Interfacing unstructured tetrahedron grids to structured-grid FDTD

Abstract

Finite-element unstructured tetrahedron grids provide considerable modeling flexibility but can give rise to an extremely large number of cells when solving open-region problems. The finite-volume hybrid-grid (FVHG) algorithm enables unstructured grids to be combined with traditional structured-grid, rectangular-cell, finite-difference time-domain (FDTD), thereby considerably reducing the unstructured-mesh overhead in surrounding space. In this letter, a simple technique to interface free-meshed, tetrahedron grids with FDTD is described. The two grids are directly coupled without the need for spatial interpolation. The tetrahedron mesh is defined to terminate on a rectangular surface that may be located very close to the geometry under study. Absorbing boundary conditions are easily applied in the surrounding FDTD grid. This technique provides finite-element modeling flexibility with the benefits of explicit time differencing and limited unstructured-mesh overhead. Multimaterial regions can be solved. The FVHG algorithm has been found to be accurate and generally stable for the long-term, even with complex free meshes generated by advanced solid-modeling software.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>