论文标题
波动方程的非著作重叠的Schwarz波形松弛算法
A Non-iterative Overlapping Schwarz Waveform Relaxation Algorithm for Wave Equation
论文作者
论文摘要
Schwarz波形弛豫算法（SWR）交换了相邻子域之间边界值的波形，这比其他Schwarz算法提供了更有效的方法以实现分布式计算。但是，传统SWR的收敛速度很慢，并且已经提出了各种优化策略来加速融合。在本文中，我们提出了一个用于波方程的SWR的非题重叠变体，该变体称为相对Schwarz波形弛豫算法（RSWR）。 RSWR的灵感来自于物理观察，即基于相对论的理论，波的速度受到限制。一个空间点的价值变化将花费时间跨度$ΔT$传输到另一个空间点，反之亦然。像我们在RSWR中所做的那样，该$ΔT$可用于设计分布式的数值算法。在每个时间范围内，RSWR只需使用预测选择的更策略即可达到高准确的波形。此策略的关键是找到波形的最大时间跨度。 RSWR的验证可以直接证明。数值实验表明RSWR是准确的，并且有可能可扩展和快速。
The Schwarz Waveform Relaxation algorithm (SWR) exchanges the waveform of boundary value between neighbouring sub-domains, which provides a more efficient way than the other Schwarz algorithms to realize distributed computation. However, the convergence speed of the traditional SWR is slow, and various optimization strategies have been brought in to accelerate the convergence. In this paper, we propose a non-iterative overlapping variant of SWR for wave equation, which is named Relative Schwarz Waveform Relaxation algorithm (RSWR). RSWR is inspired by the physical observation that the velocity of wave is limited, based on the Theory of Relativity. The change of value at one space point will take time span $Δt$ to transmit to another space point and vice versa. This $Δt$ could be utilized to design distributed numerical algorithm, as we have done in RSWR. During each time span, RSWR needs only 3 steps to achieve high accurate waveform, by using the predict-select-update strategy. The key for this strategy is to find the maximum time span for the waveform. The validation of RSWR could be proved straightfowardly. Numerical experiments show that RSWR is accurate, and is potential to be scalable and fast.
