发表机构
Nanjing Forestry University; University College London（南京林业大学; 伦敦大学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种非匹配混合高阶方法求解含线性滑移不完美界面的弹性波方程，通过局部应变重构和界面稳定化处理非贴合网格，证明了最优误差估计并验证了收敛性与鲁棒性。
AI 中文摘要
我们设计并分析了一种非匹配混合高阶（HHO）方法，用于求解由线性滑移型不完美界面分隔的两种介质组成的弹性波方程，该界面处牵引力连续，位移跳跃通过柔度张量$\bK=\alpha\bI+(\beta-\alpha)\bn\otimes\bn$与牵引力成正比。网格不贴合界面：在切割单元中离散未知量加倍，小切割通过单元聚合过程修复，且界面上不附加任何未知量。该方法两个特定要素是：在每个切割子单元中进行局部对称应变重构，该重构通过正则化界面刚度$\bS_h=(h_T\delta^{-1}\bI+\bK)^{-1}$融入界面条件，其思想源自Hansbo和Hansbo的《固体力学中强和弱不连续模拟的有限元方法》（Comput. Methods Appl. Mech. Engrg., 193, 2004）；以及基于同一矩阵构建的界面稳定化。对于空间半离散问题，我们证明了离散双线性形式是强制且连续的，并推导了阶为$h^{k+1}$的能量误差估计和阶为$h^{k+2}$的$L^2$误差估计，其常数与柔度参数及界面如何切割网格无关。该方案可与精确守恒离散能量的Newmark格式结合，或与最高四阶的单对角隐式Runge-Kutta格式结合。二维数值实验证实了$k\in\{1,2,3\}$时的预测收敛阶，对跨越十六个数量级的柔度具有鲁棒性，并展示了弹性波在未解析滑移界面上的传播。
英文摘要
We design and analyse an unfitted hybrid high-order (HHO) method for the elastic wave equation in a medium made of two components separated by an imperfect interface of linear slip type, across which the traction is continuous and the displacement jump is proportional to the traction through a compliancy tensor $\bK=α\bI+(β-α)\bn\otimes\bn$. The mesh is not fitted to the interface: the discrete unknowns are doubled in the cut cells, the small cuts are cured by a cell agglomeration procedure, and no unknown is attached to the interface. The two specific ingredients of the method are a local symmetric strain reconstruction in each cut subcell, which incorporates the interface condition through the regularised interface stiffness $\bS_h=(h_Tδ^{-1}\bI+\bK)^{-1}$ in the spirit of Hansbo and Hansbo {\em{A finite element method for the simulation of strong and weak discontinuities in solid mechanics.}} {Comput. Methods Appl. Mech. Engrg.}, 193, 2004, and an interface stabilisation built from the same matrix. For the space semi-discrete problem we prove that the discrete bilinear form is coercive and continuous, and we derive an energy-error estimate of order $h^{k+1}$ and an $L^2$-error estimate of order $h^{k+2}$, with constants independent of the compliancy parameters and of how the interface cuts the mesh. The scheme is combined either with the Newmark scheme, which conserves a discrete energy exactly, or with singly diagonally implicit Runge--Kutta schemes of order up to four. Numerical experiments in two dimensions confirm the predicted convergence rates for $k\in\{1,2,3\}$, the robustness with respect to the compliancy over sixteen orders of magnitude, and illustrate the propagation of elastic waves across an unresolved slipping interface.
