We introduce a new symmetric treatment of anisotropic viscous terms in the viscoelastic wave equation. An appropriate memory variable treatment of stress-strain convolution terms, result into a symmetric system of first order linear hyperbolic partial differential equations, which we discretize using a high-order discontinuous Galerkin finite element method. The accuracy of the resulting numerical scheme is verified using convergence studies against analytical plane wave solutions and analytical solutions of the viscoelastic wave equation. Computational experiments are shown for various combinations of homogeneous and heterogeneous viscoelastic media in two and three dimensions.

中文翻译：

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各向异性粘弹性波动方程对称形式的一种高阶不连续Galerkin方法

我们在粘弹性波动方程中引入了对各向异性粘性项的新对称处理。应力-应变卷积项的适当记忆变量处理导致一阶线性双曲偏微分方程的对称系统，我们使用高阶不连续伽辽金有限元方法对其进行离散化。使用针对解析平面波解和粘弹性波方程解析解的收敛研究来验证所得数值方案的准确性。计算实验显示了在二维和三维中均质和异质粘弹性介质的各种组合。