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A fully discrete BEM-FEM scheme for transient acoustic waves

机译：瞬态声波的完全离散BEM-FEM方案

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摘要

We study a symmetric BEM-FEM coupling scheme for the scattering of transient acoustic waves by bounded inhomogeneous anisotropic obstacles in a homogeneous field. An incident wave in free space interacts with the obstacles and produces a combination of transmission and scattering. The transmitted part of the wave is discretized in space by finite elements while the scattered wave is reduced to two fields defined on the boundary of the obstacles and is discretized in space with boundary elements.. We choose a coupling formulation that leads to a symmetric system of integro-differential equations. The retarded boundary integral equations are discretized in time by Convolution Quadrature, and the interior field is discretized in time with the trapezoidal rule. We show that the scattering problem generates a C-0 group of isometries in a Hilbert space, and use associated estimates to derive stability and convergence results. We provide numerical experiments and simulations to validate our results and demonstrate the flexibility of the method. (C) 2016 Elsevier B.V. All rights reserved.
机译：我们研究了对称BEM-FEM耦合方案，用于通过均匀场中有界非均匀各向异性障碍物散射瞬态声波。自由空间中的入射波与障碍物相互作用并产生透射和散射的组合。波的透射部分在空间中由有限元离散化，而散射波被简化为在障碍物边界上定义的两个场，并在空间中由边界元离散化。我们选择导致对称系统的耦合公式积分微分方程组。通过卷积求积，将时滞边界积分方程及时离散，并利用梯形法则及时离散内部场。我们证明了散射问题在希尔伯特空间中产生了C-0组的等距线，并使用相关的估计来推导稳定性和收敛性结果。我们提供数值实验和仿真以验证我们的结果并证明该方法的灵活性。 （C）2016 Elsevier B.V.保留所有权利。

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