Publications de l'Institut Mathématique, Nouvelle Série Vol. 96[110], pp. 103–123 (2014) 

EXACT NONREFLECTING BOUNDARY CONDITIONS FOR EXTERIOR WAVE EQUATION PROBLEMSSilvia Falletta and Giovanni MonegatoDepartment of Mathematical Sciences, Politecnico di Torino, Torino, ItalyAbstract: 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 multidomain, 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 timedomain 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. Keywords: wave equation, Helmholtz equation, exterior problems, absorbing boundary conditions, numerical methods Classification (MSC2000): 65M60, 65M06, 65M38 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 30 Oct 2014. This page was last modified: 24 Nov 2014.
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