Recovery of the rod cross section shape

TL;DR

This paper introduces a direct, efficient numerical method for reconstructing the cross-sectional shape of a rod from inverse problem data, utilizing Bessel function series and Sturm-Liouville equations.

Contribution

It presents a novel direct approach using Neumann series for solving the inverse shape determination problem of rods, simplifying the recovery process.

Findings

The method accurately recovers the cross section shape.

It reduces the inverse problem to a linear algebraic system.

The approach is computationally efficient.

Abstract

A direct method for solving the inverse problem of determining the shape of the cross section of a rod is proposed. The method is based on Neumann series of Bessel functions representations for solutions of Sturm-Liouville equations. The first coefficient of the representation is sufficient for the recovery of the unknown function. A system of linear algebraic equations for finding this coefficient is obtained. The proposed method leads to an efficient numerical algorithm.