Fourier analysis of Schwarz domain decomposition methods for the biharmonic equation (Q1047264)

The authors consider the solution of the inhomogeneous biharmonic equation in \(H^2_0(\mathbb{R^2})\) by the alternating and the additive Schwarz method. The domain is decomposed into the overlapping halfspaces \((-\infty,L) \times \mathbb{R}\) and \((0,\infty) \times \mathbb{R}\), where \(L>0\). The convergence of both methods is proved with the aid of Fourier analysis. It turns out that the alternating variant converges twice as fast as the additive one.