A fractional splitting algorithm for nonoverlapping domain decomposition for parabolic problem

Abstract

In this article we study the convergence of the nonoverlapping domain decomposition for solving large linear system arising from semi-discretization of two-dimensional initial value problem with homogeneous boundary conditions and solved by implicit time stepping using first and two alternatives of second-order FS-methods. The interface values along the artificial boundary condition line are found using explicit forward Euler's method for the first-order FS-method, and for the second-order FS-method to use extrapolation procedure for each spatial variable individually. The solution by the nonoverlapping domain decomposition with FS-method is applicable to problems that requires the solution on nonuniform meshes for each spatial variable, which will enable us to use different time-stepping over different subdomains and with the possibility of extension to three-dimensional problem. (C) 2002 Wiley Periodicals, Inc.