Shape optimization with p adaptivity

Abstract

The p method of analysis, when used with shape optimization, has certain advantages over the h method. The method of h adaptivity results in fine meshes with small elements in areas of stress concentration. The presence of these small elements prevents the shape from changing significantly during optimization due to mesh distortion. The p-adaptive method uses relatively large sized elements, and adaptivity is achieved by increasing the polynomial order of the shape functions rather than by introducing small elements as in the h method. Thus, the p-adaptive method allows for greater shape changes without sacrificing the accuracy of the analysis. A methodology is developed in this paper to integrate p-adaptive analysis with shape optimization for general velocity fields. The key contributions lie in an easily implementable shape update strategy and an adaptive scheme to locally increase the polynomial order based on error indicators. Numerical results show that significant shape change is achievable prior to serious mesh distortion. In addition, need for an h-p adaptive strategy rather than a pure p-adaptive strategy is also highlighted.