Publications de l'Institut Mathematique 2014 Volume 96, Issue 110, Pages: 103-123
https://doi.org/10.2298/PIM1410103F
Full text ( 812 KB)
Cited by
Exact nonreflecting boundary conditions for exterior wave equation problems
Falletta Silvia (Politecnico di Torino, Department of Mathematical Sciences, Torino, Italy)
Monegato Giovanni (Politecnico di Torino, Department of Mathematical Sciences, Torino, Italy)
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.
Keywords: Wave equation, Helmholtz equation, exterior problems, absorbing boundary conditions, numerical methods