An overdetermined Schwarz alternating method

Developing modem extensions of the Schwarz alternating method (SAM) has been a primary focus in the research of domain decomposition during the part 10 years. Among the various research efforts, the generalized Schwarz alternating method (GSAM) was an attempt to use the Robin condition omega u + (1 - omega)partial derivative u/partial derivative n on those artificial boundaries to improve the performance of the SAM. Its convergence rate is much faster than the classical SAM (with a large overlap), yet only a minimum overlap is required. Unfortunately, sensitivity of the convergence of the GSAM to the parameter omega has limited its practical applications, In this paper, a nerv kind of coupling is proposed which possesses the same benefits as the GSAM. The advantage of our new algorithm over the GSAM is that the optimal convergence rate is achieved on a wider range of the parameter. That is, selection of the optimal parameter is not crucial to the new algorithm's performance. Numerical teats have been carried out for a variety of difficult problems including nonsymmetric and indefinite problems.