  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 $\Delta t$ to transmit to another
space point and vice versa. This $\Delta t$ 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.
