Discontinuous Galerkin timedomain solution of Maxwell's equations on locallyrefined nonconforming Cartesian grids

• Published in: Compel 2005-12, Vol.24 (4), p.1381-1401
• Main Authors: Canouet, N., Fezoui, L., Piperno, S.
• Format: Article
• Language: English
• Subjects: Electromagnetic radiation; Galerkin method; Numerical analysis
• ISSN: 0332-1649
• DOI: 10.1108/03321640510615670

Purpose The use of the prominent 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 very important computational time and storage. The purpose is to develop a numerical method able to handle possibly nonconforming locally refined grids, based on portions of Cartesian grids in order to use existing pre and postprocessing tools. Designmethodologyapproach A Discontinuous Galerkin method is built based on bricks and its stability, accuracy and efficiency are proved. Findings It is found to be possible to conserve exactly the electromagnetic energy and weakly preserves the divergence of the fields on conforming grids. For nonconforming grids, the local sets of basis functions are enriched at subgrid interfaces in order to get rid of possible spurious wave reflections. Research limitationsimplications Although the dispersion analysis is incomplete, the numerical results are really encouraging it is shown the proposed numerical method makes it possible to handle devices with extremely small details. Further investigations are possible with different, higherorder discontinuous finite elements. Originalityvalue This paper can be of great value for people wanting to migrate from FDTD methods to more up to date timedomain methods, while conserving existing pre and postprocessing tools.