An exact non reflecting boundary condition for 2D time-dependent wave equation problems

Abstract

We consider some 2D wave equation problems defined in an unbounded domain, possibly with far field sources. 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 known 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. We discretize it by using a fast convolution quadrature technique in time and a collocation method in space. Besides showing a good accuracy and numerical stability, the proposed NRBC has the property of being suitable for artificial boundaries of general shapes; moreover, from the computational point of view, it is competitive with well known existing NRBCs of local type. It also allows the treatment of far field sources, that do not have to be necessarily included in the finite computational domain, being transparent for both incoming and outgoing waves.