Geodesic
Exact Nonreflecting Boundary Conditions for Exterior Wave Equation Problems
Publications de l'Institut Mathématique, _N_S_96 (2014) no. 110, p. 103

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We consider the classical wave equation problem defined on the exterior of a bounded 2D space domain, possibly having far field sources. We consider this problem in the time domain, but also in the frequency domain. For its solution we propose to associate with it a boundary integral equation (BIE) defined on an artificial boundary surrounding the region of interest. This boundary condition is nonreflecting (or transparent) for both outgoing and incoming waves and it does not have to include necessarily the problem datum supports. The problem physical domain can even be a multi-domain, defined by the union of several disjoint domains. These domains can be convex or nonconvex. This transparent boundary condition is imposed pointwise on the chosen artificial boundary; therefore, its (space collocation) discretization can be coupled with a (space) finite difference or finite element method for the associated PDE problem. In the time-domain case, a classical (explicit or implicit) time integrator is also used. We present a consistency result for the BIE discretization and a sample of the intensive numerical testing we have performed.
Classification : 65M60 65M06 65M38
Keywords: wave equation, Helmholtz equation, exterior problems, absorbing boundary conditions, numerical methods 
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     author = {Silvia Falletta and Giovanni Monegato},
     title = {Exact {Nonreflecting} {Boundary} {Conditions} for {Exterior} {Wave} {Equation} {Problems}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {103 },
     publisher = {mathdoc},
     volume = {_N_S_96},
     number = {110},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_2014_N_S_96_110_a8/}
}
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Silvia Falletta; Giovanni Monegato. Exact Nonreflecting Boundary Conditions for Exterior Wave Equation Problems. Publications de l'Institut Mathématique, _N_S_96 (2014) no. 110, p. 103 . http://geodesic.mathdoc.fr/item/PIM_2014_N_S_96_110_a8/