发表机构
Institute for Applied and Numerical Mathematics, Karlsruhe Institute of Technology (KIT)（应用与数值数学研究所，卡尔斯鲁厄理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种非迭代重叠域分解时间积分器，通过局部隐式预测提供界面数据，避免CFL限制，误差随重叠指数衰减，支持任意阶有限元，数值实验验证稳定性和并行潜力。
AI 中文摘要
我们提出并分析了一种用于线性声波方程的非迭代域分解时间积分器。该方法基于空间上的重叠分解，并利用局部隐式预测在界面处提供人工边界数据。我们使用任意阶的协调有限元进行空间离散，并允许材料系数随空间变化。我们证明了相对于全局Crank--Nicolson近似的误差界，该误差界随子域和预测重叠的大小呈指数衰减。与早期工作相比，该新方法避免了CFL型步长限制，并允许使用任意阶有限元。该分析结合了离散Saint-Venant原理以及针对局部预测的新的衰减和截断估计。数值实验支持该分析，并展示了在所有测试时间步长下的稳定行为、与全局Crank--Nicolson近似相当的精度，以及高效并行执行的潜力。
英文摘要
We propose and analyze a non-iterative domain decomposition time integrator for the linear acoustic wave equation. The method is based on an overlapping decomposition in space and uses a localized implicit prediction to provide artificial boundary data at the interfaces. We use conforming finite elements of arbitrary order to discretize in space and allow spatially varying material coefficients. We prove an error bound relative to the global Crank--Nicolson approximation that decays exponentially with the size of both the subdomain and prediction overlaps. Compared to earlier work, this new method avoids a CFL-type step size restriction and allows the use of finite elements of arbitrary order. The analysis combines a discrete Saint-Venant principle with new decay and truncation estimates for the localized prediction. Numerical experiments support the analysis and demonstrate stable behavior for all tested time step sizes, accuracy comparable to that of the global Crank--Nicolson approximation, and the potential for efficient parallel execution.
Comments33 pages, 9 figures
