A multiscale homogenization procedure for analysis of processes involving heat deposition using constrained parameter optimization

We present aspects of a general procedure to be used in conjunction with co nstrained parameter optimization for the analysis of processes involving he at deposition such as welding processes and those involving rapid prototypi ng by means of powder deposition. Our emphasis in this report is on the con struction of generating functions and subdomain elliptic solvers useful for the practical application of constrained parameter optimization for the ca lculation of thermal histories. The procedure for constructing generating f unctions and elliptic solvers is based on the concept of multiscale homogen ization. We discuss those elements of the theoretical foundation of the gen eral methodology based on constrained parameter optimization as these eleme nts relate to the application of generating functions and subdomain solvers . In addition, we present a prototype weld analysis, which serves to demons trate many of the details associated with the application of this methodolo gy.