A High Accurate Topology Optimization Method by Using the Gradient Type Method and the Lattice-Free Finite Difference Method

Abstract

Abstract. In this paper, we consider a high accurate method for SIMP (Solid Isotropic Material with Penalization) type topology optimization problem. We adopt the gradient type method to solve our problem. In order to get high accurate solution of the partial difference equation in our algorithm, we use the lattice-free finite difference method which is a kind of the differential quadrature method. The library “exflib” for the scientific multiple-precision arithmetic is used in our calculation. By the numerical experiments, we check the effectiveness, stability, and convergency of our algorithm with the steepest descent and H¹ gradient method.