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<p>This work introduces a topology optimization design methodology that specifically deals with the magnetic field and heat transfer phenomena that arise from applying&#xa0;an electric current. In addition, we provide the Pareto front for the objective functions, demonstrating the influence of the saturation effect on the Pareto front obtained by using both linear and nonlinear magnetic reluctivity. The optimization method employs the phase-field design method, which integrates the reaction–diffusion equation with the double-well potential method. Furthermore, the Adam algorithm has been introduced to enhance convergence speed and overall performance. The code is designed for educational purposes, specifically focusing on parameter initialization, weak form derivation for each physical system, sensitivity calculations, and update formulas for design variables. The code was developed using FreeFEM++, which is an open-source software. It is available for download from the website <a href="http://ssd.yonsei.ac.kr">http://ssd.yonsei.ac.kr</a>.</p>

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Multi-physics topology optimization for nonlinear magnetic field and heat transfer using a phase-field design method

  • 期刊论文

  • 发表日期：

    2025年10月10日

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  • Minkyu Oh,
  • Jeonghoon Yoo

摘要

This work introduces a topology optimization design methodology that specifically deals with the magnetic field and heat transfer phenomena that arise from applying an electric current. In addition, we provide the Pareto front for the objective functions, demonstrating the influence of the saturation effect on the Pareto front obtained by using both linear and nonlinear magnetic reluctivity. The optimization method employs the phase-field design method, which integrates the reaction–diffusion equation with the double-well potential method. Furthermore, the Adam algorithm has been introduced to enhance convergence speed and overall performance. The code is designed for educational purposes, specifically focusing on parameter initialization, weak form derivation for each physical system, sensitivity calculations, and update formulas for design variables. The code was developed using FreeFEM++, which is an open-source software. It is available for download from the website http://ssd.yonsei.ac.kr.