Parametric Shape and Topology Optimization with Radial Basis Functions and Partition of Unity Method

Abstract

This paper presents the parametric approach of the shape and topology optimization that combines the theory of radial basis function (RBF) interpolation with a partition of unity (POU) method. A surface is represented implicitly through a level function and its boundary is the zero level set, the evolution of the dynamic boundary is determined by the parameters of the RBF. In order to deal with large point sets, we organize the point sets into some overlapping local sub‐domains and reconstruct these local surfaces in the octree cells; POU method blends them into a global surface with higher numerical efficiency. The computational complexity and the underlying data structure are carefully studied. Finally, we give the numerical examples to demonstrate the versatility of these methods.