Novel Time-Domain Electromagnetic Simulation Using Triangular Meshes by Applying Space Curvature

Abstract

A novel stable, accurate and fast numerical method based on triangular meshing and space transformations for electrodynamics problems with arbitrary boundaries is developed. Using transformation optics it is possible to convert non uniform domains into uniform rectangular ones allowing Maxwell's Equations to be solved quickly and simply using a modified finite difference time domain (FDTD) algorithm. A novel averaging method is presented to ensure the stability and accuracy of our algorithm when dealing with anisotropic and inhomogeneous materials in the transformed space. Finally we demonstrate the advantages of the present technique compared with conventional FDTD and transformation optics FDTD through a couple of scattering problems. These show that this method is more than one thousand times faster than classical FDTD in the presence of curved boundaries.

Keywords

• Numerical analysis
• computational optics
• FDTD