# A prediction-correction based iterative convolution-thresholding method for topology optimization of heat transfer problems

arXiv: https://arxiv.org/abs/2401.01069 · HTML: https://mlsanity.com/paper/2401.01069/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jan 2024.

## Built on by (most cited first, 1 of 1)

- [Topology preserving Image segmentation using the iterative convolution-thresholding method](https://mlsanity.com/paper/2503.17792/) (2025)

## Abstract (arXiv)

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.