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We present a Waveform Relaxation (WR) version of the Neumann-Neumannalgorithm for the wave equation in space-time. The method is based on anon-overlapping spatial domain decomposition, and the iteration involvessubdomain solves in space-time with corresponding interface condition, followedby a correction step. Using a Fourier-Laplace transform argument, for aparticular relaxation parameter, we prove convergence of the algorithm in afinite number of steps for finite time intervals. The number of steps dependson the size of the subdomains and the time window length on which the algorithmis employed. We illustrate the performance of the algorithm with numericalresults, followed by a comparison with classical and optimized Schwarz WRmethods.

Neumann-Neumann Waveform Relaxation Algorithm in Multiple subdomains for Hyperbolic Problems in 1D and 2D