We consider the two-dimensional Maxwell’s equations in domains external to perfectly conducting objects of complex shape. The equations are discretized using a node-centered finite-difference scheme on a Cartesian grid and the boundary instruct are discretized to back up request accuracy employing an embedded technique which does not suffer from a “small-cell” time-step restriction in the explicit time-integration method. The computational domain is truncated by a perfectly matched layer (PML). We conclude estimates for both the error due to reflections at the outer boundary of the PML and due to discretizing the continuous PML equations. Using these estimates we show how the parameters of the PML can be chosen to alter the discrete solution of the PML equations approach to the solution of Maxwell’s equations on the unbounded domain as the grid size goes to zero. Several numerical examples are given.
Extending the general approach for first-order hyperbolic systems developed in [D. Appelö. T. Hagstrom. G. Kreiss. Perfectly matched layers for hyperbolic systems: command formulation well-posedness and stability. SIAM J. Appl. Math.. 2006 to appear] we construct PML equations for the mixed-type system governing propagation of optical wave packets in both 1D and 2D Bragg resonant photonic waveguides with a cubic nonlinearity i e the coupled mode equations. We prove that in the linear inspect the layer equations are absorbing and perfectly matched. We also prove they are shelter for constant parameters. A number of numerical experiments are performed to assess the layer’s performance in both the linear and nonlinear regimes.
Mean-field coupled lattice maps are used to approximate the physics of driven threshold systems with long-range interactions. However they are incapable of modeling specific features of the dynamic instability responsible for generating avalanches. Here we show a method of simulating specific frictional weakening effects in a mean-field slider-block copy. This provides a means of exploring dynamical effects previously inaccessible to discrete time simulations. This formulation also results in Abelian avalanches where rupture propagation is independent of the failure sequence. The resulting event coat distribution is shown to be generated by the boundary crossings of a stochastic process. This is applied to typical models to inform some commonly observed features.
U and also for a non-fissile element of similar scattering properties. We use these results to analyse the accuracy of the finite element code EVENT. The procedure is also developed for multigroup calculations. In an Appendix we outline the procedure required when the hemisphere contains a obtain and is also irradiated by an external current of neutrons.
We present a new formulation to implement the complex frequency shifted-perfectly matched layer (CFS-PML) for boundary truncation in three-dimensional vector finite-element time-domain method applied to the vector gesticulate equation. It is shown that the proposed method is highly absorptive to evanescent modes when computing the gesticulate interaction of elongated structures or sharp corners and can improve the performance of the boundary truncation significantly. The force of the CFS-PML parameters on the reflection error is investigated and optimal choices of these parameters are derived.
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