Domain decomposition methods for welding problems

The welding of metals and alloys is a widely used industrial process. Many types of analysis have been carried out on such problems [MUB67]. The numerical thermal analysis of welding is required to take into account such features as temperature dependent material properties, phase change, non-uniform distribution of energy from heat source etc. In 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 efficiently, 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 [ILP99] for metal cutting problems. A parallel algorithm based on the concept of coupling heterogeneous numerical models in different subdomains is given in the third section. Accuracy of the numerical simulation is compared with results that are generated by a known heat source [ASW85][DM93] and with temperature measurements that are obtained by using experimental thermocouples as shown in [ASW85].