A computational method for the Helmholtz equation in unbounded domains based on the minimization of an integral functional

TL;DR

This paper introduces a novel computational approach for solving the Helmholtz equation in unbounded domains by minimizing an integral functional, accommodating variable refractive indices and demonstrating convergence through analytical and numerical results.

Contribution

It presents a new method based on integral functional minimization for Helmholtz problems with non-constant refractive indices in unbounded domains.

Findings

Proves convergence of the approximate solution.

Demonstrates effectiveness with numerical examples.

Handles variable and angular-dependent refractive indices.

Abstract

We study a new approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. Our approach is based on the minimization of an integral functional arising from a volume integral formulation of the radiation condition. The index of refraction does not need to be constant at infinity and may have some angular dependency as well as perturbations. We prove analytical results on the convergence of the approximate solution. Numerical examples for different shapes of the artificial boundary and for non-constant indexes of refraction will be presented.