  In this paper, we propose an iterative convolution-thresholding method (ICTM)
based on prediction-correction for solving the topology optimization problem in
steady-state heat transfer equations. The problem is formulated as a
constrained minimization problem of the complementary energy, incorporating a
perimeter/surface-area regularization term, while satisfying a steady-state
heat transfer equation. The decision variables of the optimization problem
represent the domains of different materials and are represented by indicator
functions. The perimeter/surface-area term of the domain is approximated using
Gaussian kernel convolution with indicator functions. In each iteration, the
indicator function is updated using a prediction-correction approach. The
prediction step is based on the variation of the objective functional by
imposing the constraints, while the correction step ensures the monotonically
decreasing behavior of the objective functional. Numerical results demonstrate
the efficiency and robustness of our proposed method, particularly when
compared to classical approaches based on the ICTM.
