A multigrid assisted reanalysis method for accelerated heat transfer topology optimization

Abstract

Heat sinks are widely applied in industry, and heat transfer topology optimization can improve their performance while saving materials. However, the prohibitive computational cost hinders its development. Therefore, the Multigrid Assisted Reanalysis (MGAR) method is proposed to address the issue. The Combined Approximate Reduced Order Model (CAROM) is employed to reduce the dimensionality of governing equations, and computational efficiency is significantly improved. In addition, CAROM should be dynamically updated to ensure the accuracy of solutions, thus constructing the CAROM also take up a major computational cost. For this purpose, the V-cycle multigrid is employed to construct basis vectors of CAROM instead of direct solvers. Since the MGAR involves almost no matrix decomposition, except for solving the reduced linear systems, the MGAR is equipped to handle large-scale problems due to the advantage of high computational efficiency and low memory requirements. The competence of the MGAR is verified by several cases including thermal compliance minimization and maximum temperature minimization.