Numerical solution of two-dimensional radially symmetric inverse heat conduction problem

Abstract

We investigate a two-dimensional radially symmetric inverse heat conduction problem, which is ill-posed in the sense that the solution does not depend continuously on input data. By generalizing the idea of kernel approximation, we devise a modi ed kernel in the frequency domain to reconstruct a numerical solution for the inverse heat conduction problem from the given noisy data. For the stability of the numerical approximation, we develop seven regularization techniques with some stability and convergence error estimates to reconstruct the unknown solution. Numerical experiments illustrate that the proposed numerical algorithm with regularization techniques provides a feasible and e ective approximation to the solution of the inverse and ill-posed problem.

A Backward Identification Problem for an Axis-Symmetric Fractional Diffusion Equation

“…Motivated by the filter methods [19], we can approximate the amplifying factor stably and thus stabilize the ill-posed problem. By introducing a regularization parameterα, we propose a general principle for constructing the stabilized amplifying factor Kα(r, µ i ) which approaches the amplifying factor K(r, µ i ):…”

Regularization methods for the inverse initial value problem for the time-fractional diffusion equation with robin boundary condition ★

“…There have been many studies of the articles on equation (1.1), such as, Cheng [13] considered a simplified Tikhonov regularization method to identify heat source about a time diffusion equation on a columnar axissymmetric area, Qian [14] develop seven regularization techniques to recover the inverse problem of the time diffusion-heat equation on a columnar radially symmetric region. We find that studies of integer order equations in cylindrical region have been abundant, while the study of fractional order equations in the same region are scarce.…”

Space–Time Radial Basis Function–Based Meshless Approach for Solving Convection–Diffusion Equations

“…Subsequently, the Kansa method [17,18] that directly adopts the MQ RBF has been indicated to be an effective numerical tool for approximating PDE solutions. Numerous engineering problems, including Burgers' equation [19,20], heat transfer [21][22][23], and groundwater contaminant transport [24], have been solved using the Kansa method.…”