A boundary determination problem in steady-state heat conduction – a solution and sensitivity analysis

Abstract

Purpose The purpose of this paper is to propose a numerical procedure for discrete identification of the missing part of the domain boundary in a heat conduction problem. A new approach to sensitivity analysis is intended to give a better understanding of the influence of measurement error on boundary reconstruction. Design/methodology/approach The solution of Laplace’s equation is obtained using the Trefftz method, and then each of the sought boundary points can be derived numerically from a nonlinear equation. The sensitivity analysis comes down to the analytical evaluation of a sensitivity factor. Findings The proposed method very accurately recovers the unknown boundary, including irregular shapes. Even a very large number of the boundary points can be determined without causing computational problems. The sensitivity factor provides quantitative assessment of the relationship between the temperature measurement errors and boundary identification errors. The numerical examples show that some boundary reconstruction problems are error-sensitive by nature but such problems can be recognized with the use of a sensitive factor. Originality/value The present approach based on the Trefftz method separates, in terms of computation, specification of the coefficients appearing in the Trefftz method and missing coordinates of the sought boundary points. Due to introducing a sensitivity factor, a more profound sensitivity analysis was successfully conducted.