Algorithmic aspects of wave propagation through stretched unstructured cells for problems in computational electromagnetics

Abstract

Attempts at accurate prediction of scattering from large targets of small radar cross-section (RCS) using Maxwell's equations have exposed significant difficulties for all current numerical methods, including fast integral equation solvers in the frequency domain and finite-difference/-volume/- element schemes in the time domain. Because interactions among features separated by many wavelengths along the target are important, methods that explicitly propagate scattered waves over the target must satisfy stringent requirements with regard to preserving their phase and amplitude, while accurately representing their interaction with each feature. Conventional time integration schemes exhibit minimum phase and amplitude errors on uniform Cartesian grids, but minimum interaction errors on clustered, body- fitted grids. Consequently, their overall accuracy becomes highly dependent on grid design. To overcome these limitations, it is proposed to develop an efficient, high order of accuracy time integration scheme for unstructured grids that can be appropriately clustered and de-clustered along a general boundary.