The paper deals with the numerical solution of 2D wave propagation exterior problems including viscous and material damping coefficients and equipped by Neumann boundary condition, hence modeling the hard scattering of damped waves. The differential problem, which includes, besides diffusion, advection and reaction terms, is written as a space–time boundary integral equation (BIE) whose kernel is given by the hypersingular fundamental solution of the 2D damped waves operator. The resulting BIE is solved by a modified Energetic Boundary Element Method, where a suitable kernel treatment is introduced for the evaluation of the discretization linear system matrix entries represented by space–time quadruple integrals with hypersingular kernel in space variables. A wide variety of numerical results, obtained varying both damping coefficients and discretization parameters, is presented and shows accuracy and stability of the proposed technique, confirming what was theoretically proved for the simpler undamped case. Post-processing phase is also taken into account, giving the approximate solution of the exterior differential problem involving damped waves propagation around disconnected obstacles and bounded domains.

本文研究了二维波传播的外部问题的数值解，包括粘性和材料阻尼系数，并通过Neumann边界条件进行了拟合，从而对阻尼波的硬散射进行了建模。除扩散，对流和反应项外，该微分问题还写为一个时空边界积分方程（BIE），其内核由2D阻尼波算子的超奇异基本解给出。通过改进的“能量边界元法”解决由此产生的BIE，其中引入了适当的核处理，以评估由时空四重积分表示的离散线性系统矩阵项，在空间变量中具有超奇异核。各种各样的数值结果，给出了通过改变阻尼系数和离散化参数而获得的结果，并显示了所提出技术的准确性和稳定性，从而证实了在较简单的无阻尼情况下的理论证明。还考虑了后处理阶段，从而给出了外部差分问题的近似解决方案，该问题涉及阻尼波在断开的障碍物和有界域周围传播。