Local convergence of an adaptive scalar method and its application in a nonoverlapping domain decomposition scheme

In this paper, we demonstrate a local convergence of an adaptive scalar solver which is practical for strongly diagonal dominant Jacobian problems such as in some systems of nonlinear equations arising from the application of a nonoverlapping domain decomposition method. The method is tested to a nonlinear interface problem of a multichip heat conduction problem. The numerical results show that the method performs slightly better than a Newton-Krylov method. (C) 2011 Elsevier B.V. All rights reserved.