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Abstract: The Huygens subgridding (HSG) is a subgridding technique developed for the numerical solution of the Maxwell equations. It relies on the theoretical equivalence of any physical volume with two or more fictitious volumes connected by equivalent currents. The application of this concept to the finite-difference time-domain (FDTD) method has been previously published in the one dimensional and two dimensional cases. In this paper the HSG is extended to the general three dimensional case, the exchange of the electromagnetic energy between the two FDTD grids is investigated theoretically, and some modifications to the HSG algorithm are presented with the objective of simplifying its implementation. [Copyright &y& Elsevier]

This paper extends to two dimensions the finite-difference time-domain Huygens subgridding algorithm previously published in the one dimensional case. The algorithm is described in detail and several numerical experiments are provided to illustrate its possibilities and to demonstrate its effectiveness. [ABSTRACT FROM AUTHOR]

We present an extension module for the D une system. This module, called dune-subgrid, allows to mark elements of another D une hierarchical grid. The set of marked elements can then be accessed as a D une grid in its own right. dune-subgrid is free software and is available for download (External D une Modules: ). We describe the functionality and use of dune-subgrid, comment on its implementation, and give two example applications. First, we show how dune-subgrid can be used for micro-FE simulations of trabecular bone. Then we present an algorithm that allows to use exact residuals for the adaptive solution of the spatial problems of time-discretized evolution equations. [ABSTRACT FROM AUTHOR]

A finite-different time-domain subgrid algorithm locally refines the mesh at regions requiring higher resolution. A novel separation of spatial and temporal subgridding interfaces is presented that allows implementing a novel spatial subgridding method and investigating the stability of each subalgorithm individually. Details are given for a spatial subgridding algorithm having a 1:3 mesh ratio. In the spatial subgridding algorithm, the fine-mesh is constructed with a recessed interface and the interpolation scheme is designed to be symmetric to maintain the stability of the update process. The stability of the spatial subgridding algorithm is analyzed with a matrix method. Numerical examples showing stability and accuracy are provided. [ABSTRACT FROM AUTHOR]