A Virtual Element Method coupled with a Boundary Integral Non Reflecting condition for 2D exterior Helmholtz problems

We present a new numerical approach to solve 2D exterior Helmholtz problems defined in unbounded domains. This consists in reducing the infinite region to a finite computational one Ω, by the introduction of an artificial boundary B, and by applying in Ω a Virtual Element Method (VEM). The latter is coupled with a Boundary Integral Non Reflecting Condition defined on B (in short BI-NRBC), discretized by a standard collocation Boundary Element Method (BEM). We show that, by choosing the same approximation order of the VEM and of the BI-NRBC discretization spaces, the corresponding method allows to obtain the optimal order of convergence. We test the efficiency and accuracy of the proposed approach on various numerical examples, arising both from literature and real life application problems.