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The commonly used one step methods and linear multi-step methods all have a global error that is of the same order as the local truncation error (as defined in [6,13,1,8,15]). In fact, this is true of the entire class of general linear methods. In practice, this means that the order of the method is typically defined solely by order conditions which are derived by studying the local truncation error. In this work we investigate the interplay between the local truncation error and the global error, and develop a methodology which defines the construction of explicit error inhibiting block one-step methods (alternatively written as explicit general linear methods [2]). These error inhibiting schemes are constructed so that the accumulation of the local truncation error over time is controlled, which results in a global error that is one order higher than the local truncation error. In this work, we delineate how to carefully choose the coefficient matrices so that the growth of the local truncation error is inhibited. We then use this theoretical understanding to construct several methods that have higher order global error than local truncation error, and demonstrate their enhanced order of accuracy on test cases. These methods demonstrate that the error inhibiting concept is realizable. Future work will further develop new error inhibiting methods and will analyze the computational efficiency and linear stability properties of these methods.

A stable Cartesian grid staircase-free finite-difference time-domain formulation for arbitrary material distributions in general geometries is introduced. It is shown that the method exhibits higher accuracy than the classical Yee scheme for complex geometries since the computational representation of physical structures is not of a staircased nature. Furthermore, electromagnetic boundary conditions are correctly enforced. The method significantly reduces simulation times as fewer points per wavelength are needed to accurately resolve the wave and the geometry. Both perfect electric conductors and dielectric structures have been investigated. Numerical results are presented and discussed.Index Terms-Computational models in electromagnetics and optics, finite-difference time-domain methods, numerical solution of partial differential equations, staircase, time-domain solution of Maxwell's equations.

The model developed here describes compressive stress evolution during the growth of continuous, polycrystalline films ͑i.e., beyond the point where individual islands have coalesced into a continuous film͒. These stresses are attributed to the insertion of excess adatoms at grain boundaries. Steady state occurs when the strain energy at the top of the film is balanced by the local excess chemical potential of surface adatmos. Strain gradients associated with this compressive stress mechanism depend on the kinetics of the process. In the absence of grain boundary diffusion, these strain profiles are determined by the ratio of the atom insertion and growth rates. The steady-state strain and the strain evolution kinetics also depend on the two key length scales, the grain size, and the film thickness. The ratio of these two lengths ͑i.e., the grain aspect ratio͒ can also have a significant influence on the thermodynamic driving force for strain evolution if the grain sizes are sufficiently small. The model is fit to existing data for the growth of AlN films. However, more detailed comparisons will require experiments that are specifically designed to test this model.

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In their classical paper [2], the authors presented a methodology for the derivation of far field boundary conditions for the absorption of waves that are almost perpendicular to the boundary. In this paper we derive a general order absorbing boundary conditions of the type suggested by Engquist and Majda. The derivation utilizes a different methodology which is more general and simpler. This methodology is applied to the two and three dimensional wave equation, to the three dimensional Maxwell's equations and to the equations of advective acoustics in two dimensions.