A Domain Decomposition Based Algorithm For Non-linear 2D Inverse Heat Conduction Problems

Inverse heat conduction problems (IHCPs) appear in many important scientific and technological fields. Hence analysis, design, implementation and testing of inverse algorithms are also of great scientific and technological interest. The numerical simulation of 2-D and 3-D inverse (or even direct) problems involves a considerable amount of computation. Therefore, the investigation and exploitation of parallel properties of such algorithms are equally becoming very important [9, 2]. Domain decomposition (DD) methods are widely used to solve large scale engineering problems and to exploit their inherent ability for the solution of such problems. An area of particular interest in IHCPs is the cutting of sheet material such as metal. An accurate simulation of the temperature distribution of the metal, subject to cutting, is vital in order to lengthen the life time of the cutting tool and to guarantee the quality of the cutting. In addition, the real-time simulation of such temperature distributions is of industrial interest. For example, it is important to regulate the cutter speed and coolant application in order to keep the temperature (especially at the cutter points) below a threshold. When the temperature rises above the threshold this will cause deformation of the metal or it may become fatigued. In reality, the accurate measurement of temperature at the cutter points is not possible. Therefore, a direct problem cannot be formulated. Inverse methods can be used to retrieve the temperature at these points. It has been shown that accurate estimates can be obtained using such methods [1]. IHCPs, such as the metal cutting problem described above, are more difficult to solve analytically than direct problems [1]. Therefore, various approximation methods have been developed to solve such problems. These include graphical[10], polynomial [5], Laplace transform [7], dynamic programming [11], finite difference [3], finite elements [6]