Domain-overriding and digital filtering for 3-D FDTD subgridded simulations

We report on an extension of finite-difference time-domain (FDTD) subgridding (SG) algorithms incorporating digital filters and domain-overriding to three-dimensional (3-D) simulations and to problems involving materials traversing the SG interfaces. We show that significant improvements in accuracy can be obtained for these cases as well.     

Metamaterial Blueprints for Reflectionless Waveguide Bends

A derivation of metamaterial blueprints for the reflectionless (perfectly matched) guiding of electromagnetic waves through waveguide bends is performed. The sensitivity of the response with respect to small perturbations in the associated constitutive tensors is examined.     

Improved FDTD subgridding algorithms via digital filtering and domain overriding

In numerical simulations of Maxwell's equations for problems with disparate geometric scales, it is often advantageous to use grids of varying densities over different portions of the computational domain. In simulations involving structured finite-difference time-domain (FDTD) grids, this strategy is often referred as subgridding (SG). Although SG can lead to major computational savings, it is known to cause instabilities, spurious reflections, and other accuracy problems. In this paper, we introduce two strategies to combat these problems. First, we present an overlapped SG (OSG) approach combined with digital filters (in space). OSG can recover standard SG (SSG) schemes but it is based upon a more general, explicit separation between interpolation/decimation operations and the FDTD field update itself. This allows for a better classification of errors associated with the subgrid interface. More importantly, digital filters and phase matching techniques can be then employed to combat those errors. Second, we introduce SG with a domain overriding (SG-DO) strategy, consisting of overlapped (sub)grid regions that contain auxiliary (buffer) subdomains with perfectly matched layers (PML) to allow explicit control on the reflection and transmission properties at SG interfaces. We provide two-dimensional (2-D) numerical examples showing that residual errors from 2-D SG-DO FDTD simulations can be significantly reduced when compared to SSG schemes.     

Accurate interfacing of heterogeneous structured FDTD grid components

We study strategies to interface finite-difference time-domain (FDTD) update equations in heterogeneous structured grid components for overset composite FDTD grids. An overset composite grid (or "chimera" grid) is a heterogeneous grid formed by the combination of structured FDTD subgrid components chosen to better conform to local geometrical features. We study the performance of various analytical filters and phase matching techniques to reduce problems associated with such heterogeneous grid interfacing, including spatial frequency aliasing and (numerical) phase velocity mismatch. We demonstrate the performance of interfacing algorithms in some canonical examples.     

Conformal Perfectly Matched Layer for the Mixed Finite Element Time-Domain Method

We introduce a conformal perfectly matched layer (PML) for the finite-element time-domain (FETD) solution of transient Maxwell equations in open domains. The conformal PML is implemented in a mixed FETD setting based on a direct discretization of the first-order coupled Maxwell curl equations (as opposed to the second-order vector wave equation) that employs edge elements (Whitney 1-form) to expand the electric field and face elements (Whitney 2-form) to expand the magnetic field. We show that the conformal PML can be easily incorporated into the mixed FETD algorithm by utilizing PML constitutive tensors whose discretization is naturally decoupled from that of Maxwell curl equations (spatial derivatives). Compared to the conventional (rectangular) PML, a conformal PML allows for a considerable reduction on the amount of buffer space in the computational domain around the scatterer(s).     

Mixed Finite-Element Time-Domain Method for Transient Maxwell Equations in Doubly Dispersive Media

We describe a mixed finite-element time-domain algorithm to solve transient Maxwell equations in inhomogeneous and doubly dispersive linear media where both the permittivity and permeability are functions of frequency. The mixed finite-element time-domain algorithm is based on the simultaneous use of both electric and magnetic field as state variables with a mix of edge (Whitney 1-form) and face (Whitney 2-form) elements for discretization of the coupled first-order Maxwell curl equations. The constitutive relations are decoupled from the curl equations and cast in terms of (auxiliary) ordinary differential equations involving time derivatives. Permittivity and permeability dispersion models considered here are quite general and recover Lorentz, Debye, and Drude models as special cases. The present finite-element time-domain algorithm also incorporates the perfectly matched layer absorbing boundary conditions in a natural way.