A fundamental solution method for inverse heat conduction problem

Abstract

In this paper, we develop a new meshless and integration-free numerical scheme for solving an inverse heat conduction problem. The numerical scheme is developed based on the use of the fundamental solution as a radial basis function. To regularize the resultant ill-conditioned linear system of equations, we apply successfully both the Tikhonov regularization technique and the L-curve method to obtain a stable numerical approximation to the solution. The approach is readily extendable to solve high-dimensional problems under irregular domain.