on the values of the functionũ s on the surface ∂ . Moreover, condition (22) at time t depends on the values ofũ s (x, τ ) with τ ∈ IR. 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).…”
Section: Mathematical Formulation Of the Definite-band Ghost-obstaclementioning
confidence: 99%
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