Helmholtz equation in unbounded domains: some convergence results for a constrained optimization problem

TL;DR

This paper investigates the convergence properties of a constrained optimization approach for approximating solutions to the Helmholtz equation in unbounded domains, providing theoretical estimates on the convergence rate.

Contribution

It offers new convergence estimates for a constrained optimization method applied to the Helmholtz equation in unbounded domains.

Findings

Established convergence rate estimates for the approximation method.

Provided theoretical bounds on the error between approximate and exact solutions.

Abstract

We consider a constrained optimization problem arising from the study of the Helmholtz equation in unbounded domains. The optimization problem provides an approximation of the solution in a bounded computational domain. In this paper we prove some estimates on the rate of convergence to the exact solution.