A nonstationary form of the range refraction parabolic equation and its application as an artificial boundary condition for the wave equation in a waveguide

TL;DR

This paper introduces a nonstationary version of Tappert's range refraction parabolic equation, derived via noncommutative analysis, serving as an effective artificial boundary condition for wave equations in waveguides, with promising numerical results.

Contribution

It presents a novel nonstationary form of the range refraction parabolic equation derived through noncommutative analysis, used as an artificial boundary condition for waveguides.

Findings

Good boundary condition quality at low computational cost

Numerical comparison with Higdon's conditions shows promising results

Effective for wave equation simulations in waveguides

Abstract

The time-dependent form of Tappert's range refraction parabolic equation is derived using Daletskiy-Krein formula form noncommutative analysis and proposed as an artificial boundary condition for the wave equation in a waveguide. The numerical comparison with Higdon's absorbing boundary conditions shows sufficiently good quality of the new boundary condition at low computational cost.