A new approach for solving inverse solidification design problems

Inverse solidification design analysis represents an evolving area of research that can potentially affect a large segment of the manufacturing community. The objective of the analysis involves designing a transient boundary condition that produces a prescribed interfacial surface motion to ensure a desired morphology. The solution is developed in the context of a weighted residual methodology in which the temporal variable is treated in an elliptic fashion. This approach does not exhibit any of the symptoms associated with the solution of mildly ill-posed formulations. Finally, a conventional test case is presented indicating the accuracy, convergence, and stability of the new methodology.