Global space–time multiquadric method for inverse heat conduction problem

Abstract

AbstractIn this paper, a radial basis collocation method (RBCM) based on the global space–time multiquadric (MQ) is proposed to solve the inverse heat conduction problem (IHCP). The global MQ is simply constructed by incorporating time dimension into the MQ function as a new variable in radial coordinate. The method approximates the IHCP as an over‐determined linear system with the use of two sets of collocation points: one is satisfied with the governing equation and another is for the given conditions. The least‐square technique is introduced to find the solution of the over‐determined linear system. The present work investigates two types of the ill‐posed heat conduction problems: the IHCP to recover the surface temperature and heat flux history on a source point from the measurement data at interior locations, and the backward heat conduction problem (BHCP) to retrieve the initial temperature distribution from the known temperature distribution at a given time. Numerical results of four benchmark examples show that the proposed method can provide accurate and stable numerical solutions for one‐dimensional and two‐dimensional IHCP problems. The sensitivity of the method with respect to the measured data, location of measurement, time step, shape parameter and scaling factor is also investigated. Copyright © 2010 John Wiley & Sons, Ltd.