Total field scattering field formulation in a non-uniform grid by means of FDTD-DPW

ABSTRACT

Finite-difference time-domain discrete plane wave technique (FDTD-DPW) is a numerical method which by using total the field/scattered field scheme allows one to propagate a plane wave quasi-perfectly isolated. This means a propagation in the total field domain without reflexions to the scattered field domain on the order of machine precision (−300 dB). This technique is valid for any angle of propagation, and for any gridcell aspect ratio. In this work, we extend this numerical illumination procedure for uniform three-dimensional grids to domains that are meshed by a non-uniform grid. To do so, we introduce some modifications to the original FDTD-DPW technique.

Keywords:

• Non uniform grids
• discrete finite difference time domain
• total field scattering field scheme
• multi-scale electromagnetic problems

Notes

1. Every electromagnetic component in the three-dimensional grid has at least one corresponding electromagnetic component in IFA.

2. A bijection from ${\mathbb{R}}^3$ to ${\mathbb{I}}_r$ has an inverse function from ${\mathbb{I}}_r$ to ${\mathbb{R}}^3$, all elements of ${\mathbb{R}}^3$ has a corresponding element in ${\mathbb{I}}_r$ which is a unique and vice verse. In our domains, ${\mathbb{I}}_r$ and ${\mathbb{R}}^3$ are finite sets, then the existence of a bijection means they have the same number of elements.

3. Every element of the function’s codomain is the image of at most one element of its domain.

Additional information

Funding

This work was carried out within the framework of the Research Project 3180130 supported by FONDECYT.