Exact non-reflecting boundary condition for 3D time-dependent multiple scattering–multiple source problems

On the discretization and application of two space–time boundary integral equations for 3D wave propagation problems in unbounded domains

“…The time integrals appearing in the definition of the single and double layer operators (see (3), (4)) are discretized by means of the above mentioned second order Lubich convolution quadrature formula (see [14]). We obtain:…”

“…Furthermore, they are generally used to determine the problem solution at chosen points. Only in the last few years (see [13], [2], [14], [6]), a BIE for the classical wave equation has been used to define a Non Reflecting Boundary Condition (NRBC) on a chosen artificial boundary, surrounding the computational domain. Its discretization is then coupled with that of the domain of interest by means of finite elements or finite differences.…”

“…To solve problem (1) we will consider the following single-double layer BIE (see [14]): 1 2 u e (x, t) − (V∂ n u e )(x, t) + (Ku e )(x, t) = I u 0 (x, t) + The last expressions in (3) and (4) have been obtained by interchanging (see [15]) the time and space integrals in the corresponding representations, and using the wave equation fundamental solution expression…”

“…Very recently, in [14] (see also [6]), for the solution of (1), we have proposed to use (2) as a global Non Reflecting Boundary Condition, to be imposed on a chosen artificial boundary B delimiting the domain of interest Ω. This NRBC is interpreted as a relationship that the problem solution and its normal derivative must satisfy on B, to avoid spurious wave reflections.…”

A fully discrete BEM–FEM scheme for transient acoustic waves

“…The papers [1,9] deal with four-field formulations (two fields in the interior domain and two on the boundary) and aim at coupling an explicit interior time-stepping method with the retarded boundary integral equations on the boundary, differing in the use of Galerkin-in-time or CQ for the equations on the boundary. The papers [15,13,14] contain successful computational studies of one-equation couplings, although a theoretical understanding of their stability is still missing. A preliminary semidiscrete stability analysis in the Laplace domain of the coupling method we will study here appears in [24].…”