Identification of source terms in 2-D IHCP

Abstract

We introduce a stable numerical space marching scheme based on discrete mollification-implemented as an automatic adaptive filter--for the approximate identification of temperature, temperature gradient, and source terms in the two-dimensional inverse heat conduction problem (IHCP).The stability and error analysis of the algorithm, together with some numerical examples, are provided. (~)

The method of simplified Tikhonov regularization for dealing with the inverse time-dependent heat source problem

“…As we know, there has been lots of research on identification of heat source adopting numerical algorithms [9][10][11][12][13][14][15][16]. But to the author's knowledge there are few papers, using the regularization method, with strict theoretical analysis, on identifying the heat source.…”

Two regularization methods to identify time-dependent heat source through an internal measurement of temperature

“…As we know, there is a lot of research on identification of heat source adopted numerical algorithms, such as the mollification method [8,9], the finite difference method [10,11], the modified genetic algorithm [12], the meshless method [13] and the conditional stability [14,15]. But by the regularization method, there are a few papers with strict theoretical analysis on identifying the heat source.…”

A Two Dimensional Discrete Mollification Operator and the Numerical Solution of an Inverse Source Problem

“…Applications of one-dimensional mollification methods are found, for instance, in References [6][7][8]. Mollification in two dimensions is less common and it is worth mentioning that it serves as a smoothing operator in Reference [9], appears as an accelerator of explicit schemes in Reference [4], and is a regularization tool for an identification problem in Reference [10].…”