This work is concerned with implementing the hybridizable discontinuous Galerkin (HDG) method to solve the linear anisotropic elastic equation in the frequency domain. First-order formulation with the compliance tensor and Voigt notation are employed to provide a compact description of the discretized problem and flexibility with highly heterogeneous media. We further focus on the question of optimal choices of stabilization in the definition of HDG numerical traces. For this purpose, we construct a hybridized Godunov-upwind flux for anisotropic elastic media possessing three distinct wavespeeds. This stabilization removes the need to choose a scaling factor, contrary to the identity and Kelvin-Christoffel based stabilizations which are popular choices in the literature. We carry out comparisons among these families for isotropic and anisotropic material, with constant background and highly heterogeneous ones, in two and three dimensions. These experiments establish the optimality of the Godunov stabilization which can be used as a reference choice for a generic material in which different types of waves propagate.

翻译：本文致力于实现混合化不连续伽辽金（HDG）方法，以求解频域中的线性各向异性弹性方程。采用柔度张量和Voigt记号的首次公式化描述，为离散化问题提供了简洁的表述，并适应高度非均匀介质。我们进一步聚焦于HDG数值通量定义中稳定化的最优选择问题。为此，针对具有三种不同波速的各向异性弹性介质，我们构建了一种混合化Godunov-迎风通量。与文献中流行的恒等和Kelvin-Christoffel基稳定化方法不同，该稳定化消除了选择缩放因子的需要。我们在二维和三维空间中，针对各向同性和各向异性材料，以及常背景和高度非均匀介质，对这些家族进行了比较。这些实验确立了Godunov稳定化的最优性，该稳定化可作为描述不同波传播的通用材料的参考选择。