Domain decomposition methods for welding problems

This paper, a 2-D non-linear electric arc-welding problem is considered. It is assumed that the moving arc generates an unknown quantity of energy which makes the problem an inverse problem with an unknown source. Robust algorithms to solve such problems e#ciently, and in certain circumstances in real-time, are of great technological and industrial interest. There are other types of inverse problems which involve inverse determination of heat conductivity or material properties [CDJ63][TE98], inverse problems in material cutting [ILPP98], and retrieval of parameters containing discontinuities [IK90]. As in the metal cutting problem, the temperature of a very hot surface is required and it relies on the use of thermocouples. Here, the solution scheme requires temperature measurements lied in the neighbourhood of the weld line in order to retrieve the unknown heat source. The size of this neighbourhood is not considered in this paper, but rather a domain decomposition concept is presented and an examination of the accuracy of the retrieved source are presented. This paper is organised as follows. The inverse problem is formulated and a method for the source retrieval is presented in the second section. The source retrieval method is based on an extension of the 1-D source retrieval method as proposed in [ILP].