A meshless method for solving a two-dimensional transient inverse geometric problem

Purpose – The purpose of this paper is to apply the meshless method of fundamental solutions (MFS) to the two-dimensional time-dependent heat equation in order to locate an unknown internal inclusion. Design/methodology/approach – The problem is formulated as an inverse geometric problem, using non-invasive Dirichlet and Neumann exterior boundary data to find the internal boundary using a non-linear least-squares minimisation approach. The solver will be tested when locating a variety of internal formations. Findings – The method implemented was proven to be both stable and reasonably accurate when data were contaminated with random noise. Research limitations/implications – Owing to limited computational time, spatial resolution of internal boundaries may be lower than some similar case investigations. Practical implications – This research will have practical implications to the modelling and monitoring of crystalline deposit formations within the nuclear industry, allowing development of future designs. Originality/value – Similar work has been completed in regards to the steady state heat equation, however to the best of the authors' knowledge no previous work has been completed on a time-dependent inverse inclusion problem relating to the heat equation, using the MFS. Preliminary results presented here will have value for possible future design and monitoring within the nuclear industry