A parallel space-time finite difference solver for periodic solutions of the shallow-water equation

Abstract

We investigate parallel algorithms for the solution of the shallow-water equation in a space-time framework. For periodic solutions, the discretized problem can be written as a large cyclic non-linear system of equations. This system of equations is solved with a Newton iteration which uses two levels of preconditioned GMRES solvers. The parallel performance of this algorithm is illustrated on a number of numerical experiments. © 2012 Springer-Verlag.