Energetic boundary element method for accurate solution of damped waves hard scattering problems
Energetic boundary element method for accurate solution of damped waves hard scattering problems
复制标题
精确求解阻尼波硬散射问题的能量边界元法
DOI：
10.1007/s10665-021-10100-y
复制
发表时间：
2021
影响因子：
1.3
通讯作者：
C. Guardasoni
中科院分区：
文献类型：
--
作者：
A. Aimi;M. Diligenti;C. Guardasoni
本文研究了二维波传播外部问题（包括粘性阻尼系数和材料阻尼系数）的数值求解，并配备了诺依曼边界条件，从而对阻尼波的硬散射进行了建模。除了扩散项、平流项和反应项之外，微分问题被写成时空边界积分方程（BIE），其核由二维阻尼波算子的超奇异基本解给出。由此产生的 BIE 通过改进的能量边界元法求解，其中引入了合适的核处理来评估由空间变量中具有超奇异核的时空四重积分表示的离散化线性系统矩阵项。提出了通过改变阻尼系数和离散化参数获得的各种数值结果，并显示了所提出技术的准确性和稳定性，证实了对于更简单的无阻尼情况的理论证明。还考虑了后处理阶段，给出了涉及断开障碍物和有界域周围阻尼波传播的外部微分问题的近似解。
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.