Efficient Filtering in Topology Optimization via B Splines1

Abstract

This paper presents a Bspline based approach for topology optimization of threedimensional (3D) problems where the density representation is based on Bsplines. Compared with the usual density filter in topology optimization, the new Bspline based density representation approach is advantageous in both memory usage and central processing unit (CPU) time. This is achieved through the use of tensorproduct form of Bsplines. As such, the storage of the filtered density variables is linear with respect to the effective filter size instead of the cubic order as in the usual density filter. Numerical examples of 3D topology optimization of minimal compliance and heat conduction problems are demonstrated. We further reveal that our Bspline based density representation resolves the bottleneck challenge in multiple density per element optimization scheme where the storage of filtering weights had been prohibitively expensive.