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 $\Omega$, by the introduction of an artificial boundary $\mathcal{B}$, and by applying in $\Omega$ a Virtual Element Method (VEM). The latter is coupled with a Boundary Integral Non Reflecting Condition defined on $\mathcal{B}$ (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.

我们提出了一种新的数值方法来解决在无界域中定义的二维外部亥姆霍兹问题。这包括将无限区域缩小为有限的计算区域$\Omega$，通过引入人工边界 $\mathcal{乙}$，并通过申请 $\Omega$虚拟元素方法（VEM）。后者与边界积分非反射条件定义于$\mathcal{乙}$（简称BI-NRBC），通过标准配置边界元素方法（BEM）离散化。我们表明，通过选择VEM和BI-NRBC离散空间的相同逼近顺序，相应的方法可以获取最佳收敛顺序。我们在各种数值示例上测试了该方法的效率和准确性，这些示例来自文献和现实生活中的应用问题。