Neumann–Neumann waveform relaxation algorithm in multiple subdomains for hyperbolic problems in 1D and 2D

Document Type


Publication Date



© 2016 Wiley Periodicals, Inc. We present a Waveform Relaxation (WR) version of the Neumann–Neumann algorithm for the wave equation in space-time. The method is based on a nonoverlapping spatial domain decomposition, and the iteration involves subdomain solves in space-time with corresponding interface conditions, followed by a correction step. Using a Fourier-Laplace transform argument, for a particular relaxation parameter, we prove convergence of the algorithm in a finite number of steps for the finite time intervals. The number of steps depends on the size of the subdomains and the time window length on which the algorithm is employed. We illustrate the performance of the algorithm with numerical results, followed by a comparison with classical and optimized Schwarz WR methods. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 514–530, 2017.

Publication Title

Numerical Methods for Partial Differential Equations