A time-dependent absorbing boundary condition for the numerical solution of exterior wave equation problems
Vortrag von Prof. Dr. Silvia Falletta
Sprecher eingeladen von: Prof. Dr. Stefan Sauter
Datum: 18.04.13 Zeit: 16.00 - 17.00 Raum: Y27H35/36
Abstract: We consider some 2D wave equation problems defined in an unbounded domain. For their solution, by means of standard finite element or finite difference methods, we propose a non reflecting boundary condition (NRBC) on the chosen artificial boundary $\B$, which is based on a space-time integral equation defining a relationship between the solution of the differential problem and its normal derivative on $\B$. Such a NRBC is exact, non local both in space and time and allows the treatment of incoming and outgoing waves. We discretize it by using a fast convolution quadrature in time, based on a second order BDF rule, and a collocation method in space based on continuous piecewise linear approximants. The proposed NRBC has the property of being suitable for artificial boundaries of general shapes (even of non-convex type, and having also corners, if necessary). From the computational point of view, it is competitive with well known existing NRBCs of local type. Furthermore, it allows the treatment of far field sources that do not have to be necessarily included in the finite computational domain.