We study a symmetric BEM-FEM coupling scheme for the scattering of transientacoustic waves by bounded inhomogeneous anisotropic obstacles in a homogeneousfield. An incident wave in free space interacts with the obstacles and producesa combination of transmission and scattering. The transmitted part of the waveis discretized in space by finite elements while the scattered wave is reducedto two fields defined on the boundary of the obstacles and is discretized inspace with boundary elements. We choose a coupling formulation that leads to asymmetric system of integro-differential equations. The retarded boundaryintegral equations are discretized in time by Convolution Quadrature, and theinterior field is discretized in time with the trapezoidal rule. We show thatthe scattering problem generates a C_0 group of isometries in a Hilbert space,and use associated estimates to derive stability and convergence results. Weprovide numerical experiments and simulations to validate our results anddemonstrate the flexibility of the method.
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