Optimize heat conduction problem using level set method with a weighting based velocity constructing scheme

This paper is devoted to develop an efficient computational procedure for the level set-based topological design of heat conducting fields. Firstly, the level set model with a distance-suppression scheme (generalized Hamilton-Jacobi equation) is used to implicitly represent boundary of heat conductive material so that the periodical re-initialization can be avoided. Secondly, after demonstrating that the finite element thermal analysis takes the major portion of the total computational time, we present a weighting based velocity constructing method inspired from the conjugate gradient method to avoid performing finite element thermal analysis for solving the generalized Hamilton-Jacobi equation. Thirdly, a velocity renewing procedure and criteria for stopping the weighting method are developed for insuring the stability and a quick convergence. Finally, two dimensional topology optimization results of heat conduction problem under both single and multiple load cases are presented to demonstrate the validity of the proposed method. (C) 2016 Elsevier Ltd. All rights reserved.