Treating Non-conforming Sensitivity Fields by Mortar Mapping and Vertex Morphing for Multi-disciplinary Shape Optimization

This study investigates the sensitivity filtering properties of the Mortar Mapping method and correlates it to the Vertex Morphing method in order to demonstrate the advantages of such a procedure in the context of shape optimization. It points out the importance of a common design control approach in a Multi-Disciplinary Optimization (MDO) environment. In particular, individual components of MDO have nonmatching interfaces when Fluid-Structure Interaction (FSI) problems are of interest. Since the numerical models of dissimilar discretizations deliver nonconforming sensitivity fields with respect to the design variables defined at their interfaces, the shape optimization of the common surfaces necessitates a third field which unifies the optimization variables and acts as a control field. This approach not only covers this necessity by facilitating the Mortar Mapping method but also reveals that such a procedure acts as a sensitivity filter similar to the Vertex Morphing method without altering the optimality of the solution.