2015/07/14 by Bankim C. Mandal, Mandal, Bankim C.
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1507.04008
openalex publication_date 2015/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a Waveform Relaxation (WR) version of the Neumann-Neumann\nalgorithm for the wave equation in space-time. The method is based on a\nnon-overlapping spatial domain decomposition, and the iteration involves\nsubdomain solves in space-time with corresponding interface condition, followed\nby a correction step. Using a Fourier-Laplace transform argument, for a\nparticular relaxation parameter, we prove convergence of the algorithm in a\nfinite number of steps for finite time intervals. The number of steps depends\non the size of the subdomains and the time window length on which the algorithm\nis employed. We illustrate the performance of the algorithm with numerical\nresults, followed by a comparison with classical and optimized Schwarz WR\nmethods.\n