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In this paper, we propose nonoverlapping localized exponential time differencing (ETD) methods for diffusion problems. The model time-dependent diffusion equation is first reformulated on subdomains based on the nonoverlapping domain decomposition, in which Neumann boundary conditions are imposed on the interfaces for the subdomain problems and Dirichlet type conditions are enforced to form a space-time interface problem. After spatial discretization by standard central finite differences and temporal integration with the first or second order ETD methods, the fully discrete interface problem is obtained. Such an interface problem is then solved iteratively either at each time step or over the whole time interval: the former involves the solution of stationary problems in each subdomain at each iteration while the latter involves the solution of time-dependent subdomain problems at each iteration. For both approaches, we prove that localized ETD solutions conserve mass exactly and converge in time to the exact space semidiscrete solution. Numerical experiments in two dimensions are also presented to illustrate the performance of the proposed methods. [ABSTRACT FROM AUTHOR]

In recent years, a nonoverlapping domain decomposition iterative procedure, which is based on using Robin-type boundary conditions as information transmission conditions on the subdomain interfaces, has been developed and analyzed. It is known that the convergence rate of this method is 1 − O( h), where h is mesh size. In this paper, the convergence rate is improved to be 1 − O( h 1/2H−1/2) sometime by choosing suitable parameter, where H is the subdomain size. Counter examples are constructed to show that our convergence estimates are sharp, which means that the convergence rate cannot be better than 1 − O( h 1/2H−1/2) in a certain case no matter how parameter is chosen. [ABSTRACT FROM AUTHOR]