Discontinuous Galerkin time‐domain solution of Maxwell's equations on locally refined grids with fictitious domains

Abstract

Purpose

The use of the prominent finite difference time‐domain (FDTD) method for the time‐domain solution of electromagnetic wave propagation past devices with small geometrical details can require very fine grids and can lead to unmanageable computational time and storage. The purpose of this paper is to extend the analysis of a discontinuous Galerkin time‐domain (DGTD) method (able to handle possibly non‐conforming locally refined grids, based on portions of Cartesian grids) and investigate the use of perfectly matched layer regions and the coupling with a fictitious domain approach. The use of a DGTD method with a locally refined, non‐conforming mesh can help focusing on these small details. In this paper, the adaptation to the DGTD method of the fictitious domain approach initially developed for the FDTD is considered, in order to avoid the use of a volume mesh fitting the geometry near the details.

Design/methodology/approach

Based on a DGTD method, a fictitious domain approach is developed to deal with complex and small geometrical details.

Findings

The fictitious domain approach is a very interesting complement to the FDTD method, since it makes it possible to handle complex geometries. However, the fictitious domain approach requires small volume elements, thus making the use of the FDTD on wide, regular, fine grids often unmanageable. The DGTD method has the ability to handle easily locally refined grids and the paper shows it can be coupled to a fictitious domain approach.

Research limitations/implications

Although the stability and dispersion analysis of the DGTD method is complete, the theoretical analysis of the fictitious domain approach in the DGTD context is not. It is a subject of further investigation (which could provide important insights for potential improvements).

Originality/value

This is believed to be the first time a DGTD method is coupled with a fictitious domain approach.

Citation

Bouquet, A., Dedeban, C. and Piperno, S. (2010), "Discontinuous Galerkin time‐domain solution of Maxwell's equations on locally refined grids with fictitious domains", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 29 No. 3, pp. 578-601. https://doi.org/10.1108/03321641011028206