Topology Optimization of Thermal Initial Value Problems Exploiting Efficient Harmonic Analysis

Abstract Topology optimization can be employed to manipulate transient thermal behavior for heat transfer devices. As a gradient-based approach, transient topology optimization faces challenges with the CPU cost of the associated forward and backward time-stepping procedure. This study introduces a harmonic analysis-based substitute optimization method to alleviate these computational challenges. Using an analytical solution for a one-dimensional heat conduction problem, we derive a conversion coefficient linking harmonic excitation frequency to the desired transient time instance. Applying this harmonic formulation in the topology optimization of a two-dimensional transient heat conduction problem shows a remarkable speedup, around a factor of 20 per design iteration, with less than a 5% decrease (at most) in the figure of merit compared to the transient approach. Extending the study to include heat convection displays a stable region where the proposed harmonic substitute method sustains the same computational efficiency with less than a 10% difference for objective value comparison in the worst-case scenario.