Inverse Conduction Problem for a Parabolic Equation using a Boundary Integral Method

TL;DR

This paper introduces a boundary integral method to solve an inverse heat conduction problem in 2D, estimating heat flux from partial boundary measurements using fundamental solutions.

Contribution

It presents a novel boundary integral algorithm for inverse heat conduction problems based on fundamental solutions, enhancing solution accuracy for partial boundary data.

Findings

Effective boundary integral algorithm developed

Accurate heat flux estimation from partial boundary data

Applicable to 2D inverse heat conduction problems

Abstract

In this paper, a boundary integral method is used to solve an inverse linear heat conduction problem in two-dimensional bounded domain. An inverse problem of measuring the heat flux from partial (on part of the boundary) dynamic boundary measurements is considered. An algorithm is given by using the fundamental solution.