# Accurate Nonstandard Path Integral Models for Arbitrary Dielectric Boundaries in 2-D NS-FDTD Domains

## TL;DR

This paper introduces a new method for accurately modeling curved dielectric structures in simulations using a more efficient approach on coarse grids.

## Contribution

The novel PI model uses dielectric occupation ratios to handle curved surfaces in NS-FDTD simulations.

## Key findings

- The PI model reliably models arbitrarily shaped dielectrics on coarse grids.
- Verification tests on reflection and scattering show the method's precision and reliability.
- The approach simplifies handling practical applications with curved dielectric structures.

## Abstract

An efficient path integral (PI) model for the accurate analysis of curved dielectric structures on coarse grids via the two-dimensional nonstandard finite-difference time-domain (NS-FDTD) technique is introduced in this paper. In contrast to previous PI implementations of the perfectly electric conductor case, which accommodates orthogonal cells in the vicinity of curved surfaces, the novel PI model employs the occupation ratio of dielectrics in the necessary cells, providing thus a straightforward and instructive means to treat an assortment of practical applications. For its verification, the reflection from a flat plate and the scattering from a cylinder using the PI model are investigated. Results indicate that the featured methodology can enable the reliable and precise modeling of arbitrarily shaped dielectrics in the NS-FDTD algorithm on coarse grids.