An investigation of overlapping domain decomposition methods for one-dimensional dispersive long wave equations

摘要: Abstract This paper contains a thorough investigation of the numerical accuracy and efficiency an overlapping domain decomposition (Schwarz iteration) method for weakly dispersive non-linear water waves. The is restricted to one-dimensional wave propagation. In our tests, global divided into two subdomains. A local boundary value problem (at time level) solved in each subdomain, with values extracted from neighboring domains. size overlap number iterations over domains are principal parameters that influence convergence speed accuracy. We also investigate different finite difference element formulations. signal problems makes methods particularly efficient, proposed converges satisfactorily already some typical depths few (2–3) iterations. Numerical artifacts instabilities may develop at subdomain boundaries certain choices overlap, lengths, grid sizes, (discrete) velocities. special filtering technique designed make more robust respect such instabilities.